Stochastic Dynamics of a Vortex Loop. Thermal Equilibrium.pdfVIP

0 Stochastic Dynamics of a Vortex Loop. 0 0 Thermal Equilibrium 2 v o 1 1 2 S.K. Nemirovskii , L.P. Kondaurova , and M.Tsubota N 0 1 Institute for Thermophysics, Lavrentyeva,1, 630090 Novosibirsk, Russia 1 2 Department of Physics, Osaka City University, Osaka, Japan ] h Abstract. We study stochastic behavior of a single vortex loop appeared in imperfect c e Bose gas. Dynamics of Bose-condensate is supposed to obey Gross-Pitaevskii equa- tion with additional noise satisfying fluctuation-dissipation relation. The correspond- m ing Fokker-Planck equation for probability functional has a solution P ({ (r)}) = - t N exp(−H { (r)} /T ), where H { (r)} is a Ginzburg-Landau free energy. Consider- a ing a vortex filaments as a topological defects of the field (r) we derive a Langevin- t s type equation of motion of the line with correspondingly transformed stirring force. . t The respective Fokker-Planck equation for probability functional P ({s(ξ)}) in vor- a tex loop configuration space is shown to have a solution of the form P ({s(ξ)}) = m N exp(−H {s} /T ), where N is a normalizing factor and H {s} is energy of vortex line - configurations. In other words a thermal equilibrium of Bose-condensate results in a d thermal equilibrium of vortex loops appeared in Bose-condensate. Some consequences n o of that fact an