Berlin 2024 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 12: Statistical Physics far from Thermal Equilibrium II
DY 12.8: Talk
Monday, March 18, 2024, 16:45–17:00, BH-N 334
The spectral boundary of the Asymmetric Simple Exclusion Process (ASEP) - free fermions, Bethe ansatz and random matrix theory — •Goran Nakerst1, Tomaz Prosen2, and Masud Haque1,3 — 1Institut für Theoretische Physik, Technische Universität Dresden, D-01062 Dresden, Germany — 2University of Ljubljana, Faculty for Mathematics and Physics, Jadranska 19, Ljubljana, Slovenia — 3Max-Planck-Institut für Physik komplexer Systeme, D-01187 Dresden, Germany
The dynamical timescales of Markov processes are determined by the spectrum of their generator matrices. In this talk, we explore the spectral boundary characteristics of the generator matrix in a paradigmatic model: the 1D Asymmetric Simple Exclusion Process (ASEP) with both periodic and open boundary conditions. Our focus centers on the emergence of a distinctive spiky spectral boundary (SSB). We will illustrate how the ASEP generator is represented by an interacting fermion model, which, in its non-interacting variant, exhibits a pronounced SSB. Notably, the SSB persists upon the reintroduction of interactions, which revert to the conventional generator of ASEP. Furthermore, we will establish the universality of the SSB, illustrating its prevalence in random matrix ensembles characterized by particular trace correlations and, equivalently, in random graphs with specific cycle structures. This presentation aims to meld concepts from stochastic processes, quantum mechanics, and random matrix theory.
Keywords: Asymmetric Simple Exclusion Process; ASEP; markov processes; random matrix theory; spectrum