2018/08/31 by Maksim Tomchenko
Mathematics · Physics and Astronomy · #Bose gas #Bose–Einstein condensate #Cold Atom Physics and Bose-Einstein Condensates #Eigenfunction #Fragmentation (computing) #Hamiltonian (control theory) #Physics of Superconductivity and Magnetism #Spectral Theory in Mathematical Physics #Wave function #cond-mat.quant-gas
paper · pdf · doi:10.1007/s10909-019-02252-0
published as J. Low Temp. Phys. 198, 100 (2020) · 24 pages, 3 figures; v.3: Published version. On page 9, we have made an additional correction that is absent in the published version
openalex created_date 2018/08/31 · openalex publication_date 2019/11/15 · arxiv created 2021/07/19 · arxiv updated 2021/07/20 · openalex updated_date 2026/08/05
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.