Stability of Exponentially Damped Oscillations under Perturbations of the Mori-Chain

TL;DR

This paper investigates the stability of exponentially damped oscillations in relaxation dynamics under perturbations of the Mori chain, using the recursion method and numerical experiments aligned with the universal operator growth hypothesis.

Contribution

It introduces a new stability analysis of relaxation dynamics via the recursion method and proposes a criterion to identify perturbations causing atypical dynamics.

Findings

Exponential damped oscillations show stability under certain perturbations.

A criterion is proposed to detect pathological perturbations leading to unusual dynamics.

Numerical experiments support the stability of a broader class of relaxation behaviors.

Abstract

There is an abundance of evidence that some relaxation dynamics, e.g., exponential decays, are much more common in nature than others. Recently, there have been attempts to trace this dominance back to a certain stability of the prevalent dynamics versus generic Hamiltonian perturbations. In the paper at hand, we tackle this stability issue from yet another angle, namely in the framework of the recursion method. We investigate the behavior of various relaxation dynamics with respect to alterations of the so-called Lanczos coefficients. All considered scenarios are set up in order to comply with the "universal operator growth hypothesis". Our numerical experiments suggest the existence of stability in a larger class of relaxation dynamics consisting of exponentially damped oscillations. Further, we propose a criterion to identify "pathological" perturbations that lead to uncommon dynamics.