From Feshbach-resonance managed Bose–Einstein condensates to anisotropic universes: Applications of the Ermakov–Pinney equation with time-dependent nonlinearity

2007/01/30 by G. Herring, P. G. Kevrekidis, Floyd L. Williams +3 · 3 citations
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum Electrodynamics and Casimir Effect #Quantum, superfluid, helium dynamics #cond-mat.other

paper · pdf · doi:10.1016/j.physleta.2007.01.087

published as Phys.Lett.A367:140-148,2007 · 9 pages, 4 figures

arxiv created 2007/01/30 · openalex publication_date 2007/03/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work we revisit the topic of two-dimensional Bose-Einstein condensates under the influence of time-dependent magnetic confinement and time-dependent scattering length. A moment approach reduces the examination of moments of the wavefunction (in particular, of its width) to an Ermakov-Pinney (EP) ordinary differential equation (ODE). We use the well-known structure of the solutions of this nonlinear ODE to ``engineer'' trapping and interatomic interaction conditions that lead to condensates dispersing, breathing or even collapsing. The advantage of the approach is that it is fully tractable analytically, in excellent agreement with our numerical observations. As an aside, we also discuss how similar time-dependent EP equations may arise in the description of anisotropic scalar field cosmologies.

Citations

• Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor

Cited by

• Modulation of breathers in cigar-shaped Bose–Einstein condensates
• Integrable equations with Ermakov–Pinney nonlinearities and Chiellini damping
• A dynamic correspondence between Bose–Einstein condensates and Friedmann–Lemaître–Robertson–Walker and Bianchi I cosmology with a cosmological constant