Eigenvalue crossing as a phase transition in relaxation dynamics
Statistical Mechanics
2023-05-23 v1
Abstract
When a system's parameter is abruptly changed, a relaxation towards the new equilibrium of the system follows. We show that a crossing between the second and third eigenvalues of the relaxation matrix results in a relaxation trajectory singularity, which is analogous to a first-order equilibrium phase transition. We demonstrate this in a minimal 4-state system and in the thermodynamic limit of the 1D Ising model.
Cite
@article{arxiv.2209.09307,
title = {Eigenvalue crossing as a phase transition in relaxation dynamics},
author = {Gianluca Teza and Ran Yaacoby and Oren Raz},
journal= {arXiv preprint arXiv:2209.09307},
year = {2023}
}