On a linear equation arising in the study of phase separation of Bose-Einstein condensates

TL;DR

This paper analyzes a linear equation related to phase separation in two-component Bose-Einstein condensates, providing optimal estimates for Fourier modes without orthogonality assumptions.

Contribution

It introduces new invertibility estimates for the linearized system in a phase separation model, removing the need for orthogonality conditions.

Findings

Optimal invertibility estimates for Fourier modes

Results applicable to infinite strip boundary conditions

Advances understanding of phase separation in Bose-Einstein condensates

Abstract

We consider the inner limit system describing the phase separation in two-component Bose-Einstein condensates linearized around the one-dimensional solution in an infinite strip with zero and periodic boundary conditions, and obtain optimal invertibility estimates for the Fourier modes without necessarily assuming orthogonality conditions.