# Correlations in disordered quantum harmonic oscillator systems: The effects of excitations and quantum quenches

## TL;DR

This paper establishes exponential decay of disorder-averaged position-momentum correlations in disordered quantum harmonic oscillator systems, analyzing both eigenstates and post-quench dynamics, highlighting the effects of excitations and quantum quenches.

## Contribution

It provides new decay estimates for correlations in disordered oscillator models, including dynamic correlations in eigenstates and time-evolved states after a quantum quench.

## Key findings

- Decay estimates depend on excitation levels
- Correlations decay exponentially in space after quenches
- Results hold uniformly in time for initial product states

## Abstract

We prove spatial decay estimates on disorder-averaged position-momentum correlations in a gapless class of random oscillator models. First, we prove a decay estimate on dynamic correlations for general eigenstates with a bound that depends on the magnitude of the maximally excited mode. Then, we consider the situation of a quantum quench. We prove that the full time-evolution of an initially chosen (uncorrelated) product state has disorder-averaged correlations which decay exponentially in space, uniformly in time.