We investigate the behavior of a dilute quasi two-dimensional, harmonically confined, weakly interacting Bose gas within the finite-temperature Thomas-Fermi approximation. We find that the thermodynamic properties of the system are markedly different for repulsive and attractive interactions. Specifically, in contrast to the repulsive case, there appears to be a phase transition when the atoms interact with an attractive pseudo-potential, in the sense that there is no self-consistent solution for the normal ground state below a certain temperature $T^{\star}$ . These numerical findings are supported by analytical investigations of the thermodynamics of the system in the complex fugacity plane, and within the random-phase approximation. We also show that the temperature $T^{\star}$ can be interpreted as the limiting temperature below which the system cannot be described as a collection of noninteracting {\em haldons}.We investigate the behavior of a dilute quasi two-dimensional, harmonically confined, weakly interacting Bose gas within the finite-temperature Thomas-Fermi approximation. We find that the thermodynamic properties of the system are markedly different for repulsive and attractive interactions. Specifically, in contrast to the repulsive case, there appears to be a phase transition when the atoms interact with an attractive pseudo-potential, in the sense that there is no self-consistent solution for the normal ground state below a certain temperature $T^{\star}$. These numerical findings are supported by analytical investigations of the thermodynamics of the system in the complex fugacity plane, and within the random-phase approximation. We also show that the temperature $T^{\star}$ can be interpreted as the limiting temperature below which the system cannot be described as a collection of noninteracting {\em haldons}.

arXiv:cond-mat/0106410Journal of Physics B Atomic Molecular and Optical PhysicsJun 20, 200111 citations

The Dilute Bose Gas in 2D

Birkhäuser-Verlag eBooksDec 22, 20050 citations

Thermally induced rotons in two-dimensional dilute Bose gases

Flavio S. Nogueira, Hagen M. Kleinert

We show that rotonlike excitations are thermally induced in a two-dimensional dilute Bose gas as a consequence of the strong phase fluctuations in two dimensions. At low momentum, the rotonlike excitations lead for small enough temperatures to an anomalous phonon spectrum with a temperature-dependent exponent reminiscent of the Kosterlitz-Thouless transition. Despite the anomalous form of the energy spectrum, it is shown that the corresponding effective theory of vortices describes the usual Kosterlitz-Thouless transition. The possible existence of an anomalous normal state in a small temperature interval is also discussed.We show that rotonlike excitations are thermally induced in a two-dimensional dilute Bose gas as a consequence of the strong phase fluctuations in two dimensions. At low momentum, the rotonlike excitations lead for small enough temperatures to an anomalous phonon spectrum with a temperature-dependent exponent reminiscent of the Kosterlitz-Thouless transition. Despite the anomalous form of the energy spectrum, it is shown that the corresponding effective theory of vortices describes the usual Kosterlitz-Thouless transition. The possible existence of an anomalous normal state in a small temperature interval is also discussed.

arXiv:cond-mat/0503523Physical Review BMar 28, 20069 citations

Thermodynamically activated vortex-dipole formation in a two-dimensional Bose-Einstein condensate

Dániel Schumayer, David A. W. Hutchinson

Three distinct types of behavior have recently been identified in the two-dimensional trapped bosonic gas, namely, a phase-coherent Bose-Einstein condensate (BEC), a Berezinskii-Kosterlitz-Thouless-type (BKT) superfluid, and normal gas phases in order of increasing temperature. In the BKT phase the system favors the formation of vortex-antivortex pairs, since the free energy is lowered by this topological defect. We provide a simple estimate of the free energy of a dilute Bose gas with and without such vortex dipole excitations and show how this varies with particle number and temperature. In this way we can estimate the temperature for crossover from the coherent BEC to the (only) locally ordered BKT-like phase by identifying when vortex-dipole excitations proliferate. Our results are in qualitative agreement with recent, numerically intensive, classical field simulations.Three distinct types of behavior have recently been identified in the two-dimensional trapped bosonic gas, namely, a phase-coherent Bose-Einstein condensate (BEC), a Berezinskii-Kosterlitz-Thouless-type (BKT) superfluid, and normal gas phases in order of increasing temperature. In the BKT phase the system favors the formation of vortex-antivortex pairs, since the free energy is lowered by this topological defect. We provide a simple estimate of the free energy of a dilute Bose gas with and without such vortex dipole excitations and show how this varies with particle number and temperature. In this way we can estimate the temperature for crossover from the coherent BEC to the (only) locally ordered BKT-like phase by identifying when vortex-dipole excitations proliferate. Our results are in qualitative agreement with recent, numerically intensive, classical field simulations.

arXiv:cond-mat/0601500Physical Review AJan 8, 20077 citations

T^{\star}

. These numerical findings are supported by analytical investigations of the thermodynamics of the system in the complex fugacity plane, and within the random-phase approximation. We also show that the temperature

T^{\star}

can be interpreted as the limiting temperature below which the system cannot be described as a collection of noninteracting {\em haldons}.