Involved institute: Institute of Theoretical Physics (from 2018)
Year 2020-2025
Public type of publication: Articles ref. in Journals
"Online First" included

Study of QED singular properties for variable gyromagnetic ratio g≃2

Rafelski, J.; Evans, S.; Labun, L.

Using the external field method, {\it i.e.\/} evaluating the effective action $V_{\mathrm{eff}}$ for an arbitrarily strong constant and homogeneous field, we explore nonperturbative properties of QED allowing arbitrary gyromagnetic ratio $g$. We find a cusp at $g = 2$ in: a) The QED $b_0$-renormalization group coefficient, and in the infinite wavelength limit in b) a subclass containing the pseudoscalar ${\cal P}^{2n}= (\vec E\cdot\vec B)^{2n} $ of light-light scattering coefficients. Properties of $b_0$ imply for certain domains of $g$ asymptotic freedom in an Abelian theory.

Keywords: Schwinger effect; vacuum stability; magnetic moment

Improving Euler-Heisenberg-Schwinger Effective Action with Dressed Photons

Evans, S.; Rafelski, J.

We implement a longstanding proposal by Weisskopf to apply virtual polarization corrections to
the in/out external fields in study of the Euler-Heisenberg-Schwinger effective action. Our approach
requires distinguishing the electromagnetic and polarization fields based on mathematical tools
developed by Bia lynicki-Birula, originally for the Born-Infeld action. Our solution is expressed
as a differential equation where the one-loop effective action serves as input. As a first result of
our approach, we recover the higher-order one-cut reducible loop diagrams discovered by Gies and

Keywords: Euler–Heisenberg–Schwinger (EHS); non-perturbative vac-uum structure; quantum electrodynamics (QED)

Dimer Coupling Energies of the Si(001) Surface

Schützhold, R.; Brand, C.; Hucht, A.; Jnawali, G.; Fortmann, J. D.; Sothmann, B.; Mehdipour, H.; Kratzer, P.; Horn-Von Hoegen, M.

The coupling energies between the buckled dimers of the Si(001) surface were determined through analysis of the anisotropic critical behavior of its order-disorder phase transition. Spot profiles in high-resolution low-energy electron diffraction as a function of temperature were analyzed within the framework of the anisotropic two-dimensional Ising model. The validity of this approach is justified by the large ratio of correlation lengths, ζ +/ζ∥+=5.2 of the fluctuating c(4×2) Domains above the critical temperature Tc=(190.6±10) K. We obtain effective couplings J∥=(-24.9±1.3) meV along the dimer rows and J⊥=(-0.8±0.1) meV across the dimer rows, i.e., antiferromagneticlike coupling of the dimers with c(4×2) symmetry.

Keywords: Dimers; Electrons; Ising model; Correlation lengths; Coupling energies; Critical behaviour; Critical temperatures; Effective coupling; High resolution; Low-energy electron diffraction; Order/disorder phase transition; Spot profile; Two-dimensional; Anisotropy

Fresh look at experimental evidence for odderon exchange

Schmidt, S. M.; Cui, Z.-F.; Binosi, D.; Roberts, C. D.; Triantafyllopoulos, D. N.

Theory suggests that in high-energy elastic hadron+hadron scattering, t-channel exchange of a family of colourless crossingodd
states – the odderon – may generate differences between pp¯ and pp cross-sections in the neighbourhood of the
diffractive minimum. Using a mathematical approach based on interpolation via continued fractions enhanced by statistical
sampling, we develop robust comparisons between pp¯ elastic differential cross-sections measured at √s=1.96 TeV by the
D0 Collaboration at the Tevatron and function-form-unbiased extrapolations to this energy of kindred pp measurements at
√s/TeV=2.76,7,8,13 by the TOTEM Collaboration at the LHC and a combination of these data with earlier cross-section
measurements at √s/GeV=23.5,30.7,44.7,52.8,62.5 made at the intersecting storage rings. Focusing on a domain that
straddles the diffractive minimum in the pp¯ and pp cross-sections, we find that these two cross-sections differ at the
(2.2−2.6)σ level; hence, supply evidence with this level of significance for the existence of the odderon. If combined with
evidence obtained through different experiment-theory comparisons, whose significance is reported to lie in the range
(3.4−4.6)σ, one arrives at a (4.0−5.2)σ signal for the odderon.

Keywords: Diffractive processes; High-energy hadron; Odderon; Regge phenomenology; Schlessinger point; Strong interactions in the standard model of particle physics; hadron interactions

Generalized Gelfand-Dikii equation and solitonic electric fields for fermionic Schwinger pair production

Ahmadiniaz, N.; Fedotov, A. M.; Gelfer, E. G.; Pyo Kim, S.; Schubert, C.

Schwinger pair creation in a purely time-dependent electric field can be reduced to an effective quantum mechanical problem using a variety of formalisms. Here we develop an approach based on the Gelfand-Dikii equation for scalar QED, and extent it to spinor QED. We discuss some solvable special cases from this point of view. It was previously shown how to use the well-known solitonic solutions of the KdV equation to construct “solitonic” electric fields that do not create scalar pairs with an arbitrary fixed momentum. We show that this construction can be adapted to the fermionic case in two inequivalent ways, both leading to the vanishing of the pair-creation rate at certain values of the P ̈oschl-Teller like index of the associated Schr ̈odinger equation. Thus for any given momentum, we can construct electric fields that create scalar particles but not spinor particles, and also the other way round. Therefore, while often spin is even neglected in Schwingerpair creation, in such cases it becomes decisive.

Keywords: Schwinger mechanism; Pair production; Gelfand-Dikii equation


Precision Storage Rings for Electric Dipole Moment Searches: A Tool En Route to Physics Beyond-the-Standard-Model

Ströher, H.; Schmidt, S. M.; Lenisa, P.; Pretz, J.

Electric Dipole Moments (EDM) of particles (leptons, nucleons and light nuclei) are currently deemed one of the best indicators for new physics, i.e. phenomena, which lie outside the Stand-ard Model (SM) of elementary particle physics – so called physics “Beyond-the-Standard-Model” (BSM). Since EDMs of the SM are vanishingly small, a finite permanent EDM would indicate charge-parity symmetry (CP-) violation in addition to the well-known sources of the SM and could explain the baryon asymmetry of the Universe, while an oscillating EDM would hint at a possible Dark Matter (DM) field comprising axions or axion-like particles (ALPs). A new ap-proach exploiting polarized charged particles (proton, deuteron, 3He) in precision storage rings offers the prospect to push current experimental EDM upper limits significantly further includ-ing the possibility of an EDM discovery. In this paper, we describe the scientific background and the steps towards the realization of a precision storage ring, which will make such measure-ments possible.

Keywords: Baryon Asymmetry; Dark Matter; Electric Dipole Moments; Storage Rings; Polarized Beams

Detection schemes for quantum vacuum diffraction and birefringence

Ahmadiniaz, N.; Cowan, T.; Grenzer, J.; Franchino-Vinas, S.; Laso García, A.; Smid, M.; Toncian, T.; Trejo Espinosa, M. A.; Schützhold, R.

