arXiv:1207.6591 · Journal of Low Temperature Physics

Relaxation Rates and Collision Integrals for Bose-Einstein Condensates

Erich D. Gust, L. E. Reichl

Published Aug 14, 2012• 15 citations

arXiv HTML PDF

DOI: 10.1007/s10909-012-0675-7

Related papers

Collision of Bose-Einstein Condensates

Fabio Lingua, Luca Lepori, F. Minardi +2 more

Bulletin of the American Physical SocietyMar 7, 20190 citations

Relaxation modes in Bose–Einstein condensates

Erich D. Gust, L. E. Reichl

The rate of relaxation to equilibrium in Bose–Einstein condensates (BECs), and the modes of relaxation, are determined by the collision operators of the kinetic equation. In this work, we give the linearized kinetic equation for uniform dilute BECs and write the solution in terms of relaxation modes. We then present numerical results for both the relaxation rates and the relaxation modes for three atomic BECs, 23 Na, 87 Rb and 133 Cs, that are commonly used in experiments.

Physica ScriptaNov 1, 20124 citations

Collision Integrals in the Kinetic Equations of dilute Bose-Einstein Condensates

Erich D. Gust, L. E. Reichl

arXiv:1202.3418Feb 15, 20125 citations

Kinetics of the Bose–Einstein condensation

Herbert E. Spohn

Physica D Nonlinear PhenomenaFeb 2, 201064 citations

Transport theory for a dilute Bose-Einstein condensate

L. E. Reichl, Erich D. Gust

Physical Review ANov 6, 201315 citations

Properties of cold collisions in relation to Bose-Einstein condensation

AJ Ard-Jan Moerdijk

Jan 1, 19960 citations

arXiv:1207.6591 · Journal of Low Temperature Physics

Relaxation Rates and Collision Integrals for Bose-Einstein Condensates

Erich D. Gust, L. E. Reichl

Published Aug 14, 2012• 15 citations

arXiv HTML PDF

DOI: 10.1007/s10909-012-0675-7

Related papers

Collision of Bose-Einstein Condensates

Fabio Lingua, Luca Lepori, F. Minardi +2 more

Bulletin of the American Physical SocietyMar 7, 20190 citations

Relaxation modes in Bose–Einstein condensates

Erich D. Gust, L. E. Reichl

Physica ScriptaNov 1, 20124 citations

Collision Integrals in the Kinetic Equations of dilute Bose-Einstein Condensates

Erich D. Gust, L. E. Reichl

We derive the mean field kinetic equation for the momentum distribution of Bogoliubov excitations (bogolons) in a spatially uniform Bose-Einstein condensate (BEC), with a focus on the collision integrals. We use the method of Peletminksii and Yatsenko rather than the standard non-equilibrium Green's function formalism. This method produces three collision integrals ${\cal G}^{12}$ , ${\cal G}^{22}$ and ${\cal G}^{31}$ . Only ${\cal G}^{12}$ and ${\cal G}^{22}$ have been considered by previous authors. The third collision integral ${\cal G}^{31}$ contains the effects of processes where one bogolon becomes three and vice versa. These processes are allowed because the total number of bogolons is not conserved. Since ${\cal G}^{31}$ is of the same order in the interaction strength as ${\cal G}^{22}$ , we predict that it will significantly influence the dynamics of the bogolon gas, especially the relaxation of the total number of bogolons to its equilibrium value.We derive the mean field kinetic equation for the momentum distribution of Bogoliubov excitations (bogolons) in a spatially uniform Bose-Einstein condensate (BEC), with a focus on the collision integrals. We use the method of Peletminksii and Yatsenko rather than the standard non-equilibrium Green's function formalism. This method produces three collision integrals ${\cal G}^{12}$, ${\cal G}^{22}$ and ${\cal G}^{31}$. Only ${\cal G}^{12}$ and ${\cal G}^{22}$ have been considered by previous authors. The third collision integral ${\cal G}^{31}$ contains the effects of processes where one bogolon becomes three and vice versa. These processes are allowed because the total number of bogolons is not conserved. Since ${\cal G}^{31}$ is of the same order in the interaction strength as ${\cal G}^{22}$, we predict that it will significantly influence the dynamics of the bogolon gas, especially the relaxation of the total number of bogolons to its equilibrium value.

arXiv:1202.3418Feb 15, 20125 citations

Kinetics of the Bose–Einstein condensation

Herbert E. Spohn

Physica D Nonlinear PhenomenaFeb 2, 201064 citations

Transport theory for a dilute Bose-Einstein condensate

L. E. Reichl, Erich D. Gust

We obtain microscopic expressions for the six hydrodynamic modes of a dilute Bose-Einstein condensate: two transverse (shear) modes and four longitudinal modes corresponding to the first sound (elastic waves) and second sound (temperature waves). Our microscopic expressions include both the speed of the two types of sound and the rate of relaxation of the sound waves. We obtain numerical values for the shear viscosity of a dilute BEC composed of bosons which interact via a contact potential. Our values for the shear viscosity are obtained using the eigenvalues and eigenvectors of the three types of collision operators that govern the relaxation of the condensate.We obtain microscopic expressions for the six hydrodynamic modes of a dilute Bose-Einstein condensate: two transverse (shear) modes and four longitudinal modes corresponding to the first sound (elastic waves) and second sound (temperature waves). Our microscopic expressions include both the speed of the two types of sound and the rate of relaxation of the sound waves. We obtain numerical values for the shear viscosity of a dilute BEC composed of bosons which interact via a contact potential. Our values for the shear viscosity are obtained using the eigenvalues and eigenvectors of the three types of collision operators that govern the relaxation of the condensate.

Physical Review ANov 6, 201315 citations

Properties of cold collisions in relation to Bose-Einstein condensation

AJ Ard-Jan Moerdijk

Jan 1, 19960 citations

{\cal G}^{12}

{\cal G}^{22}

and

{\cal G}^{31}

. Only

{\cal G}^{12}

and

{\cal G}^{22}

have been considered by previous authors. The third collision integral

{\cal G}^{31}

contains the effects of processes where one bogolon becomes three and vice versa. These processes are allowed because the total number of bogolons is not conserved. Since

{\cal G}^{31}

is of the same order in the interaction strength as

{\cal G}^{22}

, we predict that it will significantly influence the dynamics of the bogolon gas, especially the relaxation of the total number of bogolons to its equilibrium value.