Re-examining the quadratic approximation in theory of a weakly interacting Bose gas with condensate: the role of nonlocal interaction potentials

Autor: Yu. V. Slyusarenko, A. S. Peletminskii, Andrii Sotnikov, M. S. Bulakhov, S. V. Peletminskii
Rok vydání: 2018
Předmět:
Zdroj: Journal of Physics B: Atomic, Molecular and Optical Physics
ISSN: 0953-4075
0368-3400
0038-5646
1054-660X
0132-6414
1063-7796
0367-2026
1742-6596
1751-8113
DOI: 10.1088/1361-6455/aae061
Popis: We derive and analyze the coupled equations of quadratic approximation of the Bogoliubov model for a weakly interacting Bose gas. The first equation determines the condensate density as a variational parameter and ensures the minimum of the grand thermodynamic potential. The second one provides a relation between the total number of particles and chemical potential. Their consistent theoretical analysis is performed for a number of model interaction potentials including contact (local) and nonlocal interactions, where the latter provide nontrivial dependencies in momentum space. We demonstrate that the derived equations have no solutions for the local potential, although they formally reproduce the well-known results of the Bogoliubov approach. At the same time, it is shown that these equations have the solutions for physically relevant nonlocal potentials. We show that in the regimes close to experimental realizations with ultracold atoms, the contribution of the terms originating from the quadratic part of the truncated Hamiltonian to the chemical potential can be of the same order of magnitude as from its $c$-number part. Due to this fact, in particular, the spectrum of single-particle excitations in the quadratic approximation acquires a gap. The issue of the gap is also discussed.
22 pages, 5 figures
Databáze: OpenAIRE
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