# Exponential damping induced by random and realistic perturbations

## TL;DR

This paper investigates how random and realistic perturbations cause exponential damping in the expectation-value dynamics of quantum many-body systems, combining theoretical analysis with numerical simulations.

## Contribution

It reveals that random-matrix structured perturbations induce exponential damping and demonstrates relevance to realistic models using numerical methods.

## Key findings

- Random-matrix perturbations lead to exponential damping of dynamics.
- Theoretical predictions match numerical results in spin ladder models.
- Decay of current autocorrelation functions is well-described by the theory.

## Abstract

Given a quantum many-body system and the expectation-value dynamics of some operator, we study how this reference dynamics is altered due to a perturbation of the system's Hamiltonian. Based on projection operator techniques, we unveil that if the perturbation exhibits a random-matrix structure in the eigenbasis of the unperturbed Hamiltonian, then this perturbation effectively leads to an exponential damping of the original dynamics. Employing a combination of dynamical quantum typicality and numerical linked cluster expansions, we demonstrate that our theoretical findings for random matrices can, in some cases, be relevant for the dynamics of realistic quantum many-body models as well. Specifically, we study the decay of current autocorrelation functions in spin-$1/2$ ladder systems, where the rungs of the ladder are treated as a perturbation to the otherwise uncoupled legs. We find a convincing agreement between the exact dynamics and the lowest-order prediction over a wide range of interchain couplings.