[GTP] NCAR-GTP Seminar next week- Marc Brachet

[Silvia Gentile]

A simple model of dissipative dynamics in superfluids: the 
(spectrally-truncated) Gross-Pitaevski Equation
Marc Brachet
CNRS, Laboratoire de Physique Statistique
Tuesday, October 11, 2011
Mesa Laboratory, Main Auditorium
Lecture at 11:00am

Systems of conservative partial differential equation can relax to 
thermodynamic equilibrium, provided that a Galerkin truncation of the 
Fourier modes is performed. The relaxation is slow and proceeds through 
a partial thermalization at small scale that induces an effective 
dissipation, while conserving the global invariants. This type of 
behavior is demonstrated in the spectrally-truncated incompressible 
Euler equation (describing a perfect fluid) where effective viscosity 
effects are exhibited.
The (truncated) Gross-Pitaevski Equation can be used generalize this to 
the case of superfluids and Bose-Einstein condensate. The thermodynamic 
equilibrium of the truncated system has a phase transition of second 
order (n = 2, D = 3) which describes the condensation. The dynamics of 
relaxation towards equilibrium provides a simple and rich model of 
dissipative phenomena in superfluids at finite temperature.
We present a slowdown of thermalization which is produced by a 
bottleneck that is caused by dispersive effects and could be observed in 
Bose-Einstein condensate.
We also show that mutual friction and counterflow effects are naturally 
present in the model. The thermal excitations of Kelvin waves are found 
to produce a strong slowing-down effect on the superfluid vortex rings 
that is not included in the standard phenomenological descriptions 
because they are of mean-field type. It is argued that his effect of the 
thermal fluctuations must also be present in physical superfluids.
References (downloadable at: 
http://www.lps.ens.fr/~brachet/Publications_%26_Reprints.html):
- Dispersive bottleneck delaying thermalization of turbulent 
Bose-Einstein condensate, Giorgio Krstulovic and Marc Brachet, Phys. 
Rev. Lett. 106, 115303 (2011)
- Anomalous vortex-ring velocities induced by thermally excited Kelvin 
waves and counterflow effects in superfluids, Giorgio Krstulovic and 
Marc Brachet, Phys. Rev. B 83, 132506 (2011)
- Energy cascade with small-scale thermalization, counterflow 
metastability, and anomalous velocity of vortex rings in 
Fourier-truncated Gross-Pitaevskii equation, Giorgio Krstulovic and Marc 
Brachet, Phys. Rev. E 83, 066311 (2011)


-- 
Silvia Gentile
NCAR IMAGe
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Boulder, CO 80305
303 497 2480
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