Quantum quench and thermalization to GGE in arbitrary dimensions and the odd-even effect

TL;DR

This paper generalizes quantum quench and thermalization analysis to free scalar fields in arbitrary dimensions, demonstrating how local correlators evolve towards GGE or thermal states with dimension-dependent rates, and exploring effects of different quench protocols.

Contribution

It extends previous 1+1 dimensional results to arbitrary dimensions, providing explicit calculations of local correlator dynamics and equilibration rates after quantum quenches.

Findings

Long-time local correlators are described by GGE or thermal ensembles.

Equilibration rate is exponential for odd dimensions, power law for even.

Quench protocols influence long-term behavior and irrelevant operators affect IR dynamics.

Abstract

In many quantum quench experiments involving cold atom systems the post-quench system can be described by a quantum field theory of free scalars or fermions, typically in a box or in an external potential. We work with free scalars in arbitrary dimensions generalizing the techniques employed in our earlier work \cite{Mandal:2015kxi} in 1+1 dimensions. In this paper, we generalize to $d$ spatial dimensions for arbitrary $d$. The system is considered in a box much larger than any other scale of interest. We start with the ground state, or a squeezed state, with a high mass and suddenly quench the system to zero mass ("critical quench"). We explicitly compute time-dependence of local correlators and show that at long times they are described by a generalized Gibbs ensemble (GGE), which, in special cases, reduce to a thermal (Gibbs) ensemble. The equilibration of {\it local} correlators can be regarded as `subsystem thermalization' which we simply call 'thermalization' here (the notion of thermalization here also includes equlibration to GGE). The rate of approach to equilibrium is exponential or power law depending on whether $d$ is odd or even respectively. As in 1+1 dimensions, details of the quench protocol affect the long time behaviour; this underlines the importance of irrelevant operators at IR in non-equilibrium situations. We also discuss quenches from a high mass to a lower non-zero mass, and find that in this case the approach to equilibrium is given by a power law in time, for all spatial dimensions $d$, even or odd.