Motivated by recent experimental initiatives, such as at the
Helmholtz International Beamline for Extreme Fields (HIBEF)
at the European X-ray Free Electron Laser (XFEL), we calculate
the birefringent scattering of x-rays at the combined field of
two optical (or near-optical) lasers and compare various scenarios.
In order to facilitate an experimental detection of quantum vacuum diffraction and
birefringence, special emphasis is placed on scenarios where the initial
and final x-ray photons differ not just in polarization, but also in
propagation direction (corresponding to scattering angles in the mrad regime)
and possibly energy.

Keywords: Strong Field QED; Vacuum qirefringence; Quantum vacuum diffraction; Euler-Heisenberg Lagrangian; XFEL; Laser; Light-by-light scattering


Resummed heat-kernel and form factors for surface contributions: Dirichlet semitransparent boundary conditions

Franchino-Vinas, S.

In this article we consider resummed expressions for the heat-kernel's
trace of a Laplace operator, the latter including a potential and imposing Dirichlet semitransparent boundary conditions on a surface of codimension one in flat space.
We obtain resummed expressions that correspond to the first and second order expansion of the heat-kernel in powers of the potential.
We show how to apply these results to obtain the bulk and surface form factors of a scalar quantum field theory in $d=4$ with a Yukawa coupling to a background.
A characterization of the form factors in terms of pseudo-differential operators is given.


Geometrizing the Klein–Gordon and Dirac equations in Doubly Special Relativity

Franchino-Vinas, S.; Relancio, J. J.

In this work we discuss the deformed relativistic wave equations, namely the Klein--Gordon and Dirac equations in a Doubly Special Relativity scenario.
We employ what we call a geometric approach, based on the geometry of a curved momentum space, which should be seen as complementary to the more spread algebraic one.
In this frame we are able to rederive well-known algebraic expressions, as well as to treat yet unresolved issues, to wit, the explicit relation between both equations, the discrete symmetries for Dirac particles, the fate of covariance, and the formal definition of a Hilbert space for the Klein--Gordon case.

Keywords: Doubly Special Relativity; Klein-Gordon equation; Dirac equation; Curved momentum space


Scalable quantum control and non-Abelian anyon creation in the Kitaev honeycomb model

Raii, O.; Mintert, F.; Burgarth, D.

The Kitaev honeycomb model is a system allowing for experimentally realizable quantum computation with
topological protection of quantum information. Practical implementation of quantum information processing
typically relies on adiabatic, i.e., slow dynamics. Here we show that the restriction to adiabatic dynamics can be
overcome with optimal control theory, enabled by an extension of the fermionization of the Kitaev honeycomb
model to the time-dependent case. Moreover, we present a quantum control method that is applicable to large
lattice models due to subexponential scaling.


Local Neumann semitransparent layers: Resummation, pair production, and duality

Ahmadiniaz, N.; Franchino-Vinas, S.; Manzo, L.; Mazzitelli, F. D.

We consider local semitransparent Neumann boundary conditions for a quantum scalar field as imposed by a quadratic coupling to a source localized on a flat codimension-one surface. Upon a proper regularization to give meaning to the interaction, we interpret the effective action as a theory in a first-quantized phase space. We compute the relevant heat-kernel to all order in a homogeneous background and quadratic order in perturbations, giving a closed expression for the corresponding effective action in $D=4$. In the dynamical case, we analyze the pair production caused by a harmonic perturbation and a Sauter pulse. Notably, we prove the existence of a strong/weak duality that links this Neumann field theory to the analogue Dirichlet one.

Keywords: Neumann boundary conditions; Dynamical Casimir effect; Quantum field theory in background fields; Effective action; Pair creation; Duality; Dirichlet semitransparent boundary conditions


Suppression of Interband Heating for Random Driving

Zhao, H.; Knolle, J.; Moessner, R.; Mintert, F.

Heating to high-lying states strongly limits the experimental observation of driving induced nonequilibrium phenomena, particularly when the drive has a broad spectrum. Here we show that, for entire
families of structured random drives known as random multipolar drives, particle excitation to higher bands
can be well controlled even away from a high-frequency driving regime. This opens a window for
observing drive-induced phenomena in a long-lived prethermal regime in the lowest band.

Iterative quantum optimization with an adaptive problem Hamiltonian for the shortest vector problem

Zhu, Y. R.; Joseph, D.; Ling, C.; Mintert, F.

Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems
in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite (and currently
small) number of qubits, however, poses the risk of finding only the optimum within the restricted space
supported by this Hamiltonian. We describe an iterative algorithm in which a solution obtained with such
a restricted problem Hamiltonian is used to define a new problem Hamiltonian that is better suited than the
previous one. In numerical examples of the shortest vector problem, we show that the algorithm with a sequence
of improved problem Hamiltonians converges to the desired solution.


Identifying Time Scales in Particle Production from Fields

Diez, M.; Alkofer, R.; Kohlfürst, C.

Particle production through ultra-strong electric fields is a well-studied research field. Nevertheless, despite repeated attempts to relate the production rate within the field to the formation time of a particle, the latter is still shrouded in mystery. We provide an interpretation of a particle
distribution at finite times enabling us to isolate and, therefore, identify the relevant time scales
regarding particle formation in quantum physics within and beyond perturbation theory.

Keywords: Non-equilibrium Quantum Field Theory; Strong-Field Quantum Electrodynamics; Schwinger effect; Time scales

Emergence of Hadron Mass and Structure

Ding, M.; Roberts, C. D.; Schmidt, S. M.

Visible matter is characterised by a single mass scale; namely, the proton mass. The proton’s existence and structure are supposed to be described by quantum chromodynamics (QCD); yet, absent Higgs boson couplings, chromodynamics is scale invariant. Thus, if the Standard Model is truly a part of the theory of Nature, then the proton mass is an emergent feature of QCD; and emergent hadron mass (EHM) must provide the basic link between theory and observation. Nonperturbative tools are necessary if such connections are to be made; and in this context, we sketch recent progress in the application of continuum Schwinger function methods to an array of related problems in hadron and particle physics. Special emphasis is given to the three pillars of EHM – namely, the running gluon mass, process-independent effective charge, and running quark mass; their role in stabilising QCD; and their measurable expressions in a diverse array of observables.

Keywords: confinement of gluons and quarks; continuum Schwinger function methods; Dyson- Schwinger equations

Performance boost of a collective qutrit refrigerator

Kolisnyk, D.; Schaller, G.

A single qutrit with transitions selectively driven by weakly-coupled reservoirs can implement one of the world's smallest refrigerators. We analyze the performance of N such fridges that are collectively coupled to the reservoirs. We observe a quantum boost, manifest in a quadratic scaling of the steady-state cooling current with N. As N grows further, the scaling reduces to linear, since the transitions responsible for the quantum boost become energetically unfavorable. Fine-tuned inter-qutrit interactions may be used to maintain the quantum boost for all N and also for not-perfectly collective scenarios.

