2017/10/31 by M. D. Tomchenko · 1 citation
Mathematics · Physics and Astronomy · #Bose gas #Boundary value problem #Cold Atom Physics and Bose-Einstein Condensates #Coupling constant #Density matrix #Exact solutions in general relativity #Hamiltonian (control theory) #Periodic boundary conditions #Spectral Theory in Mathematical Physics #Strong Light-Matter Interactions #Wave function #Zero (linguistics) #cond-mat.quant-gas
paper · pdf · doi:10.15407/ujpe64.3.250
published as Ukr. J. Phys. 64, 250 (2019) · 18 pages, 1 figure; v3: minor changes; final version
openalex created_date 2017/10/20 · openalex publication_date 2019/04/01 · arxiv created 2019/04/07 · arxiv updated 2019/04/09 · openalex updated_date 2026/08/05
We diagonalize the second-quantized Hamiltonian of a one-dimensional Bose gas with a non-point repulsive interatomic potential and zero boundary conditions. At a weak coupling, the solutions for the ground-state energy E0 and the dispersion law E(k) coincide with the Bogoliubov solutions for a periodic system. In this case, the single-particle density matrix F1(x, x′) at T = 0 is close to the solution for a periodic system and, at T > 0, is significantly different from it. We also obtain that the wave function ⟨w(x, t)⟩ of the effective condensate is close to a constant √︀N0/L inside the system and vanishes on the boundaries (here, N0 is the number of atoms in the effective condensate, and L is the size of the system). We find the criterion of applicability of the method, according to which the method works for a finite system at very low temperature and with a weak coupling (a weak interaction or a large concentration).