On a fragmented condensate in a uniform Bose system

TL;DR

This paper challenges previous assumptions by Noziéres, demonstrating that in dense, low-temperature, weakly interacting one-dimensional Bose systems, a fragmented condensate can form, potentially leading to a crystal-like structure.

Contribution

It provides a new analysis showing that condensate fragmentation is possible in certain conditions, contrary to earlier beliefs that it increases energy and is thus unfavorable.

Findings

Fragmented condensates can form in dense, low-temperature 1D Bose systems.

Wave functions constructed as Hamiltonian eigenfunctions support condensate fragmentation.

Fragmentation is associated with a crystal-like structure in the condensate.

Abstract

According to the well-known analysis by Nozi\'{e}res, the fragmentation of the condensate increases the energy of a uniform interacting Bose system. Therefore, at $T= 0$ the condensate should be nonfragmented. We perform a more detailed analysis and show that the result by Nozi\'{e}res is not general. We find that, in a dense Bose system, the formation of a crystal-like structure with a fragmented condensate is possible. The effect is related to a nonzero size of real atoms. Moreover, the wave functions studied by Nozi\'{e}res are not eigenfunctions of the Hamiltonian and, therefore, do not allow one to judge with confidence about the structure of the condensate in the ground state. We have constructed the wave functions in such a way that they are eigenfunctions of the Hamiltonian. The results show that the fragmentation of the condensate (quasicondensate) is possible for a finite one-dimensional uniform system at low temperatures and a weak coupling.