Connecting real-time properties of the massless Schwinger model to the massive case

Abstract

Quantum electrodynamics in 1 + 1 space-time dimensions is analytically solvable for massless fermions, while no solution is known for massive fermions. Employing the classical-statistical approach, we simulate the real-time dynamics on a lattice using Wilson fermions with mass m at gauge coupling g. It is shown that quantitative properties of the massless Schwinger model are emerging in the limit of large g/m. We investigate two scenarios corresponding to opposite charges which are either held fixed or moving back-to-back along the light cone, as employed in effective descriptions for jet energy loss and photon production in the context of heavy-ion collisions. Remarkably, we find that the dynamics is rather well described by the massless limit for a wide range of mass values at fixed coupling. Moreover, our study shows that previous approximate scenarios with external charges on the light cone rather accurately capture the self-consistent dynamics of the energy conserving simulation.

Implementing quantum electrodynamics with ultracold atomic systems

“…This confining string can break in theories with dynamical fermions by the production of charged particle-antiparticle pairs which result in a screening of the static sources [69][70][71][72][73][74]. QED in one spatial dimension shares important aspect of dynamical string breaking and, therefore, serves as a toy model for addressing related questions [33,38,40,41,44]. To study dynamical string breaking in QED in one spatial dimension we prepare two static charges Q located at d 2 on the spatial lattice with N 2 lattice sites.…”

“…In the cold atom setup, this corresponds to a bosonic species imbalance of ( ) = I Q g 0 2 inside the string | | < x d 2 whereas it vanishes outside of it. We first make contact to the corresponding QED literature [33,44] by considering the limit ℓ  ¥ and choosing = g M 1, a S M = 0.1 and N=1024. To this end, we study the time-evolution of the electric field E n for = d a 287 S and display different instances of time in figure 7.…”

“…Accordingly, the external charges are gradually screened and finally result in the breaking of the string. At asymptotic times, the external charges are then supposed to become screened by an exponential cloud of dynamical fermions [24,33,44,75].…”

“…The construction of a hermitean, local and translation-invariant lattice theory of fermions necessarily entails the appearence of unphysical degrees of freedom, the so-called fermion doublers [42]. One possibility to resolve this problem is by making the spurious doubler modes heavy via a Wilson term [43] and we refer to [32,33,44] for numerical studies using this approach. In this work, we employ the alternative staggered fermion discretization where the Dirac spinor is decomposed in such a way that the doubler modes can be disregarded as they decouple.…”

“…. The corresponding cold atom setup is characterized by , the FI approach of [32,34,44,55,56] allows us to study the dynamics in this regime. To make contact with the Truncated Wigner approach, we start from a purely bosonic theory [57].…”