Solitary-wave solutions in binary mixtures of Bose-Einstein condensates under periodic boundary conditions

TL;DR

This paper derives and analyzes solitary-wave solutions in binary Bose-Einstein condensates under periodic boundary conditions, focusing on gray-bright solutions, their energy, dispersion, and excitation spectrum.

Contribution

It introduces a comprehensive analytical framework for solitary waves in binary BECs, including energy minima and excitation spectra under periodic conditions.

Findings

Gray-bright solutions are the energy minima.

Dispersion relations for solitary waves are derived.

Full excitation spectrum is obtained analytically for weak coupling.

Abstract

We derive solitary-wave solutions within the mean-field approximation in quasi-one-dimensional binary mixtures of Bose-Einstein condensates under periodic boundary conditions, for the case of an effective repulsive interatomic interaction. The particular gray-bright solutions that give the global energy minima are determined. Their characteristics and the associated dispersion relation are derived. In the case of weak coupling, we diagonalize the Hamiltonian analytically to obtain the full excitation spectrum of "quantum" solitary-wave solutions.