Existence of minimizers in generalized Gross-Pitaevskii theory with the Lee-Huang-Yang correction

2019/04/24 by Triay, Arnaud
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Gases (cond-mat.quant-gas)

paper · doi:10.48550/arxiv.1904.10672

Abstract

We study the dipolar Gross-Piteavskii functional with the Lee-Huang-Yang (LHY) correction term without trapping potential and in the regime where the dipole-dipole interaction dominates the repulsive short-range interaction. We show that, above a critical mass, the functional admits minimizers and we prove their regularity and exponential decay. We also estimate the critical mass in terms of the parameters of the system.

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