Stochastic Dynamics of a Vortex Loop. Thermal Equilibrium

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dc.creatorNemirovskii, Sergey K.
dc.creatorKondaurova, Luiza P.
dc.creatorTsubota, Makoto
dc.date2000-11-10
dc.date.accessioned2026-07-07T02:39:18Z
dc.date.available2026-07-07T02:39:18Z
dc.descriptionWe study stochastic behavior of a single vortex loop appeared in imperfect Bose gas. Dynamics of Bose-condensate is supposed to obey Gross-Pitaevskii equation with additional noise satisfying fluctuation-dissipation relation. The corresponding Fokker-Planck equation for probability functional has a solution $\mathcal{P}(\{ψ(\mathbf{r})\})=\mathcal{N}\exp (-Hψ(\mathbf{r)} /T),$ where $Hψ(\mathbf{r})$ is a Ginzburg-Landau free energy. Considering a vortex filaments as a topological defects of the field $ψ(\mathbf{r})$ we derive a Langevin-type equation of motion of the line with correspondingly transformed stirring force. The respective Fokker-Planck equation for probability functional $\mathcal{P}(\{\mathbf{s}(ξ)\})$ in vortex loop configuration space is shown to have a solution of the form $\mathcal{P}(\{\mathbf{s}(ξ)\})=\mathcal{N}\exp (-H{\mathbf{s}} /T),$ where $\mathcal{N}$ is a normalizing factor and $H{\mathbf{s}}$ is energy of vortex line configurations. In other words a thermal equilibrium of Bose-condensate results in a thermal equilibrium of vortex loops appeared in Bose-condensate. Some consequences of that fact and possible violations are discussed.
dc.descriptionlatex, 7 pages, uses subeqnar.sty, sprmindx.sty, cropmark.sty, physprbb.sty, svmult.cls, to be published in "Quantized vortex dynamics and superfluid turbulence", Ed. C. Barenghi (Springer Verlag, Berlin, 2001)
dc.identifierhttps://arxiv.org/abs/cond-mat/0011175
dc.identifierhttp://arxiv.org/abs/cond-mat/0011175
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/17005
dc.subjectStatistical Mechanics
dc.subjectSoft Condensed Matter
dc.titleStochastic Dynamics of a Vortex Loop. Thermal Equilibrium
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