Superfluid Bose gas in two dimensions

Abstract

We investigate Bose-Einstein condensation for ultracold bosonic atoms in two-dimensional systems. The functional renormalization group for the average action allows us to follow the effective interactions from molecular scales (microphysics) to the characteristic extension of the probe $l$ (macrophysics). In two dimensions the scale dependence of the dimensionless interaction strength $\lambda$ is logarithmic. Furthermore, for large $l$ the frequency dependence of the inverse propagator becomes quadratic. We find an upper bound for $\lambda$, and for large $\lambda$ substantial deviations from the Bogoliubov results for the condensate depletion, the dispersion relation and the sound velocity. The melting of the condensate above the critical temperature $T_c$ is associated to a phase transition of the Kosterlitz-Thouless type. The critical temperature in units of the density, $T_c/n$, vanishes for $l\to \infty$ logarithmically.

10 pages, 12 figures, reference added

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• Dimensional crossover of nonrelativistic bosons
• Renormalization group study of Bose polarons
• Thermodynamics of the two-dimensional XY model from functional renormalization
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• Hydrodynamic collective modes for cold trapped gases
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• Simulating the Berezinskii-Kosterlitz-Thouless Transition with Complex Langevin
• Vortex Formation in Two-Dimensional Bose Gas
• Functional Renormalization Analytically Continued
• Density of condensate of a dilute Bose gas in improved Hartree-Fock approximation
• The condensed fraction of a homogeneous dilute Bose gas within the improved Hartree-Fock approximation