Many-body physics with ultracold gases

I Bloch, J Dalibard, W Zwerger - Reviews of modern physics, 2008 - APS
This paper reviews recent experimental and theoretical progress concerning many-body
phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling …

One dimensional bosons: From condensed matter systems to ultracold gases

MA Cazalilla, R Citro, T Giamarchi, E Orignac… - Reviews of Modern …, 2011 - APS
The physics of one-dimensional interacting bosonic systems is reviewed. Beginning with
results from exactly solvable models and computational approaches, the concept of bosonic …

Mathematical theory and numerical methods for Bose-Einstein condensation

W Bao, Y Cai - arxiv preprint arxiv:1212.5341, 2012 - arxiv.org
In this paper, we mainly review recent results on mathematical theory and numerical
methods for Bose-Einstein condensation (BEC), based on the Gross-Pitaevskii equation …

Numerical solution of the Gross–Pitaevskii equation for Bose–Einstein condensation

W Bao, D Jaksch, PA Markowich - Journal of Computational Physics, 2003 - Elsevier
We study the numerical solution of the time-dependent Gross–Pitaevskii equation (GPE)
describing a Bose–Einstein condensate (BEC) at zero or very low temperature. In …

Dark solitons in atomic Bose–Einstein condensates: from theory to experiments

DJ Frantzeskakis - Journal of Physics A: Mathematical and …, 2010 - iopscience.iop.org
This review paper presents an overview of the theoretical and experimental progress on the
study of matter-wave dark solitons in atomic Bose–Einstein condensates. Upon introducing …

Mass-radius relation of Newtonian self-gravitating Bose-Einstein condensates<? format?> with short-range interactions. I. Analytical results

PH Chavanis - Physical Review D—Particles, Fields, Gravitation, and …, 2011 - APS
We provide an approximate analytical expression of the mass-radius relation of a Newtonian
self-gravitating Bose-Einstein condensate (BEC) with short-range interactions described by …

[BOOK][B] The mathematics of the Bose gas and its condensation

EH Lieb, R Seiringer, JP Solovej, J Yngvason - 2005 - books.google.com
The mathematical study of the Bose gas goes back to the? rst quarter of the twentieth
century, with the invention of quantum mechanics. The name refers to the Indian physicist …

Computing the ground state solution of Bose--Einstein condensates by a normalized gradient flow

W Bao, Q Du - SIAM Journal on Scientific Computing, 2004 - SIAM
In this paper, we present a continuous normalized gradient flow (CNGF) and prove its
energy diminishing property, which provides a mathematical justification of the imaginary …

Proof of Bose-Einstein condensation for dilute trapped gases

EH Lieb, R Seiringer - Physical review letters, 2002 - APS
The ground state of bosonic atoms in a trap has been shown experimentally to display Bose-
Einstein condensation (BEC). We prove this fact theoretically for bosons with two-body …

[BOOK][B] The defocusing nonlinear Schrödinger equation: from dark solitons to vortices and vortex rings

The phenomenon of Bose–Einstein condensation is a phase transition originally predicted
by Bose and Einstein in 1924. In particular, it was shown that below a critical temperature T …