Dynamics of Bose-Einstein Condensates
نویسنده
چکیده
We report on some recent results concerning the dynamics of Bose-Einstein condensates, obtained in a series of joint papers [5, 6] with L. Erdős and H.-T. Yau. Starting from many body quantum dynamics, we present a rigorous derivation of a cubic nonlinear Schrödinger equation known as the Gross-Pitaevskii equation for the time evolution of the condensate wave function.
منابع مشابه
Effective Low-dimensional Polynomial Equations for Bose-einstein Condensates
In the first part of this article we briefly overview the fundamentals of Bose-Einstein condensation and survey a series of results concerning the effective equations which describe the dynamics of elongated and oblate Bose-Einstein condensates. In the second part of the paper we show how one can construct effective oneand two-dimensional polynomial Schrödinger equations which describe the long...
متن کاملQuasiperiodic and Chaotic Dynamics in Bose-Einstein Condensates in Periodic Lattices and Superlattices
We employ KAM theory to rigorously investigate the transition between quasiperiodic and chaotic dynamics in cigar-shaped Bose-Einstein condensates (BEC) in periodic lattices and superlattices. Toward this end, we apply ∗Corresponding author
متن کاملChaotic dynamics in spinor Bose–Einstein condensates
Concentrating on experimentally relevant cases we discuss nonlinear dynamics and deterministic chaos in F = 1 and F = 2 spinor Bose–Einstein condensates. A thorough numerical and analytical treatment of the equations of motion of symmetric F = 2 spin dynamics in the single-mode approximation elucidates the complex dynamics and uncovers regions of classical chaos in this important quantum gas sy...
متن کاملA perturbative analysis of modulated amplitude waves in Bose-Einstein condensates.
We apply Lindstedt's method and multiple scale perturbation theory to analyze spatio-temporal structures in nonlinear Schrödinger equations and thereby study the dynamics of quasi-one-dimensional Bose-Einstein condensates with mean-field interactions. We determine the dependence of the amplitude of modulated amplitude waves on their wave number. We also explore the band structure of Bose-Einste...
متن کاملEntanglement of two-mode Bose-Einstein condensates
We investigate the entanglement characteristics of two general bimodal Bose-Einstein condensates—a pair of tunnel-coupled Bose-Einstein condensates and the atom-molecule Bose-Einstein condensate. We argue that the entanglement is only physically meaningful if the system is viewed as a bipartite system, where the subsystems are the two modes. The indistinguishibility of the particles in the cond...
متن کاملQuantized Vortex States and Dynamics in Bose-einstein Condensates
In this thesis, we analytically and numerically study quantized vortex states aswell as their dynamics in rotating Bose-Einstein condensate at extremely low tem-perature.We present an efficient method–gradient flow with discrete normalization tofind the stationary solutions of the Gross-Pitaevskii equation and coupled Gross-Pitaevskii equations. We give a mathematical justif...
متن کامل