Quasi-condensation in low-dimensional Bose gases

The subject of the present thesis is the one-dimensional Bose gas. Since long-rang order is destroyed by infra-red fluctuations in one dimension, only the formation of a quasi-condensate is possible, which exhibits suppressed density fluctuations, but whose phase fluctuates strongly. It is shown that modified mean-field theories based on a symmetry-breaking approach can even characterise phase coherence properties of such a quasi-condensate properly. A correct description of the transition from the degenerate ideal Bose gas to the quasi-condensate, which is a smooth cross-over rather than a phase transition, is not possible though. Basic conditions for the applicability of the theories are not fulfilled in this regime, such that the existence of a critical point is predicted. The theories are compared on the basis of their excitation sprectum, equation of state, density fluctuations and related correlation functions. High-temperature expansions of the corresponding integrals are derived analytically for the numerical evaluation of the self-consistent integral equations. Apart from that, the Stochastic Gross-Pitaevskii equation (SGPE), a non-linear Langevin equation, is analysed numerically by means of Monte-Carlo simulations and the results are compared to those of the mean-field theories. In this context, a lot of attention is payed to the appropriate choice of the parameters. The simulations prove that the SGPE is capable of describing the cross-over properly, but highlight the limitations of the widely used local density approximation as well.

Level thesis:degree_level

master

Grantor dc:publisher

Universität Potsdam

Year

2015

Author dc:creator

• Sauer, Tim-Oliver

Contributors dc:contributor

• Henkel, Carsten
• Proukakis, Nikolaos

• Bose-Einstein Kondensation
• Quasi-Kondensat
• kritische Fluktuationen
• Mean-field Theorie
• Stochastische Gross-Pitaevskii Gleichung
• Bogoliubov-Theorie
• lokale Dichte-Näherung
• Bosegas
• Phasenübergang
• Bose-Einstein condensation
• quasi-condensate
• critical fluctuations
• mean-field theory
• stochastic Gross-Pitaevskii equation
• Bogoliubov theory
• local density approximation
• bose gas
• phase transition

Statement dc:rights

• CC-BY-NC-SA - Namensnennung, nicht kommerziell, Weitergabe zu gleichen Bedingungen 4.0 International

Repository record source_url

https://publishup.uni-potsdam.de/frontdoor/index/index/docId/8724

OAI identifier oai:identifier

oai:kobv.de-opus4-uni-potsdam:8724