TY - JOUR
AU - M. Tomchenko
PY - 2019/04/01
Y2 - 2019/11/21
TI - Low-Lying Energy Levels of a One-Dimensional Weakly Interacting Bose Gas under Zero Boundary Conditions
JF - Ukrainian Journal of Physics
JA - UJP
VL - 64
IS - 3
SE - Structure of materials
DO - 10.15407/ujpe64.3.250
UR - https://ujp.bitp.kiev.ua/index.php/ujp/article/view/2018576
AB - 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).
ER -