Real-time Fermions for Baryogenesis Simulations

TL;DR

This paper introduces a computational method combining lattice fermion implementation with low-cost fermions to efficiently simulate quantum fermions in baryogenesis, demonstrated on a 1+1D model, promising faster simulations for 3+1D physics.

Contribution

The paper develops a novel hybrid simulation approach that accurately models quantum fermions coupled to classical bosonic fields during baryogenesis, improving computational efficiency.

Findings

Successfully reproduces anomalous baryon number violation.

Demonstrates the method on a 1+1D axial U(1) model.

Potential for significant computational speed-up in 3+1D simulations.

Abstract

We study how to numerically simulate quantum fermions out of thermal equilibrium, in the context of electroweak baryogenesis. We find that by combining the lattice implementation of Aarts and Smit [1] with the "low cost" fermions of Borsanyi and Hindmarsh [2], we are able to describe the dynamics of a classical bosonic system coupled to quantum fermions, that correctly reproduces anomalous baryon number violation. To demonstrate the method, we apply it to the 1+1 dimensional axial U(1) model, and perform simulations of a fast symmetry breaking transition. Compared to solving all the quantum mode equations as in [1], we find that this statistical approach may lead to a significant gain in computational time, when applied to 3+1 dimensional physics.