Quantum Quench of the trap frequency in the harmonic Calogero model

TL;DR

This paper analytically studies a quantum quench in the harmonic Calogero model, showing that a generalized Gibbs ensemble accurately predicts long-term average local observables despite periodic dynamics.

Contribution

It provides an exact solution for the post-quench state and demonstrates the validity of the GGE in describing long-term averages in an integrable, trapped quantum system.

Findings

GGE accurately predicts long-term local observable averages

Exact initial state and time evolution derived for the model

Periodic dynamics prevent true equilibration, but GGE remains valid

Abstract

We consider a quantum quench of the trap frequency in a system of bosons interacting through an inverse-square potential and confined in a harmonic trap (the harmonic Calogero model). We determine exactly the initial state in terms of the post-quench eigenstates and derive the time evolution of simple physical observables. Since this model possesses an infinite set of integrals of motion (IoM) that allow its exact solution, a generalised Gibbs ensemble (GGE), i.e. a statistical ensemble that takes into account the conservation of all IoM, can be proposed in order to describe the values of local physical observables long after the quench. Even though, due to the presence of the trap, physical observables do not exhibit equilibration but periodic evolution, such a GGE may still describe correctly their time averaged values. We check this analytically for the local boson density and find that the GGE conjecture is indeed valid, in the thermodynamic limit.