Relaxation, pre-thermalization and diffusion in a noisy Quantum Ising Chain

TL;DR

This paper investigates how a noisy Quantum Ising Chain thermalizes after a sudden quench, revealing pre-thermalization and diffusion phenomena through analytical calculations of key physical quantities.

Contribution

It provides an analytical study of pre-thermalization and diffusion in a noisy Quantum Ising Chain, highlighting the transition from intermediate to infinite temperature states.

Findings

Identification of pre-thermalized states at intermediate times

Analytical characterization of kink density and magnetic correlators

Observation of diffusive behavior at long times

Abstract

We study the dynamics of thermalization resulting from a time-dependent noise in a Quantum Ising Chain subject to a sudden quench of the transverse magnetic field. For weak noise the dynamics shows a pre-thermalized state at intermediate time scales, eventually drifting towards an asymptotic infinite temperature steady state characterized by diffusive behavior. By computing analytically the density of kinks, as well as the transverse and longitudinal magnetic field correlators, we characterize these two regimes, their observability and their signatures in the various physical quantities.