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21 - BEC and the Relaxation Explosion in Magnetically Trapped Atomic Hydrogen
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- By T. W. Hijmans, Van der Waals-Zeeman Laboratoriwn, Universiteit van Amsterdam, Valckenierstraat 65/67 1018 XE Amsterdam The Netherlands, YU. Kagan, Permanent address: Russian Research Center, Kurchatov Institute, Moscow 123182, Russia., G. V. Shlyapnikov, Permanent address: Russian Research Center, Kurchatov Institute, Moscow 123182, Russia., J. T. M. Walraven, Van der Waals-Zeeman Laboratoriwn, Universiteit van Amsterdam, Valckenierstraat 65/67 1018 XE Amsterdam The Netherlands
- Edited by A. Griffin, University of Toronto, D. W. Snoke, University of Pittsburgh, S. Stringari, Università degli Studi di Trento, Italy
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- Book:
- Bose-Einstein Condensation
- Published online:
- 15 December 2009
- Print publication:
- 06 April 1995, pp 472-477
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Summary
Abstract
We predict and analyze non-trivial relaxational behavior of magnetically trapped gases near the Bose condensation temperature Tc. Due to strong compression of the condensate by the inhomogeneous trapping field, particularly at low densities, the relaxation rate shows a strong, almost jump wise, increase below Tc. As a consequence the maximum fraction of condensate particles is limited to a few percent. This phenomenon can be called a “relaxation explosion”. We discuss its implications for the detectability of BEC in atomic hydrogen.
Magnetostatic traps offer the possibility to study gases of Bose particles in the truly dilute limit, and have proved particularly fruitful [1, 2, 3, 4, 5] in the study of atomic hydrogen (H). In these traps, proposed for H by Hess [6], the effective elimination of physical boundaries is accomplished by creating a magnetic field minimum in free space. This minimum forms a potential well for electron spin-up polarized atoms (H↑), called low-field seekers. The occurrence of Bose–Einstein condensation (BEC) in such systems introduces qualitatively different behavior from the case of a homogeneous Bose gas. This is related to the explosive increase of the dipolar relaxation rate associated with the strong compression of the condensate in an external potential.
10 - Kinetics of Bose–Einstein Condensate Formation in an Interacting Bose Gas
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- By YU. Kagan, Department of Superconductivity and Solid State Physics Kurchatov Institute 123182 Moscow Russia
- Edited by A. Griffin, University of Toronto, D. W. Snoke, University of Pittsburgh, S. Stringari, Università degli Studi di Trento, Italy
-
- Book:
- Bose-Einstein Condensation
- Published online:
- 15 December 2009
- Print publication:
- 06 April 1995, pp 202-225
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- Chapter
- Export citation
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Summary
Abstract
The kinetics of the formation of coherent correlation properties associated with Bose condensation is studied in detail. The evolution of a nonequilibrium state with no “condensate-seed” is related to a hierarchy of relaxation times. At the first stage, a particle flux in energy space toward low energies sets in. The evolution in this case is described by a nonlinear Boltzmann equation, with a characteristic time given by interparticle collisions. When the particles which will later form the condensate have a kinetic energy which is less than the potential energy, a quasicondensate starts to form. In this stage, fluctuations of the density (but not of the phase) are suppressed and short-range coherent correlation properties are governed by the equation of motion for a quasiclassical complex field. The next stage is connected with the formation of the long-range order. The time for forming topological order and therefore genuine superfluidity proves to be dependent on the system size. The off-diagonal long-range order, arising after the attenuation of long-wave phase fluctuations, has a size-dependent relaxation time as well.
Introduction
The problem of Bose–Einstein Condensation (BEC) kinetics, being interesting in itself, has acquired a special significance in connection with experimental efforts to observe this condensation in a number of systems with particles with a finite lifetime. Such systems include spin-polarized atomic hydrogen [1], excitons [2] and biexcitons [3] in semiconductors and, more recently, laser-cooled atomic systems [4].