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Springer eBooks

Nonzero Temperatures

Gerald Dennis Mahan

Published Jan 1, 2000• 4 citations
Publisher
DOI
10.1007/978-1-4757-5714-9_3

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An extension to nonzero temperatures of the Hugenholtz-Pines procedure for the degenerate Bose gas is provided. It is shown that under certain conditions the elementary excitation spectrum must approach zero for zero momentum, at nonzero, as well as at zero temperatures. The apparent discrepancy of this result with the particular case of a charged boson gas with a uniform positive background is discussed. Finally, a suggestion is made for modifying the Bogoliubov approximation, which is particularly relevant at nonzero temperatures.
The dynamics of Bose-Einstein condensate (BEC) is studied at nonzero temperatures using our variational time-dependent-Hartree-Fock-Bogoliubov formalism. We have shown that this approach is an efficient tool to study the expansion and collective excitations of the condensate, the thermal cloud, and the anomalous correlation function at nonzero temperatures. We have found that the condensate and the anomalous density have the same breathing oscillations. We have investigated, on the other hand, the behavior of a single quantized vortex in a harmonically trapped BEC at nonzero temperatures. Generalized expressions for vortex excitations, vortex core size, and Kelvin modes have been derived. An important and somehow surprising result is that the numerical solution of our equations predicts that the vortex core is partially filled by the thermal atoms at nonzero temperatures. We have shown that the effect of thermal fluctuations is important and it may lead to enhancing the size of the vortex core. The behavior of the singly anomalous vortex has also been studied at nonzero temperatures.