Comparison between microscopic methods for finitetemperature Bose gases
Abstract
We analyze the equilibrium properties of a weakly interacting, trapped quasionedimensional Bose gas at finite temperatures and compare different theoretical approaches. We focus in particular on two stochastic theories: a numberconserving Bogoliubov (NCB) approach and a stochastic GrossPitaevskii equation (SGPE) that have been extensively used in numerical simulations. Equilibrium properties like density profiles, correlation functions, and the condensate statistics are compared to predictions based upon a number of alternative theories. We find that due to thermal phase fluctuations, and the corresponding condensate depletion, the NCB approach loses its validity at relatively low temperatures. This can be attributed to the change in the Bogoliubov spectrum, as the condensate gets thermally depleted, and to large fluctuations beyond perturbation theory. Although the two stochastic theories are built on different thermodynamic ensembles (NCB, canonical; SGPE, grandcanonical), they yield the correct condensate statistics in a large BoseEinstein condensate (BEC) (strong enough particle interactions). For smaller systems, the SGPE results are prone to anomalously large number fluctuations, well known for the grandcanonical, ideal Bose gas. Based on the comparison of the above theories to the modified Popov approach, we propose a simple procedure for approximately extracting the PenroseOnsager condensate from first and secondorder correlation functions that is both computationally convenient and of potential use to experimentalists. This also clarifies the link between condensate and quasicondensate in the Popov theory of lowdimensional systems.
 Publication:

Physical Review A
 Pub Date:
 April 2011
 DOI:
 10.1103/PhysRevA.83.043619
 arXiv:
 arXiv:1012.1512
 Bibcode:
 2011PhRvA..83d3619C
 Keywords:

 03.75.Hh;
 67.85.Bc;
 05.10.Gg;
 Static properties of condensates;
 thermodynamical statistical and structural properties;
 Stochastic analysis methods;
 Condensed Matter  Quantum Gases;
 Quantum Physics
 EPrint:
 Detailed comparison of equilibrium properties, correlation functions and condensate statistics between stochastic GrossPitaevskii, stochasticallysampled numberconserving Bogoliubov and modified Popov theory