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arXiv:cond-mat/9905062 · Physical Review A

Dissipative dynamics of a kink state in a Bose-condensed gas

Peter O. Fedichev, A. E. Muryshev, Gora V. Shlyapnikov

Published Oct 1, 1999• 138 citations
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Abstract

We develop a theory of dissipative dynamics of a kink state in a finite-temperature Bose-condensed gas. We find that, due to the interaction with the thermal cloud, the kink state accelerates towards the velocity of sound and continuously transforms to the ground-state condensate. We calculate the lifetime of a kink state in a trapped gas and discuss possible experimental implications.

DOI
10.1103/physreva.60.3220

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We develop a theory of dissipative dynamics of a kink state in a finite-temperature Bose-condensed gas. We find that, due to the interaction with the thermal cloud, the kink state accelerates towards the velocity of sound and continuously transforms to the ground-state condensate. We calculate the lifetime of a kink state in a trapped gas and discuss possible experimental implications.
We discuss dissipative dynamics of a vortex state in a trapped Bose-condensed gas at finite temperature and draw a scenario of decay of this state in a static trap. The interaction of the vortex with the thermal cloud transfers energy from the vortex to the cloud and induces the motion of the vortex core to the border of the condensate. Once the vortex reaches the border, it immediately decays through the creation of excitations. We calculate the characteristic lifetime of a vortex state and address the question of how the dissipative dynamics of vortices can be studied experimentally.
We discuss the dissipative dynamics of vortex arrays in trapped Bose-condensed gases and discuss the lifetime of the vortices as a function of trap anisotropy and temperature. In particular, we distinguish two regimes of dissipative dynamics, depending on the relative strength of the mutual friction between the vortices and the thermal component, and the friction of the thermal particles on the trap anisotropy. We study the effects of heating of the thermal cloud by the escaping vortices on the dynamics of the system.
We develop a theory of equilibrium properties and dissipative dynamics of large vortex arrays in trapped Bose-condensed gases. We prove that, in spite of the spatial inhomogeneity of the condensate density profile in trapped gases, the equilibrium configuration corresponds to a vortex array of uniform density. We show that in a static trap the interaction of the vortex array with thermal excitations leads to a nonexponential decay of the vortex structure, and the characteristic lifetime depends on the initial density of vortices. Drawing an analogy with physics of pulsars, we propose an experiment that employs the decay induced heating of the thermal cloud as a tool for a nondestructive study of the vortex dynamics.
The dissipative dynamics of a vortex in a finite temperature trapped Bose-Einstein condensate are shown to be governed by a {\em diffusive instability}. In the weakly interacting regime we find a cross-over from instability to metastability of the vortex, determined only by the relative rotation rate of the vortex and thermal cloud. Even in the thermodynamically stable regime there is a finite lifetime arising from diffusive instability. We find the mean exit time for the vortex from the condensate, and show that near the critical frequency for thermodynamic stability the lifetime has a universal form which is independent of the condensate size and the vortex precession frequency. In the thermodynamically stable regime the steady-state two-time position correlation predicts `thermal bunching', giving an increased probability of positional coincidence for short times.
We study the low-energy collective oscillations of a dilute Bose gas at finite temperature in the collisionless regime. By using a time-dependent mean-field scheme we derive for the dynamics of the condensate and noncondensate components a set of coupled equations, which we solve perturbatively to second order in the interaction coupling constant. This approach is equivalent to the finite-temperature extension of the Beliaev approximation and includes corrections to the Gross-Pitaevskii theory due to both quantum and thermal fluctuations. For a homogeneous system we explicitly calculate the temperature dependence of the velocity of propagation and damping rate of zero sound. In the case of harmonically trapped systems in the thermodynamic limit, we calculate, as a function of temperature, the frequency shift of the low-energy compressional and surface modes.