Weakly-Interacting Bosons in a Trap within Approximate Second Quantization Approach

TL;DR

This paper generalizes Bogoliubov theory for weakly-interacting bosons in a trap using an approximate second quantization approach, deriving nonlinear matrix equations and demonstrating their effectiveness through energy and condensate fraction calculations.

Contribution

It introduces a novel approximate second quantization method for analyzing weakly-interacting bosons in harmonic traps, extending Bogoliubov theory.

Findings

Derived nonlinear matrix equations for Hamiltonian diagonalization

Perturbative solutions yield accurate energy and condensate fraction estimates

Method applicable to weakly-interacting Bose gases in traps

Abstract

The theory of Bogoliubov is generalized for the case of a weakly-interacting Bose-gas in harmonic trap. A set of nonlinear matrix equations is obtained to make the diagonalization of Hamiltonian possible. Its perturbative solution is used for the calculation of the energy and the condensate fraction of the model system to show the applicability of the method.