Nonlinear corrections in the quantization of a weakly nonideal Bose gas at zero temperature. II. The general case

• Published in: Chaos, solitons and fractals Vol. 167; p. 113023
• Main Author: Smolyakov, Mikhail N.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.02.2023
• Subjects: Bose gas; Bose–Einstein condensate; Nonlinear perturbations; Quantization; Bose–Einstein condensate; Quantization; Bose gas; Nonlinear perturbations
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2022.113023

In the present paper, discussion of the canonical quantization of a weakly nonideal Bose gas at zero temperature within the framework of the Bogolyubov approach is continued. Contrary to the previous paper on this subject, here the two-body interaction potential is considered in the general form. It is shown that in such a case consideration of the first nonlinear correction also leads to the automatic particle number conservation without any additional assumptions or modification of the resulting effective Hamiltonian. •A slight modification of the original Bogolyubov approach is proposed.•Nonoscillation modes recover the commutation relations for the linear solution.•First nonlinear correction that satisfies the commutation relations is calculated.•The nonlinear correction provides the automatic particle number conservation.