At any finite temperature, the correlation function $〈{\ensuremath{\psi}}^{\ifmmode\dagger\else\textdagger\fi{}}(\mathcal{r})\ensuremath{\psi}(0)〉$ of a two-dimensional Bose system is known to approach zero as the separation $\mathcal{r}$ approaches infinity. This paper is devoted to supporting the point of view that superfluid phenomena may still persist in such a system. To describe the low-temperature behavior of a condensed two-dimensional Bose system, we use a coherent-state representation of the low-lying phonon excitations. The expectation of the particle field operator $〈\ensuremath{\psi}(\mathcal{r})〉$ in a coherent phonon state of the system is shown to be a well-defined function. This function has only small fluctuations in its magnitude and, therefore, it is possible to make the usual arguments for superfluid behavior based on the existence of the condensate wave function. The large phase fluctuations of the function, when the coherentphonon states are collected into the thermal ensemble, give rise to the spatial decay of the correlation function or reduced density matrix $〈{\ensuremath{\psi}}^{+}(\mathcal{r})\ensuremath{\psi}(0)〉$. It is concluded that two-dimensional Bose systems are superfluid at sufficiently low temperatures, even in the inifinite-volume limit. An analogous argument would indicate the possibility of superconductivity in a two-dimensional Fermi system.At any finite temperature, the correlation function $〈{\ensuremath{\psi}}^{\ifmmode\dagger\else\textdagger\fi{}}(\mathcal{r})\ensuremath{\psi}(0)〉$ of a two-dimensional Bose system is known to approach zero as the separation $\mathcal{r}$ approaches infinity. This paper is devoted to supporting the point of view that superfluid phenomena may still persist in such a system. To describe the low-temperature behavior of a condensed two-dimensional Bose system, we use a coherent-state representation of the low-lying phonon excitations. The expectation of the particle field operator $〈\ensuremath{\psi}(\mathcal{r})〉$ in a coherent phonon state of the system is shown to be a well-defined function. This function has only small fluctuations in its magnitude and, therefore, it is possible to make the usual arguments for superfluid behavior based on the existence of the condensate wave function. The large phase fluctuations of the function, when the coherentphonon states are collected into the thermal ensemble, give rise to the spatial decay of the correlation function or reduced density matrix $〈{\ensuremath{\psi}}^{+}(\mathcal{r})\ensuremath{\psi}(0)〉$. It is concluded that two-dimensional Bose systems are superfluid at sufficiently low temperatures, even in the inifinite-volume limit. An analogous argument would indicate the possibility of superconductivity in a two-dimensional Fermi system.

Physical ReviewAug 5, 196810 citations

Low-temperature behaviour of a high-density Bose model

L. S. Campana, Alvaro Caramico D’Auria, L. De Cesare +1 more

Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fieldsJul 1, 19793 citations

The viscosity of dilute Bose–Einstein condensates

Erich D. Gust, L. E. Reichl

The viscosity of a dilute Bose–Einstein condensate is obtained for a range of temperatures and densities. The kinetic equation used to derive the viscosity is based on Bogoliubov mean field theory and is a Boltzmann-like equation for the Bogoliubov excitations in the condensate. The viscosity can be assigned a numerical value for any gas for which the mass and scattering length are known. The viscosity decreases slowly as the temperature is decreased, but at low temperature (around 0.01 T c ), begins to show a much more rapid decrease with decreasing temperature. This interesting behavior of the viscosity is related to the behavior of the eigenvalues of the bogolon collision operator at these low temperatures.The viscosity of a dilute Bose–Einstein condensate is obtained for a range of temperatures and densities. The kinetic equation used to derive the viscosity is based on Bogoliubov mean field theory and is a Boltzmann-like equation for the Bogoliubov excitations in the condensate. The viscosity can be assigned a numerical value for any gas for which the mass and scattering length are known. The viscosity decreases slowly as the temperature is decreased, but at low temperature (around 0.01 T c ), begins to show a much more rapid decrease with decreasing temperature. This interesting behavior of the viscosity is related to the behavior of the eigenvalues of the bogolon collision operator at these low temperatures.

Physica ScriptaOct 1, 20153 citations

Low-Temperature Behavior of Bose-Einstein Systems in Restricted Geometries.

H. R. Pajkowski

Feb 1, 19790 citations

\mathcal{r}

approaches infinity. This paper is devoted to supporting the point of view that superfluid phenomena may still persist in such a system. To describe the low-temperature behavior of a condensed two-dimensional Bose system, we use a coherent-state representation of the low-lying phonon excitations. The expectation of the particle field operator $〈\ensuremath{\psi}(\mathcal{r})〉$ in a coherent phonon state of the system is shown to be a well-defined function. This function has only small fluctuations in its magnitude and, therefore, it is possible to make the usual arguments for superfluid behavior based on the existence of the condensate wave function. The large phase fluctuations of the function, when the coherentphonon states are collected into the thermal ensemble, give rise to the spatial decay of the correlation function or reduced density matrix $〈{\ensuremath{\psi}}^{+}(\mathcal{r})\ensuremath{\psi}(0)〉$. It is concluded that two-dimensional Bose systems are superfluid at sufficiently low temperatures, even in the inifinite-volume limit. An analogous argument would indicate the possibility of superconductivity in a two-dimensional Fermi system.