We study the kinetics of 2D Bose gas cooling provided Bose particles interact with 3D phonons. At low temperatures, phonon emission is prohibited by energy and momentum conservation. We show that both particle—particle scattering and impurity scattering assist Bose gas cooling. The temporal relaxation of temperature follows the law % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0Jd9sq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbaqcKbay-l% qa-Xgagaafaaaa!38AA! $$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} $$ above the Berezinski-Kosterlitz-Thouless phase transition point and T∼1/t after a Bose-Einstein 2D quasi-condensate develops.We study the kinetics of 2D Bose gas cooling provided Bose particles interact with 3D phonons. At low temperatures, phonon emission is prohibited by energy and momentum conservation. We show that both particle—particle scattering and impurity scattering assist Bose gas cooling. The temporal relaxation of temperature follows the law % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0Jd9sq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbaqcKbay-l% qa-Xgagaafaaaa!38AA! $$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} $$ above the Berezinski-Kosterlitz-Thouless phase transition point and T∼1/t after a Bose-Einstein 2D quasi-condensate develops.

arXiv:cond-mat/0103370Journal of Experimental and Theoretical Physics LettersMay 1, 20012 citations

Vortices in an Imperfect Bose Gas. II. Single-Particle Excitations

Alexander L. Fetter

The single-particle excitations of an imperfect Bose gas with a vortex in the condensate are studied using the Bogoliubov approximation. The problem is reduced to an eigenvalue equation, whose solution yields both the single-particle energies and the eigenfunction expansion of the single-particle Green's function. The spectrum of the eigenvalues contains a discrete portion (bound states) and a continuous portion (scattering states). The lowest eigenvalue corresponding to angular momentum $l=0$ and $l=\ifmmode\pm\else\textpm\fi{}1$ is determined variationally. In the long-wavelength limit, the eigenvalue for $l=\ifmmode\pm\else\textpm\fi{}1$ agrees with the frequency of normal modes calculated by Kelvin and Pitaevskii. The density of noncondensed particles is expressed in terms of the single-particle Green's function and is shown to be finite at the center of the vortex.The single-particle excitations of an imperfect Bose gas with a vortex in the condensate are studied using the Bogoliubov approximation. The problem is reduced to an eigenvalue equation, whose solution yields both the single-particle energies and the eigenfunction expansion of the single-particle Green's function. The spectrum of the eigenvalues contains a discrete portion (bound states) and a continuous portion (scattering states). The lowest eigenvalue corresponding to angular momentum $l=0$ and $l=\ifmmode\pm\else\textpm\fi{}1$ is determined variationally. In the long-wavelength limit, the eigenvalue for $l=\ifmmode\pm\else\textpm\fi{}1$ agrees with the frequency of normal modes calculated by Kelvin and Pitaevskii. The density of noncondensed particles is expressed in terms of the single-particle Green's function and is shown to be finite at the center of the vortex.

Physical ReviewMay 3, 196527 citations

l=0

and $l=\ifmmode\pm\else\textpm\fi{}1$ is determined variationally. In the long-wavelength limit, the eigenvalue for $l=\ifmmode\pm\else\textpm\fi{}1$ agrees with the frequency of normal modes calculated by Kelvin and Pitaevskii. The density of noncondensed particles is expressed in terms of the single-particle Green's function and is shown to be finite at the center of the vortex.