Bose-Einstein condensation and Berezinskii-Kosterlitz-Thouless transition in 2D Nonlinear Schrödinger model

Abstract

We analyse the Bose-Einstein condensation process and the Berezinskii-Kosterlitz-Thouless phase transition within the Gross-Pitaevskii model and their interplay with wave turbulence theory. By using numerical experiments we study how the condensate fraction and the first order correlation function behave with respect to the mass, the energy and the size of the system. By relating the free-particle energy to the temperature we are able to estimate the Berezinskii-Kousterlitz-Thouless transition temperature. Below this transition we observe that for a fixed temperature the superfluid fraction appears to be size-independent leading to a power-law dependence of the condensate fraction with respect to the system size.

42 pages, 15 figures

References in corpus (9)

• Observation of scale invariance and universality in two-dimensional Bose gases
• Critical Point of an Interacting Two-Dimensional Atomic Bose Gas
• Vortex proliferation in the Berezinskii-Kosterlitz-Thouless regime on a two-dimensional lattice of Bose-Einstein condensates
• Critical Dynamics of a Two-dimensional Superfluid near a Non-Thermal Fixed Point
• Kosterlitz-Thouless transition of the quasi two-dimensional trapped Bose gas
• Strongly Interacting Two-Dimensional Bose Gases
• Turbulence in the two-dimensional Fourier-truncated Gross-Pitaevskii equation
• Superfluidity of an interacting trapped quasi-2D Bose gas
• A semi-classical field method for the equilibrium Bose gas and application to thermal vortices in two dimensions

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