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

TL;DR

This paper extends the canonical quantization of a weakly nonideal Bose gas at zero temperature by considering a general two-body interaction potential, demonstrating that nonlinear corrections ensure particle number conservation.

Contribution

It introduces a general form of the two-body interaction potential into the Bogolyubov approach and shows nonlinear corrections inherently conserve particle number.

Findings

Nonlinear corrections lead to automatic particle number conservation.

General interaction potential is incorporated into the quantization framework.

The approach remains consistent without additional assumptions.

Abstract

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.