# Exact relaxation dynamics and quantum information scrambling in multiply quenched harmonic chains

## TL;DR

This paper provides exact analytical results on the relaxation and information scrambling in multiply quenched harmonic chains, revealing local thermalization despite integrability.

## Contribution

It presents the first exact analysis of relaxation dynamics and quantum information scrambling in multiply quenched harmonic chains, a trivially integrable system.

## Key findings

- Out of time correlator indicates scrambling at large times.
- Entanglement entropy saturates to a steady state.
- Reduced density matrix becomes diagonal long after quenches.

## Abstract

The quantum dynamics of isolated systems under quench condition exhibits a variety of interesting features depending on the integrable/chaotic nature of system. We study the exact dynamics of trivially integrable system of harmonic chains under a multiple quench protocol. Out of time ordered correlator of two Hermitian operators at large time displays scrambling in the thermodynamic limit. In this limit, the entanglement entropy and the central component of momentum distribution both saturate to a steady state value. We also show that reduced density matrix assumes the diagonal form long after multiple quenches for large system size. These exact results involving infinite dimensional Hilbert space are indicative of local thermal behaviour for a trivially integrable harmonic chain.