2024/02/01 by Goran Nakerst, Nakerst, Goran, Tomaž Prosen +3
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Opinion Dynamics and Social Influence #Quantum Physics (quant-ph) #Random Matrices and Applications #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2402.00662
openalex publication_date 2024/02/01 · openalex created_date 2024/02/03 · openalex updated_date 2026/07/28
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.