On a Fragmented Condensate in a Uniform Bose System

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.