Lieb–Robinson bounds and growth of correlations in Bose mixtures

Article type: Research Article

Authors: Michelangeli, Alessandro^a | Santamaria, Nicola^{b; *}

Affiliations: [a] Institute for Applied Mathematics, and Hausdorff Center for Mathematics, University of Bonn, Endenicher Allee 60, D-53115 Bonn, Germany. E-mail: michelangeli@iam.uni-bonn.de | [b] Department of Mathematics, University of Rome La Sapienza, Piazzale Aldo Moro 5, 00185 Rome, Italy. E-mail: nicola.santamaria@uniroma1.it

Correspondence: [*] Corresponding author. E-mail: nicola.santamaria@uniroma1.it.

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 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.

Keywords: Bose mixtures, composite BEC, many-body dynamics, correlation function, Lieb–Robinson bounds

DOI: 10.3233/ASY-211750

Journal: Asymptotic Analysis, vol. 130, no. 1-2, pp. 233-259, 2022