# Dynamics of Bose-Einstein condensate with account of pair correlations

## TL;DR

This paper derives dynamic equations for a Bose-Einstein condensate including pair correlations, analyzes the spectrum of small oscillations, and reveals two distinct branches: sound waves and gapped excitations.

## Contribution

It introduces a new set of dynamic equations for Bose-Einstein condensates that incorporate pair correlations, expanding understanding of their excitation spectra.

## Key findings

- Spectrum has two branches: sound wave and gapped branch
- Identifies the energy gap in the excitation spectrum
- Provides a theoretical framework for condensate dynamics

## Abstract

The system of dynamic equations for Bose-Einstein condensate at zero temperature with account of pair correlations is obtained. The spectrum of small oscillations of the condensate in a spatially homogeneous state is explored. It is shown that this spectrum has two branches: the sound wave branch and branch with an energy gap.