Lieb-Robinson bounds and growth of correlations in Bose mixtures

TL;DR

This paper establishes Lieb-Robinson bounds for multi-component Bose mixtures, showing that correlations between disjoint particle sets grow controllably over time, with correlations remaining small relative to the total particle number.

Contribution

It introduces Lieb-Robinson bounds for Bose mixtures, providing new estimates on correlation growth in multi-component quantum gases.

Findings

Correlations remain asymptotically small in large systems.

Correlation functions grow at a controlled rate over time.

Lieb-Robinson bounds are extended to multi-component Bose gases.

Abstract

For a mixture of interacting Bose gases initially prepared in a regime of condensation (uncorrelation), it is proved that in the course of the the time evolution observables of disjoint sets of particles of each species have correlation functions that remain asymptotically small in the total number of particles and display a controlled growth in time. This is obtained by means of ad hoc estimates of Lieb-Robinson type on the propagation of the interaction, established here for the multi-component Bose mixture.