Stochastic motion of the vortex filaments in He II under the influence of random force
Институт теплофизики им. С.С. Кутателадзе СО РАН, пр. Ак. Лаврентьева, 1, г. Новосибирск, 630090, Россия
Novosibirsk State University, 2 Pirogova Str., Novosibirsk 630090 Russia
Received April 10, 2018, published online August 28, 2018
Langevin dynamics is formulated — the stochastic motion of vortex filaments in He II under the action of random force. A functional formalism is described, which is a modification of the method developed earlier by Migdal to work with the stochastic dynamics of classical vortex filaments. In particular, starting from the Langevin-type equation, the Fokker–Planck functional equation for the characteristic functional obtained. On the basis of this equation and under the assumption that the random force correlator satisfies the fluctuation-dissipative theorem, thermodynamic equilibrium in a system of chaotic quantized vortices is investigated. The case of stationary helium is considered, as well as the counterflow case with a constant value of the relative velocity of the normal and superfluid components. Some physical consequences of the results are discussed.
Key words: Langevin dynamics, vortex filaments, He II, Fokker–Planck equation.