Physics – Condensed Matter – Soft Condensed Matter
Scientific paper
2003-11-14
Physics
Condensed Matter
Soft Condensed Matter
10 pages, RevTeX, submitted to JLTP
Scientific paper
We study the stochastic behavior of a set of chaotic vortex loops appeared in imperfect Bose gas. Dynamics of Bose-gas is supposed to obey Gross-Pitaevskii equation with additional noise satisfying fluctuation-dissipation relation. The corresponding Fokker-Planck equation for probability functional has solution ${\cal P}(\{{\psi}({\bf r})\})={\cal N}\exp (-H\{{\psi}({\bf r)}\} /T),$ where $H\{{\psi}({\bf r})\} $ is the Ginzburg-Landau free energy. Considering vortex filaments as topological defects of field ${\psi}({\bf r})$ we derive a Langevin-type equation of motion of the line with the correspondingly transformed stirring force. The respective Fokker-Planck equation for probability functional ${\cal P}(\{{\bf s}(\xi)\})$ in vortex loop configuration space is shown to have a solution in the form of ${\cal P}(\{{\bf s}(\xi)\})={\cal N}\exp (-H\{{\bf s}\} /T),$ where ${\cal N}$ is the normalizing factor and $H\{{\bf s}\} $ is energy of vortex line configurations. Analyzing this result we discuss possible reasons for destruction of the thermodynamic equilibrium and follow the mechanisms of transition to the turbulent state
Nemirovskii Sergey K.
Tsubota Makoto
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