Keywords: open quantum systems; Lindblad equation; Redfield equation; collective effects; quantum absorption refrigerator; qutrits; Holstein-Primakoff transform; quadratic boost; nonequilibrium steady state


Resummation for quantum propagators in bounded spaces

Edwards, J. P.; González-Domínguez, V. A.; Huet, I.; Trejo Espinosa, M. A.

We outline an approach to calculating the quantum mechanical propagator in the presence of geometrically nontrivial Dirichlet boundary conditions. The method is based on a generalization of an integral transform of the propagator studied in previous work (the so-called “hit function”) and a convergent sequence of Padé approximants that exposes the limit of perfectly reflecting boundaries. In this paper the generalized hit function is defined as a many-point propagator, and we describe its relation to the sum over trajectories in the Feynman path integral. We then show how it can be used to calculate the Feynman propagator. We calculate analytically all such hit functions in D = 1 and D = 3 dimensions, giving recursion relations between them in the same or different dimensions and apply the results to the simple cases of propagation in the presence of perfectly conducting planar and spherical plates. We use these results to conjecture a general analytical formula for the propagator when Dirichlet boundary conditions are present in a given geometry, also explaining how it can be extended for application for more general, nonlocalized potentials. Our work has resonance with previous results obtained by Grosche in the study of path integrals in the presence of delta potentials. We indicate the eventual application in a relativistic context to determining Casimir energies using this technique.

Keywords: Integral equations; Quantum theory; Bounded spaces; Convergent sequences; Dirichlet boundary conditions; Feynman path integrals; Generalisation; Integral transform; Pade approximants; Quantum mechanical; Reflecting boundary; Resummation


Kaon and pion parton distributions

Cui, Z.-F.; Ding, M.; Gao, F.; Raya, K.; Binosi, D.; Chang, L.; Roberts, C. D.; Rodriguez-Quintero, J.; Schmidt, S. M.

Beginning with results for the leading-twist two-particle distribution amplitudes of π- and K-mesons, each of which exhibits dilation driven by the mechanism responsible for the emergence of hadronic mass, we develop parameter-free predictions for the pointwise behaviour of all π and K distribution functions (DFs), including glue and sea. The large-x behaviour of each DF meets expectations based on quantum chromodynamics; the valence-quark distributions match extractions from available data, including the pion case when threshold resummation effects are included; and at ζ5=5.2GeV, the scale of existing measurements, the light-front momentum of these hadrons is shared as follows: ⟨xvalence⟩π=0.41(4), ⟨xglue⟩π=0.45(2), ⟨xsea⟩π=0.14(2); and ⟨xvalence⟩K=0.42(3), ⟨xglue⟩K=0.44(2), ⟨xsea⟩K=0.14(2). The kaon’s glue and sea distributions are similar to those in the pion, although the inclusion of mass-dependent splitting functions introduces some differences on the valence-quark domain. This study should stimulate improved analyses of existing data and motivate new experiments sensitive to all π and K DFs. With little known empirically about the structure of the Standard Model’s (pseudo-) Nambu-Goldstone modes and analyses of existing, limited data being controversial, it is likely that new generation experiments at upgraded and anticipated facilities will provide the information needed to resolve the puzzles and complete the picture of these complex bound states.

Keywords: parton; Kaon

Reflections upon the Emergence of Hadronic Mass

Roberts, C. D.; Schmidt, S. M.

With discovery of the Higgs boson, science has located the source for ≲2% of the mass of visible matter. The focus of attention can now shift to the search for the origin of the remaining ≳98%. The instruments at work here must be capable of simultaneously generating the 1 GeV mass-scale associated with the nucleon and ensuring that this mass-scale is completely hidden in the chiral-limit pion. This hunt for an understanding of the emergence of hadronic mass (EHM) has actually been underway for many years. What is changing are the impacts of QCD-related theory, through the elucidation of clear signals for EHM in hadron observables, and the ability of modern and planned experimental facilities to access these observables. These developments are exemplified in a discussion of the evolving understanding of pion and kaon parton distributions.

Keywords: hadronic; Phenomenology; physics


Nucleon elastic form factors at accessible large spacelike momenta

Schmidt, S. M.; Cui, Z.-F.; Roberts, C. D.; Chen, C.; Binosi, D.; de Soto, F.; Rodríguez-Quintero, J.; Segovia, J.

A Poincaré-covariant quark+diquark Faddeev equation is used to compute nucleon elastic form factors on 0≤Q2≤18m2N (mN is the nucleon mass) and elucidate their role as probes of emergent hadronic mass in the Standard Model. The calculations expose features of the form factors that can be tested in new generation experiments at existing facilities, e.g. a zero in GpE/GpM; a maximum in GnE/GnM; and a zero in the proton's d-quark Dirac form factor, Fd1. Additionally, examination of the associated light-front-transverse number and anomalous magnetisation densities reveals, inter alia: a marked excess of valence u-quarks in the neighbourhood of the proton's centre of transverse momentum; and that the valence d-quark is markedly more active magnetically than either of the valence u-quarks. The calculations and analysis also reveal other aspects of nucleon structure that could be tested with a high-luminosity accelerator capable of delivering higher beam energies than are currently available.

Keywords: nucleon; quark

A correspondence between the free and interacting field theories

Gao, F.; Ding, M.; Liu, Y.; Schmidt, S. M.

We discover a correspondence between the free field and the interacting states. This correspondence is firstly given from the fact that the free propagator can be converted into a tower of propagators for massive states, when expanded with the Hermite function basis. The equivalence of propagators reveals that in this particular case the duality can naturally be regarded as the equivalence of one theory on the plane wave basis to the other on the Hermite function basis. More generally, the Hermite function basis provides an alternative quantization process with the creation/annihilation operators that correspond directly to the interacting fields. Moreover, the Hermite function basis defines an exact way of dimensional reduction. As an illustration, we apply this basis on 3+1 dimensional Yang-Mills theory with three dimensional space being reduced through the Hermite function basis, and if with only the lowest order Hermite function, the equivalent action becomes the Banks-Fischler-Shenker-Susskind (BFSS) matrix model.

Quantum Zeno Manipulation of Quantum Dots

Ahmadiniaz, N.; Paul Geller, M.; König, J.; Kratzer, P.; Lorke, A.; Schaller, G.; Schützhold, R.

We investigate whether and how the quantum Zeno effect, i.e., the inhibition of quantum evolution by frequent measurements, can be employed to isolate a quantum dot from its surrounding electron reservoir. In contrast to the often studied case of tunneling between discrete levels, we consider the tunnelling of an electron from a continuum reservoir to a discrete level in the dot. Realizing the quantum Zeno effect in this scenario can be much harder because the measurements should be repeated before the wave packet of the hole left behind in the reservoir moves away from the vicinity of the dot. Thus, the required repetition rate could be lowered by having a flat band (with a slow group velocity) in resonance with the dot or a sufficiently small Fermi velocity or a strong external magnetic field.

