Нижні енергетичні рівні одновимірного слабко взаємодіючого бозе-газу з нульовими межовими умовами

• Дата: 2019
• Автор: Tomchenko, M. D.
• Формат: Стаття
• Мова: English
• Опубліковано: Publishing house "Academperiodika" 2019
• Теми: -; interacting bosons; Bogoliubov method; zero boundary conditions
• Онлайн доступ: https://ujp.bitp.kiev.ua/index.php/ujp/article/view/2018576
• Назва журналу: Ukrainian Journal of Physics

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).