Simulations of relativistic quantum plasmas using real-time lattice scalar QED

Abstract

Real-time lattice quantum electrodynamics (QED) provides a unique tool for simulating plasmas in the strong-field regime, where collective plasma scales are not well separated from relativistic-quantum scales. As a toy model, we study scalar QED, which describes self-consistent interactions between charged bosons and electromagnetic fields. To solve this model on a computer, we first discretize the scalar-QED action on a lattice, in a way that respects geometric structures of exterior calculus and U(1)-gauge symmetry. The lattice scalar QED can then be solved, in the classical-statistics regime, by advancing an ensemble of statistically equivalent initial conditions in time, using classical field equations obtained by extremizing the discrete action. To demonstrate the capability of our numerical scheme, we apply it to two example problems. The first example is the propagation of linear waves, where we recover analytic wave dispersion relations using numerical spectrum. The second example is an intense laser interacting with a one-dimensional plasma slab, where we demonstrate natural transition from wakefield acceleration to pair production when the wave amplitude exceeds the Schwinger threshold. Our real-time lattice scheme is fully explicit and respects local conservation laws, making it reliable for long-time dynamics. The algorithm is readily parallelized using domain decomposition, and the ensemble may be computed using quantum parallelism in the future.

Quantum kinetic theory of plasmas

“…Quantum relativistic treatments are of interest in several different contexts (Zhang et al 2020;Elkamash et al 2017;Shi et al 2018). Dense astrophysical objects can have a Fermi energy approaching or exceeding the electron rest mass energy, and the strong magnetic fields of magnetars give rise to relativistic Landau quantization.…”

Real-time lattice gauge theory actions: unitarity, convergence, and path integral contour deformations

“…Realtime evolution of classical lattice gauge fields has been studied in order to gain insight into electroweak sphaleron transitions in the early universe [14][15][16][17][18][19][20][21][22][23][24][25] and the evolution of quantum fermions in these classical background gauge fields has been investigated [26][27][28][29][30]. Realtime LGT calculations of fermion-antifermion pair production in quantum electrodynamics with the U (1) gauge field treated classically have also been performed [31][32][33][34][35][36]. Semi-classical real-time LGT has been studied in the context of heavy ion collisions [37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55].…”

Quantum Kinetic Theory of Plasmas

“…Quantum relativistic treatments are of interest in several different contexts [92][93][94]. Dense astrophysical objects can have a Fermi energy approaching or exceeding the electron rest mass energy, the strong magnetic fields of magnetars give rise to relativistic Landau quantization .…”