Keywords: Quantum Zeno effect; quantum dots; wave packet decay; measurement problem; perturbation theory

Decay of quantum sensitivity due to three-body loss in Bose-Einstein condensates

Schützhold, R.; Rätzel, D.

In view of the coherent properties of a large number of atoms, Bose-Einstein condensates (BECs) have a high potential for sensing applications. Several proposals have been put forward to use collective excitations such as phonons in BECs for quantum-enhanced sensing in quantum metrology. However, the associated highly nonclassical states tend to be very vulnerable to decoherence. In this article, we investigate the effect of decoherence due to the omnipresent process of three-body loss in BECs.We find strong restrictions for a wide range of parameters, and we discuss possibilities to limit these restrictions.

Keywords: quantum; Bose-Einstein


Electron spin- and photon polarization-resolved probabilities of strong-field QED processes

Chen, Y.-Y.; Hatsagortsyan, K. Z.; Keitel, C. H.; Shaisultanov, R.

A derivation of fully polarization-resolved probabilities is provided for high-energy photon emission and electron-positron pair production in ultrastrong laser fields. The probabilities resolved in both electron spin and photon polarization of incoming and outgoing particles are indispensable for developing QED Monte Carlo and QED-Particle-in-Cell codes, aimed at the investigation of polarization effects in nonlinear QED processes in ultraintense laser-plasma and laser-electron beam interactions, and other nonlinear QED processes in external ultrastrong fields, which involve multiple elementary processes of a photon emission and pair production. The quantum operator method introduced by Baier and Katkov is employed for the calculation of probabilities within the quasiclassical approach and the local constant field approximation. The probabilities for the ultrarelativistic regime are given in a compact form and are suitable to describe polarization effects in strong laser fields of arbitrary configuration, rendering them very well suited for applications.

Color-kinematics duality from the Bern-Kosower formalism

Ahmadiniaz, N.; Balli, F. M.; Lopez-Arcos, C.; Quintero Velez, A.; Schubert, C.

Berends-Giele currents are fundamental building blocks for on-shell amplitudes in non-abelian gauge theory. We present a novel procedure to construct them using the Bern-Kosower formalism forone-loop gluon amplitudes. Applying the pinch procedure of that formalism to a suitable special casethe currents are naturally obtained in terms of multi-particle fields and obeying color-kinematics duality. As a feedback to the Bern-Kosower formalism, we outline how the
multi-particle polarisations and field-strength tensors can be used to significantly streamline the pinch procedure

Keywords: Berends-Giele currents; on-shell amplitudes; Bern-Kosower formalism


Manifest colour-kinematics duality and double-copy in the string-based formalism

Ahmadiniaz, N.; Balli, F. M.; Corradini, O.; Lopez-Arcos, C.; Quintero Velez, A.; Schubert, C.

The relation for the gravity polarisation tensor as the tensor product of two gluon polarisation vectors has been well-known for a long time, but a version of this relation for multi-particle fields is presently still not known. Here we show that in order for this to happen we first have to ensure that the multi-particle polarisations satisfy color-kinematics duality. In previous work, it has been show that this arises naturally from the Bern-Kosower formalism for one-loop gluon amplitudes, and here we show that the tensor product for multi-particle fields arise naturally in the Bern-Dunbar-Shimada formalism for one-loop gravity amplitudes. This allows us to formulate a new prescription for double-copy gravity Berends-Giele currents,and to obtain both the colour-dressed Yang-Mills Berends-Giele currents in the Bern-Carrasco-Johanssongauge and the gravitational Berends-Giele currents explicitly. An attractive feature of our formalism is that it never becomes necessary to determine gauge transformation terms. Our double-copy prescription can also be applied to other cases, and to make this point we derive the double-copy perturbers for α′-deformed gravity and the bi-adjoint scalar model

Keywords: Bern-Dunbar-Shimada formalism; Berends-Giele currents; color-kinematics duality; gravity amplitudes


Worldline master formulas for the dressed electron propagato, part 2: on-shell amplitudes

Ahmadiniaz, N.; Banda Guzman, V. M.; Bastianelli, F.; Corradini, O.; Edwards, J. P.; Schubert, C.

In the first part of this series, we employed the second-order formalism and the“symbol” map to construct a particle path-integral representation of the electron propagator in a background electromagnetic field, suitable for open fermion-line calculations. Its main advantages are the avoidance of long products of Dirac matrices, and its ability to unify whole sets of Feynman diagrams related by permutation of photon legs along the fermion lines. We obtained a Bern-Kosower type master formula for the fermion propagator, dressedwithNphotons, in terms of the “N-photon kernel,” where this kernel appears also in“subleading” terms involving only N−1 of the N-photons.In this sequel, we focus on the application of the formalism to the calculation of on-shell amplitudes and cross-sections. Universal formulas are obtained for the fully polarised matrix elements of the fermion propagator dressed with an arbitrary number of photons, as well as for the corresponding spin-averaged cross-sections. A major simplification of the on-shell case is that the subleading terms drop out, but we also pinpoint other, less obvious simplifications. We use integration by parts to achieve manifest transversality of these amplitudes at the integrand level and exploit this property using the spinor helicity technique. We give a simple proof of the vanishing of the matrix element for all “+” photon helicities in the massless case and find a novel relation between the scalar and spinor spin-averaged cross-sections in the massive case. Testing the formalism on the standard linear Comptonscattering process, we find that it reproduces the known results with remarkable efficiency. Further applications and generalisations are pointed out.

Keywords: On-shell amplitudes; Dressed fermion propagator; Worldline formalism


Sauter-Schwinger effect for colliding laser pulses

Kohlfürst, C.; Ahmadiniaz, N.; Oertel, J.; Schützhold, R.

We study electron-positron pair creation by the electromagnetic field of two colliding laser pulses as described by the vector potential
A(t,r) = [f(ct−x) +f(ct+x)]ey. Employing the world-line instanton technique as well as a generalized WKB approach, we find that the pair creation rate along the symmetry axisx= 0(where one would expect the maximum contribution) displays the same exponential dependence as for a purely time-dependent electric field A(t) = 2f(ct)ey. The pre-factor in front of this exponential does also contain corrections due to focusing or de-focusing effects induced by the spatially inhomogeneous magnetic field. We compare our analytical results to numerical simulations using the Dirac-Heisenberg-Wigner method and find good agreement.

Keywords: Sauter-Schwinger effect; WKB; Worldline instanton; Numerical analysis


Generation of arbitrarily polarized GeV lepton beams via nonlinear Breit-Wheeler process

Xue, K.; Guo, R.-T.; Wan, F.; Shaisultanov, R.; Chen, Y.-Y.; Xu, Z.-F.; Ren, X.-G.; Hatsagortsyan, K. Z.; Keitel, C. H.; Li, J.-X.

