A kinetic approach to Bose-Einstein condensates (BECs) is proposed based on the Wigner-Moyal equation (WME). In the semiclassical limit, the WME reduces to the particle-number conservation equation. Two examples of applications are (i) a self-phase modulation of a BE condensate beam, where we show that part of the beam is decelerated and eventually stops as a result of the gradient of the effective self-potential, and (ii) the derivation of a kinetic dispersion relation for sound waves in BECs, including collisionless Landau damping.A kinetic approach to Bose-Einstein condensates (BECs) is proposed based on the Wigner-Moyal equation (WME). In the semiclassical limit, the WME reduces to the particle-number conservation equation. Two examples of applications are (i) a self-phase modulation of a BE condensate beam, where we show that part of the beam is decelerated and eventually stops as a result of the gradient of the effective self-potential, and (ii) the derivation of a kinetic dispersion relation for sound waves in BECs, including collisionless Landau damping.

arXiv:nlin/0502059Journal of Experimental and Theoretical PhysicsNov 1, 20056 citations

Bogoliubov Excitations of Inhomogeneous Bose-Einstein Condensates

Christopher Gaul

Jan 1, 20103 citations

Two-stream instability in quasi-one-dimensional Bose-Einstein condensates

Hugo Terças, José Tito Mendonça, Gordon R. M. Robb

We apply a kinetic model to predict the existence of an instability mechanism in elongated Bose-Einstein condensates. Our kinetic description, based on the Wigner formalism, is employed to highlight the existence of unstable Bogoliubov waves that may be excited in the counterpropagation configuration. We identify a dimensionless parameter, the Mach number at $T=0$ , that tunes different regimes of stability. We also estimate the magnitude of the main parameters at which two-stream instability is expected to be observed under typical experimental conditions.We apply a kinetic model to predict the existence of an instability mechanism in elongated Bose-Einstein condensates. Our kinetic description, based on the Wigner formalism, is employed to highlight the existence of unstable Bogoliubov waves that may be excited in the counterpropagation configuration. We identify a dimensionless parameter, the Mach number at $T=0$, that tunes different regimes of stability. We also estimate the magnitude of the main parameters at which two-stream instability is expected to be observed under typical experimental conditions.

arXiv:0911.4906Physical Review AJun 2, 20097 citations

Energetic cooling below the BEC transition: a quantum kinetic description within the Bogoliubov approximation

Arturo Camacho-Guardian, M Mendoza-López, Vı́ctor Romero-Rochı́n +1 more

The dynamics of Bose-Einstein condensation in a three-dimensional harmonic trap is studied explicitly including the Bogoliubov approximation for temperatures below the critical one. To model the evolution towards equilibrium at each cooling step, we derive quantum kinetic equations that describe the dynamics of the gas for temperatures above and below the transition temperature. These equations, valid in the Born and Markov approximations, consider the essential role of the chemical potential as the main parameter that signals the transition. The kinetic equation that describes the growth of the condensate below the transition temperature is derived within the Bogoliubov approximation. To illustrate our results we propose an energetic cooling protocol and simulate the whole sequence of the formation of a condensate.The dynamics of Bose-Einstein condensation in a three-dimensional harmonic trap is studied explicitly including the Bogoliubov approximation for temperatures below the critical one. To model the evolution towards equilibrium at each cooling step, we derive quantum kinetic equations that describe the dynamics of the gas for temperatures above and below the transition temperature. These equations, valid in the Born and Markov approximations, consider the essential role of the chemical potential as the main parameter that signals the transition. The kinetic equation that describes the growth of the condensate below the transition temperature is derived within the Bogoliubov approximation. To illustrate our results we propose an energetic cooling protocol and simulate the whole sequence of the formation of a condensate.

arXiv:1406.5932Journal of Physics B Atomic Molecular and Optical PhysicsOct 23, 20140 citations

Bogoliubov excitation spectrum of Bose gases

Phan Thành Nam

EMS Press eBooksJul 14, 20230 citations

T=0

, that tunes different regimes of stability. We also estimate the magnitude of the main parameters at which two-stream instability is expected to be observed under typical experimental conditions.