On a fragmented condensate in a uniform Bose system

Abstract

According to the well-known analysis by Noziéres, 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 Noziéres 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 Noziéres 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.

24 pages, 3 figures; v.3: Published version. On page 9, we have made an additional correction that is absent in the published version

References in corpus (9)

• Fragmentation of Bose-Einstein Condensates
• Quantum depletion of a homogeneous Bose-Einstein condensate
• Evidence of Luttinger liquid behavior in one-dimensional dipolar quantum gases
• Order parameter and detection for crystallized dipolar bosons in lattices
• Bosonic and fermionic dipoles on a ring
• Breaking the resilience of a two-dimensional Bose-Einstein condensate to fragmentation
• The low-energy excitation spectrum of one-dimensional dipolar quantum gases
• Self-consistent determination of the many-body state of ultracold bosonic atoms in a one-dimensional harmonic trap
• Low-lying energy levels of a one-dimensional weakly interacting Bose gas under zero boundary conditions

Cited by in corpus (9)

• Fragmentation and correlations in a rotating Bose-Einstein condensate undergoing breakup
• On the characterisation of fragmented Bose-Einstein condensation and its emergent effective evolution
• Interference of longitudinal and transversal fragmentations in the Josephson tunneling dynamics of Bose-Einstein condensates
• Fragmentation of a trapped bosonic mixture
• Exact crystalline solution for a one-dimensional few-boson system with point interaction
• Fragmentation of a trapped multiple-species bosonic mixture
• Nonuniform Bose-Einstein condensate. II. Doubly coherent states
• Symmetry properties of the ground state of the system of interacting spinless bosons
• Fragmentation of identical and distinguishable bosons' pairs and natural geminals of a trapped bosonic mixture