Generation of arbitrarily spin-polarized lepton (here refer in particular to electron and positron) beams has been investigated in the single-shot interaction of high-energy polarized γ photons with an ultraintense asymmetric laser pulse via nonlinear Breit-Wheeler (BW) pair production. We develop a fully spin-resolved semi-classical Monte Carlo method to describe the pair creation and polarization in the local constant field approximation. In nonlinear BW process the polarization of created pairs is simultaneously determined by the polarization of parent γ photons, the polarization and asymmetry of scattering laser field, due to the spin angular momentum transfer and the asymmetric spin-dependent pair production probabilities, respectively. In considered all-optical method, dense GeV lepton beams with average polarization degree up to about 80% (adjustable between the transverse and longitudinal components) can be obtained with currently achievable laser facilities, which could be used as injectors of the polarized e+e− collider to search for new physics beyond the Standard Model.


Photon polarization effects in polarized electron-positron pair production in a strong laser field

Dai, Y.-N.; Shen, B.-F.; Li, J.-X.; Shaisultanov, R.; Hatsagortsyan, K. Z.; Keitel, C. H.; Chen, Y.-Y.

Deep understanding of the impact of photon polarization on pair production is essential for the efficient generation of laser-driven polarized positron beams and demands a complete description of polarization effects in strong-field QED processes. Employing fully polarization-resolved Monte Carlo simulations, we investigate correlated photon and electron (positron) polarization effects in the multiphoton Breit–Wheeler pair production process during the interaction of an ultrarelativistic electron beam with a counterpropagating elliptically polarized laser pulse. We show that the polarization of e−e+ pairs is degraded by 35% when the polarization of the intermediate photon is resolved, accompanied by an ∼13% decrease in the pair yield. Moreover, in this case, the polarization direction of energetic positrons at small deflection angles can even be reversed when high-energy photons with polarization parallel to the laser electric field are involved.


Emergence of pion parton distributions

Cui, Z.-F.; Ding, M.; Morgado, J. M.; Raya, K.; Binosi, D.; Chang, L.; de Soto, F.; Roberts, C. D.; Rodriguez-Quintero, J.; Schmidt, S. M.

Supposing only that there is an effective charge which defines an evolution scheme for parton distribution functions (DFs) that is all-orders exact, strict lower and upper bounds on all Mellin moments of the valence-quark DFs of pion-like systems are derived. Exploiting contemporary results from numerical simulations of lattice-regularised quantum chromodynamics (QCD) that are consistent with these bounds, parameter-free predictions for pion valence, glue, and sea DFs are obtained. The form of the valence-quark DF at large values of the light-front momentum fraction is consistent with predictions derived using the QCD-prescribed behaviour of the pion wave function.

Concerning pion parton distributions

Cui, Z.-F.; Ding, M.; Morgado, J. M.; Raya, K.; Binosi, D.; Chang, L.; Papavassiliou, J.; Roberts, C. D.; Rodriguez-Quintero, J.; Schmidt, S. M.

Analyses of the pion valence-quark distribution function (DF), ${\mathpzc u}^\pi(x;\zeta)$, which explicitly incorporate the behaviour of the pion wave function prescribed by quantum chromodynamics (QCD), predict ${\mathpzc u}^\pi(x\simeq 1;\zeta) \sim (1-x)^{\beta(\zeta)}$, $\beta(\zeta \gtrsim m_p)>2$, where $m_p$ is the proton mass. Nevertheless, more than forty years after the first experiment to collect data suitable for extracting the $x\simeq 1$ behaviour of ${\mathpzc u}^\pi$, the empirical status remains uncertain because some methods used to fit existing data return a result for ${\mathpzc u}^\pi$ that violates this constraint. Such disagreement entails one of the following conclusions: the analysis concerned is incomplete; not all data being considered are a true expression of qualities intrinsic to the pion; or QCD, as it is currently understood, is not the theory of strong interactions. New, precise data are necessary before a final conclusion is possible. In developing these positions, we exploit a single proposition, \emph{viz}.\ there is an effective charge which defines an evolution scheme for parton DFs that is all-orders exact. This proposition has numerous corollaries, which can be used to test the character of any DF, whether fitted or calculated.

Optical absorption and carrier multiplication at graphene edges in a magnetic field

Queisser, F.; Lang, S.; Schützhold, R.

We study optical absorption at graphene edges in a transversal magnetic field. The magnetic field bends the trajectories of particle- and hole excitations into antipodal direction which generates a directed current. We find a rather strong amplification of the edge current by impact ionization processes. More concretely, the primary absorption and the subsequent carrier multiplication is analyzed for a graphene fold and a zigzag edge. We identify exact and approximate selection rules and discuss the dependence of the decay rates on the initial state.

Keywords: Graphene; Auger processes; optical absorption


Dressed Dirac Propagator from a Locally Supersymmetric N=1 Spinning Particle

Degli Esposti, G.; Corradini, O.

We study the Dirac propagator dressed by an arbitrary number N of photons by means of a worldline approach, which makes use of a supersymmetric N=1 spinning particle model on the line, coupled to an external Abelian vector field. We obtain a compact off-shell master formula for the tree level scattering amplitudes associated to the dressed Dirac propagator. In particular, unlike in other approaches, we express the particle fermionic degrees of freedom using a coherent state basis, and consider the gauging of the supersymmetry, which ultimately amounts to integrating over a worldline gravitino modulus, other than the usual worldline einbein modulus which corresponds to the Schwinger time integral. The path integral over the gravitino reproduces the numerator of the dressed Dirac propagator.

Environment-induced decay dynamics of anti-ferromagnetic order in the Mott-Hubbard system

Schaller, G.; Queisser, F.; Szpak, N.; König, J.; Schützhold, R.

We study the dissipative Fermi-Hubbard model in the limit of weak tunneling and strong repulsive interactions, where each lattice site is tunnel-coupled to a Markovian fermionic bath. For cold baths at intermediate chemical potentials, the Mott insulator property remains stable and we find a fast relaxation of the particle number towards half filling. On longer time scales, we find that the anti-ferromagnetic order of the Mott-Néel ground state on bi-partite lattices decays, even at zero temperature. For zero and non-zero temperatures, we quantify the different relaxation time scales by means of waiting time distributions which can be derived from an effective (non-Hermitian) Hamiltonian and obtain fully analytic expressions for the Fermi-Hubbard model on a tetramer ring.

Keywords: Fermi-Hubbard model; local master equation; magnetic order; waiting-time distributions


Dynamically assisted tunneling in the impulse regime

Kohlfürst, C.; Queißer, F.; Schützhold, R.

