On the Bogoliubov theory: Casimir effect in a single weakly interacting Bose gas at zero-temperature with Neumann boundary condition

TL;DR

This paper develops Bogoliubov theory for a weakly interacting Bose gas confined between two plates at zero temperature, analyzing quantum fluctuations and Casimir forces under Neumann boundary conditions.

Contribution

It introduces a detailed Bogoliubov theoretical framework for BECs with Neumann boundary conditions and compares Casimir forces across different boundary types.

Findings

Quantum fluctuation energy calculated for BEC with Neumann BC.

Casimir force analyzed and compared with other boundary conditions.

Provides insights into boundary effects on quantum gases at zero temperature.

Abstract

Developing Bogoliubov theory of weakly interacting Bose gas in uncompacted three-dimension space, quantum fluctuation energy of one component dilute gas of Bose-Einstein condensate (BEC) confined to two parallel plates investigated at zero-temperature in grand canonical ensemble (GCE) with Neumann boundary condition (BC). The Casimir force considered in comparison to the one with Robin BC, Dirichlet BC and periodic BC.