Interface layer of a two-component Bose–Einstein condensate

DOI10.1142/S0219199716500528zbMATH Open1372.34090arXiv1509.08328MaRDI QIDQ5354377

Christos Sourdis, Amandine Aftalion

Publication date: 1 September 2017

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Abstract: This paper deals with the study of the behaviour of the wave functions of a two-component Bose-Einstein condensate near the interface, in the case of strong segregation. This yields a system of two coupled ODE's for which we want to have estimates on the asymptotic behaviour, as the strength of the coupling tends to infinity. As in phase separation models, the leading order profile is a hyperbolic tangent. We construct an approximate solution and use the properties of the associated linearized operator to perturb it into a genuine solution for which we have an asymptotic expansion. We prove that the constructed heteroclinic solutions are linearly nondegenerate, in the natural sense, and that there is a spectral gap, independent of the large interaction parameter, between the zero eigenvalue (due to translations) at the bottom of the spectrum and the rest of the spectrum. Moreover, we prove a uniqueness result which implies that, in fact, the constructed heteroclinic is the unique minimizer (modulo translations) of the associated energy, for which we provide an expansion.

Full work available at URL: https://arxiv.org/abs/1509.08328

zbMATH Keywords

phase separationmatched asymptoticsBose-Einstein condensateheteroclinic solution

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Quantum equilibrium statistical mechanics (general) (82B10) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Parameter dependent boundary value problems for ordinary differential equations (34B08) Asymptotic expansions of solutions to ordinary differential equations (34E05) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Boundary value problems on infinite intervals for ordinary differential equations (34B40)

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