We study the enhancement of tunneling through a potential barrier V(x) by a time-dependent electric field with special emphasis on pulse-shaped vector potentials such as A(t)=A0/cosh^2(ωt). In addition to the known effects of pre-acceleration and potential deformation already present in the adiabatic regime, as well as energy mixing in analogy to the Franz-Keldysh effect in the non-adiabatic (impulse) regime, the pulse A(t) can enhance tunneling by ``pushing'' part of the wave-function out of the rear end of the barrier. Besides the natural applications in condensed matter and atomic physics, these findings could be relevant for nuclear fusion, where pulses A(t) with ω=1 keV and peak field strengths of 10^16 V/m might enhance tunneling rates significantly.

Keywords: Tunneling & traversal time; Nuclear fusion; Schroedinger equation

Trident process in laser pulses

Dinu, V.; Torgrimsson, G.

We study the trident process in laser pulses. We provide exact numerical results for all contributions, including the difficult exchange term. We show that all terms are in general important for a short pulse. For a long pulse, we identify a term that gives the dominant contribution even if the intensity is only moderately high, a0≳1, which is an experimentally important regime where the standard locally constant field (LCF) approximation cannot be used. We show that the spectrum has a richer structure at a0∼1, compared to the LCF regime a0≫1. We study the convergence to LCF as a0 increases and how this convergence depends on the momentum of the initial electron. We also identify the terms that dominate at high energy.

Approximating higher-order nonlinear QED processes with first-order building blocks

Dinu, V.; Torgrimsson, G.

Higher-order tree-level processes in strong laser fields, i.e., cascades, are in general extremely difficult to calculate, but in some regimes the dominant contribution comes from a sequence of first-order processes, i.e., nonlinear Compton scattering and nonlinear Breit-Wheeler pair production. At high intensity the field can be treated as locally constant, which is the basis for standard particle-in-cell codes. However, the locally-constant-field (LCF) approximation and these particle-in-cell codes cannot be used when the intensity is only moderately high, which is a regime that is experimentally relevant. We have shown that one can still use a sequence of first-order processes to estimate higher orders at moderate intensities provided the field is sufficiently long. An important aspect of our new “gluing” approach is the role of the spin and polarization of intermediate particles, which is more nontrivial compared to the LCF regime.

Nonlinear trident in the high-energy limit: Nonlocality, Coulomb field and resummations

Torgrimsson, G.

We study nonlinear trident in laser pulses in the high-energy limit, where the initial electron experiences, in its rest frame, an electromagnetic field strength above Schwinger’s critical field. At lower energies the dominant contribution comes from the “two-step” part, but in the high-energy limit the dominant contribution comes instead from the one-step term. We obtain new approximations that explain the relation between the high-energy limit of trident and pair production by a Coulomb field, as well as the role of the Weizsäcker-Williams approximation and why it does not agree with the high-χ limit of the locally-constant-field approximation. We also show that the next-to-leading order in the large-a0 expansion is, in the high-energy limit, nonlocal and is numerically very important even for quite large a0. We show that the small-a0 perturbation series has a finite radius of convergence, but using Padé-conformal methods we obtain resummations that go beyond the radius of convergence and have a large numerical overlap with the large-a0 approximation. We use Borel-Padé-conformal methods to resum the small-χ expansion and obtain a high precision up to very large χ. We also use newer resummation methods based on hypergeometric/Meijer-G and confluent hypergeometric functions.

Nonlinear photon trident versus double Compton scattering and resummation of one-step terms

Torgrimsson, G.

We study the photon trident process, where an initial photon turns into an electron-positron pair and a final photon under a nonlinear interaction with a strong plane-wave background field. We show that this process is very similar to double Compton scattering, where an electron interacts with the background field and emits two photons. We also show how the one-step terms can be obtained by resumming the small- and large-\chiχ expansions. We consider a couple of different resummation methods, and also propose new resummations (involving Meijer-G functions) which have the correct type of expansions at both small and large \chiχ. These new resummations require relatively few terms to give good precision.

Loops and polarization in strong-field QED

Torgrimsson, G.

In a previous paper we showed how higher-order strong-field-QED processes in long laser pulses can be approximated by multiplying sequences of ‘strong-field Mueller matrices’. We obtained expressions that are valid for arbitrary field shape and polarization. In this paper we derive practical approximations of these Mueller matrices in the locally-constant- and the locally-monochromatic-field regimes. The spin and polarization can also change due to loop contributions (the mass operator for electrons and the polarization operator for photons). We derive Mueller matrices for these as well, for arbitrary laser polarization and arbitrarily polarized initial and final particles.

Resummation of Quantum Radiation Reaction in Plane Waves

Torgrimsson, G.

We propose a new approach to obtain the momentum expectation value of an electron in a high-intensity laser, including multiple photon emissions and loops. We find a recursive formula that allows us to obtain the O(αn) term from O(αn-1), which can also be expressed as an integro-differential equation. In the classical limit we obtain the solution to the Landau-Lifshitz equation to all orders. We show how spin-dependent quantum radiation reaction can be obtained by resumming both the energy expansion as well as the α expansion.

Resummation of quantum radiation reaction and induced polarization

Torgrimsson, G.

In a previous paper we proposed a new method based on resummations for studying radiation reaction of an electron in a plane-wave electromagnetic field. In this paper we use this method to study the electron momentum expectation value for a circularly polarized monochromatic field with a0=1, for which standard locally constant-field methods cannot be used. We also find that radiation reaction has a significant effect on the induced polarization, as compared to the results without radiation reaction, i.e., the Sokolov-Ternov formula for a constant field, or the zero result for a circularly monochromatic field. We also study the Abraham-Lorentz-Dirac equation using Borel-Padé resummations.

Ginzburg effect in a dielectric medium with dispersion and dissipation

Lang, S.; Sauerbrey, R.; Schützhold, R.; Unruh, W.

As a quantum analog of Cherenkov radiation, an inertial photon detector moving through a medium with constant refractive index n may perceive the electromagnetic quantum fluctuations as real photons if its velocity v exceeds the medium speed of light c/n. For dispersive Hopfield type media, we find this Ginzburg effect to extend to much lower v because the phase velocity of light is very small near the medium resonance. In this regime, however, dissipation effects become important. Via an extended Hopfield model, we present a consistent treatment of quantum fluctuations in dispersive and dissipative media and derive the Ginzburg effect in such systems. Finally, we propose an experimental test.

Keywords: dielectric media; dispersion and dissipation; quantum vacuum phenomena; Ginzburg effect; inertial atom; spontaneous excitation

Generalized Landau-Khalatnikov-Fradkin transformations for arbitrary N-point fermion correlators

Ahmadiniaz, N.; Edwards, J. P.; Nicasio, J.; Schubert, C.

We examine the nonperturbative gauge dependence of arbitrary configuration space fermion correlators in quantum electrodynamics (QED). First, we study the dressed electron propagator (allowing for emission or absorption of any number of photons along a fermion line) using the first quantized approach to quantum field theory and analyze its gauge transformation properties induced by virtual photon exchange. This is then extended to the N-point functions where we derive an exact, generalized version of the fully nonperturbative Landau-Khalatnikov-Fradkin (LKF) transformation for these correlators. We discuss some general aspects of the application in perturbation theory and investigate the structure of the LKF factor aboutD¼2dimensions

Keywords: LKFT; Worldline formalism; Non-perturbative QED

Observability of Coulomb-assisted quantum vacuum birefringence

Ahmadiniaz, N.; Bussmann, M.; Cowan, T.; Debus, A.; Kluge, T.; Schützhold, R.

