On some rigorous aspects of fragmented condensation

TL;DR

This paper explores the mathematical properties of fragmented condensation in bosonic systems, providing a characterization of finite fragmentation and conditions for its persistence in large, interacting quantum systems.

Contribution

It introduces a simple characterization of finite fragmentation and analyzes the conditions under which fragmented condensation persists in mean-field and large-gap regimes.

Findings

Fragmented condensation occurs in interacting systems within the mean-field regime.

Persistence of fragmentation is shown to depend on the large gap of the one-body Hamiltonian.

A mathematical framework for understanding fragmentation in bosonic systems is developed.

Abstract

In this paper we discuss some aspects of fragmented condensation from a mathematical perspective. We first propose a simple way of characterizing finite fragmentation. Then, inspired by recent results of semiclassical analysis applied to bosonic systems with infinitely many degrees of freedom, we address the problem of persistence of fragmented condensation. We show that the latter occurs in interacting systems, in the mean-field regime, and in the limit of large gap of the one-body Hamiltonian.