Bogolyubov approximation for diagonal model of an interacting Bose gas

TL;DR

This paper uses the Bogolyubov approximation to analyze a superstable interacting Bose gas, demonstrating Bose--Einstein condensation occurs for certain chemical potentials.

Contribution

It provides a rigorous proof of Bose--Einstein condensation in a nonlinear, interacting Bose system using the Bogolyubov approximation.

Findings

Bose--Einstein condensation occurs for all chemical potentials greater than λ(0)

The system's energy operator includes nonlinear occupation number terms

The analysis applies to superstable Bose systems with specific energy conditions

Abstract

We study, using the Bogolyubov approximation, the thermodynamic behaviour of a superstable Bose system whose energy operator in the second-quantized form contains a nonlinear expression in the occupation numbers operators. We prove that for all values of the chemical potential satisfying $\mu > \lambda(0)$, where $\lambda (0)\leq 0$ is the lowest energy value, the system undergoes Bose--Einstein condensation.