We consider the scattering of an x-ray free-electron laser (XFEL) beam on the superposition of
a strong magnetic field $\bf{B}_{\rm ext}$ with the Coulomb field $\bf{E}_{\rm ext}$
of a nucleus with charge number $Z$. In contrast to Delbr\"uck scattering
(Coulomb field only), the magnetic field $\bf{B}_{\rm ext}$
introduces an asymmetry (i.e., polarization dependence) and renders the effective interaction volume quite
large, while the nuclear Coulomb field facilitates a significant momentum transfer $\Delta\bf k$.
For a field strength of $B_{\rm ext}=10^6 T$ (corresponding to an intensity of order $10^{22}~\rm W/cm^2$)
and an XFEL frequency of 24~keV, we find a differential cross section
$d\sigma/d\Omega\sim10^{-25}~Z^2/(\Delta{\bf k})^2$ in forward direction for one nucleus.
Thus, this effect might be observable in the near future at facilities such as the
Helmholtz International Beamline for Extreme Fields (HIBEF) at the European XFEL.


Superradiant many-qubit absorption refrigerator

Kloc, M.; Meier, K.; Hadjikyriakos, K.; Schaller, G.

We show that the lower levels of a large-spin network with a collective anti-ferromagnetic interaction and collective couplings to three reservoirs may function as a quantum absorption refrigerator. In appropriate regimes, the steady-state cooling current of this refrigerator scales quadratically with the size of the working medium, i.e., the number of spins. The same scaling is observed for the noise and the entropy production rate.

Keywords: open quantum systems; collective interactions; quantum heat engine; quantum absorbtion refrigerator; Dicke superradiance


Non-equilibrium boundary driven quantum systems: models, methods and properties

Gabriel, T. L.; Dario, P.; Gernot, S.

Recent years have seen tremendous progress in the theoretical understanding of quantum systems driven dissipatively by coupling them to different baths at their edges. This was possible because of the concurrent advances in the models used to represent these systems, the methods employed, and the analysis of the emerging phenomenology. Here we aim to give a comprehensive review of these three integrated research directions. We first provide an overarching view of the models of boundary driven open quantum systems, both in the weak and strong coupling regimes. This is followed by a review of state-of-the-art analytical and numerical methods, both exact, perturbative and approximate. Finally, we discuss the transport properties of some paradigmatic one-dimensional chains, with an emphasis on disordered and quasiperiodic systems, the emergence of rectification and negative differential conductance, and the role of phase transitions.

Keywords: open quantum systems; quantum transport; phase transitions; local and global master equations; chain models


Broadband frequency filters with quantum dot chains

Ehrlich, T.; Schaller, G.

Two-terminal electronic transport systems with a rectangular transmission can violate standard thermodynamic uncertainty relations. This is possible beyond the linear response regime and for parameters that are not accessible with rate equations obeying detailed-balance. Looser bounds originating from fluctuation theorem symmetries alone remain respected. We demonstrate that optimal finite-sized quantum dot chains can implement rectangular transmission functions with high accuracy and discuss the resulting violations of standard thermodynamic uncertainty relations as well as heat engine performance.

Keywords: fluctuation theorems; thermodynamic uncertainty relation; Levitov-Lesovik formula; transmission; reaction-coordinate mapping

Related publications


Coarse-graining master equation for periodically driven systems

Hotz, R.; Schaller, G.

We analyze Lindblad-Gorini-Kossakowski-Sudarshan-type generators for selected periodically driven open quantum systems. All these generators can be obtained by temporal coarse-graining procedures, and we compare different coarse-graining schemes. Similar to for undriven systems, we find that a dynamically adapted coarse-graining time, effectively yielding non-Markovian dynamics by interpolating through a series of different but invididually Markovian solutions, yields the best results among the different coarse-graining schemes, albeit at highest computational cost.

Keywords: open quantum systems; Floquet theory; periodic driving; Lindblad master equation


Autonomous implementation of thermodynamic cycles at the nanoscale

Strasberg, P.; Wächtler, C. W.; Schaller, G.

There are two paradigms to study nanoscale engines in stochastic and quantum thermodynamics.
Autonomous models, which do not rely on any external time-dependence, and models that make use of time-dependent control fields, often combined with dividing the control protocol into idealized strokes of a thermodynamic cycle. While the latter paradigm offers theoretical simplifications, its utility in practice has been questioned due to the involved approximations. Here, we bridge the two paradigms by constructing an autonomous model, which implements a thermodynamic cycle in a certain parameter regime. This effect is made possible by self-oscillations, realized in our model by the well studied electron shuttling mechanism. Based on experimentally realistic values, we find that a thermodynamic cycle analysis for a single-electron working fluid is unrealistic, but already a few-electron working fluid could suffice to justify it. We also briefly discuss additional open challenges to autonomously implement the more studied Carnot and Otto cycles.

Keywords: thermodynamic cycle; self-oscillation; autonomous control; electron shuttle


Worldline master formulas for the dressed electron propagator, part 1: Off-shell amplitudes

Ahmadiniaz, N.; Guzman, V. M. B.; Bastianelli, F.; Corradini, O.; Edwards, J. P.; Schubert, C.

In the firrst-quantised worldline approach to quantum field theory, a long-standing problem has been to extend this formalism to amplitudes involving open fermion lines while maintaining the efficiency of the well-tested closed-loop case. In the present series of papers, we develop a suitable formalism for the case of quantum electrodynamics (QED) in vacuum (part one and two) and in a constant external electromagnetic field (part three), based on second-order fermions and the symbol map. We derive this formalism from standard field theory, but also give an alternative derivation intrinsic to the worldline theory. In this first part, we use it to obtain a Bern-Kosower type master formula for the fermion propagator, dressed with N photons in configuration as well as in momentum space.

Keywords: Worlline formalism; QED; Scattering Amplitudes; Gauge Symmetry


Trapped-ion toolkit for studies of quantum harmonic oscillators under extreme conditions

Wittemer, M.; Schröder, J.-P.; Hakelberg, F.; Kiefer, P.; Fey, C.; Schützhold, R.; Warring, U.; Schaetz, T.

Many phenomena described in relativistic quantum field theory are inaccessible to direct observations, but analogue processes studied under well-defined laboratory conditions can present an alternative perspective. Recently, we demonstrated an analogy of particle creation using an intrinsically robust motional mode of two trapped atomic ions. Here, we substantially extend our classical control techniques by implementing machine-learning strategies in our platform and, consequently, increase the accessible parameter regime. As a proof of methodology, we present experimental results of multiple quenches and parametric modulation of an unprotected motional mode of a single ion, demonstrating the increased level of real-time control. In combination with previous results, we enable future experiments that may yield entanglement generation using a process in analogy to Hawking radiation. This article is part of a discussion meeting issue 'The next generation of analogue gravity experiments'.

