Ground states of Bose-Einstein condensates with higher order interaction

TL;DR

This paper investigates the complex ground state structures of Bose-Einstein condensates influenced by higher-order interactions, using a modified Gross-Pitaevskii equation to analyze existence, non-existence, and limiting behaviors in various settings.

Contribution

It introduces a comprehensive analysis of ground states with higher-order interactions, revealing new structures and behaviors not covered in previous models.

Findings

Existence and non-existence results under various parameters

Identification of ground state structures in different regimes

Analysis of limiting behaviors with combined interactions

Abstract

We analyze the ground state of a Bose-Einstein condensate in the presence of higher-order interaction (HOI), modeled by a modified Gross-Pitaevskii equation (MGPE). In fact, due to the appearance of HOI, the ground state structures become very rich and complicated. We establish the existence and non-existence results under different parameter regimes, and obtain their limiting behaviors and/or structures with different combinations of HOI and contact interactions. Both the whole space case and the bounded domain case are considered, where different structures of ground states are identified.