The spectral boundary of the Asymmetric Simple Exclusion Process (ASEP) – free fermions, Bethe ansatz and random matrix theory
arxiv(2024)
摘要
In non-equilibrium statistical mechanics, the Asymmetric Simple Exclusion
Process (ASEP) serves as a paradigmatic example. We investigate the spectral
characteristics of the ASEP, focusing on the spectral boundary of its generator
matrix. We examine finite ASEP chains of length L, under periodic (pbc) and
open boundary conditions (obc). Notably, the spectral boundary exhibits L
spikes for pbc and L+1 spikes for obc. Treating the ASEP generator as an
interacting non-Hermitian fermionic model, we extend the model to have tunable
interaction. In the non-interacting case, the analytically computed many-body
spectrum shows a spectral boundary with prominent spikes. For pbc, we use the
coordinate Bethe ansatz to interpolate between the noninteracting case to the
ASEP limit, and show that these spikes stem from clustering of Bethe roots. The
robustness of the spikes in the spectral boundary is demonstrated by linking
the ASEP generator to random matrices with trace correlations or, equivalently,
random graphs with distinct cycle structures, both displaying similar spiked
spectral boundaries.
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