Keywords: Trapped Ions; Qubits; Ion Traps (Instrumentation)

Heisenberg limit for detecting vacuum birefringence

Ahmadiniaz, N.; Cowan, T.; Sauerbrey, R.; Schramm, U.; Schlenvoigt, H.-P.; Schützhold, R.

Quantum electrodynamics predicts the vacuum to behave as a nonlinear medium, including effects such as birefringence. However, for experimentally available field strengths, this vacuum polarizability is extremely small and thus very hard to measure. In analogy to the Heisenberg limit in quantum metrology, we study the minimum requirements for such a detection in a given strong field (the pump field). Using a laser pulse as the probe field, we find that its energy must exceed a certain threshold depending on the interaction time. However, a detection at that threshold, i.e., the Heisenberg limit, requires highly nonlinear measurement schemes--while for ordinary linear-optics schemes, the required energy (Poisson or shot noise limit) is much larger. Finally, we discuss several currently considered experimental scenarios from this point of view.

Keywords: Quantum Electrodynamics; Vacuum birefringence; Heisenberg limit


Quantum radiation in dielectric media with dispersion and dissipation

Lang, S.; Schützhold, R.; Unruh, W.

By a generalization of the Hopfield model, we construct a microscopic Lagrangian describing a dielectric medium with dispersion and dissipation. This facilitates a well-defined and unambiguous ab initio treatment of quantum electrodynamics in such media, even in time-dependent backgrounds. As an example, we calculate the number of photons created by switching on and off dissipation in dependence on the temporal switching function. This effect may be stronger than quantum radiation produced by variations of the refractive index Δn(t) since the latter are typically very small and yield photon numbers of order (Δn)². As another difference, we find that the partner particles of the created medium photons are not other medium photons but excitations of the environment field causing the dissipation (which is switched on and off).


Off-shell Ward identities for N-gluon amplitudes

Ahmadiniaz, N.; Schubert, C.

Off-shell Ward identities in non-abelian gauge theory continue to be a subject of active research, since they are, in general, inhomogeneous and their form depends on the chosen gauge-fixing procedure. For the three-gluon and four-gluon vertices, it is known that a relatively simple form of the Ward identity can be achieved using the pinch technique or, equivalently, the background-field method with quantum Feynman gauge. The latter is also the gauge-fixing underlying the string-inspired formalism, and here we use this formalism to derive the corresponding form of the Ward identity for the one-loop N - gluon amplitudes.


Pair production in temporally and spatially oscillating fields

Aleksandrov, I. A.; Kohlfürst, C.

Electron-positron pair production for inhomogeneous electric and magnetic fields oscillating in space and time is investigated. By employing accurate numerical methods (Furry-picture quantization and quantum kinetic theory), final particle momentum spectra are calculated and analyzed in terms of effective models. Furthermore, criteria for the applicability of approximate methods are derived and discussed. In this context, special focus is placed on the local density approximation, where fields are assumed to be locally homogeneous in space. Eventually, we apply our findings to the multiphoton regime. Special emphasis is on the importance of linear momentum conservation and the effect of its absence in momentum spectra within approximations based on local homogeneity of the fields.


On the effect of time-dependent inhomogeneous magnetic fields on the particle momentum spectrum in electron-positron pair production

Kohlfürst, C.

Electron-positron pair production in spatially and temporally inhomogeneous electric and magnetic fields is studied within the Dirac-Heisenberg-Wigner formalism (quantum kinetic theory) through computing the corresponding Wigner functions. The focus is on discussing the particle momentum spectrum regarding signatures of Schwinger and multiphoton pair production. Special emphasis is put on studying the impact of a strong dynamical magnetic field on the particle distribution functions. As the equal-time Wigner approach is formulated in terms of partial integro-differential equations an entire section of the manuscript is dedicated to present numerical solution techniques applicable to Wigner function approaches in general.

Relaxation dynamics in a Hubbard dimer coupled to fermionic baths: phenomenological description and its microscopic foundation

Schützhold, R.; Kleinherbers, E.; Szpak, N.; König, J.

We study relaxation dynamics in a strongly-interacting two-site Fermi-Hubbard model that is induced by fermionic baths. To derive the proper form of the Lindblad operators that enter an effective description of the system-bath coupling in different temperature regimes, we employ a diagrammatic real-time technique for the reduced density matrix. An improvement on the commonly-used secular approximation, referred to as coherent approximation, is presented. We analyze the spectrum of relaxation rates and identify different time scales that are involved in the equilibration of the Hubbard dimer after a quantum quench.


Hierarchy of double-time correlations

Queißer, F.; Schützhold, R.

The hierarchy of correlations is an analytical approximation method which allows us to study non-equilibrium phenomena in strongly interacting quantum many-body systems on lattices in higher dimensions. So far, this method was restricted to equal-time correlators ⟨A ^ μ (t)B ^ ν (t)⟩ . In this work, we generalize this method to double-time correlators ⟨A ^ μ (t)B ^ ν (t ′ )⟩ , which allows us to study effective light cones and Green functions and to incorporate finite initial temperatures.

Boltzmann relaxation dynamics of strongly interacting spinless fermions on a lattice

Queißer, F.; Schützhold, R.; Schreiber, S.; Kratzer, P.

Motivated by the recent interest in non-equilibrium phenomena in quantum many-body systems, we study strongly interacting fermions on a lattice by deriving and numerically solving quantum Boltzmann equations that describe their relaxation to thermodynamic equilibrium.The derivation is carried out by inspecting the hierarchy of correlations within the framework of the 1/Z-expansion. Applying the Markov approximation, we obtain the dynamic equations for the distribution functions. Interestingly, we find that in the strong-coupling limit, collisions between particles and holes dominate over particle-particle and hole-hole collisions -- in stark contrast to weakly interacting systems. As a consequence, our numerical simulations show that the relaxation time scales strongly depend on the type of excitations (particles or holes or both) that are initially present.


Compton-like scattering of a scalar particle with N photons and one graviton

Ahmadiniaz, N.; Balli, F. M.; Corradini, O.; Dávila, J. M.; Schubert, C.

Tree-level scattering amplitudes for a scalar particle coupled to an arbitrary number N of photons and a single graviton are computed. We employ the worldline formalism as the main tool to compute the irreducible part of the amplitude, where all the photons and the graviton are directly attached to the scalar line, then derive a tree replacement rule to construct the reducible parts of the amplitude which involve irreducible pure N-photon two-scalar amplitudes where one photon line emits the graviton. We test our construction by verifying the on-shell gauge and diffeomorphism Ward identities, at arbitrary N.

Keywords: Scattering amplitudes; gravitons; Ward identities