Abstract
Stochastic behavior of a single vortex loop in HeII moving in its self-induced velocity field under the influence of an additional external random force has been discussed. The model under consideration is connected to the so-called low-temperature superfluid turbulence. The character of a stirring force has been determined by random actions of medium which are thermal excitations, of large-scale nonuniformities of flow and of chaotic motion of other loops. In the paper we have studied in details the first case which of course leads to the thermal equilibrium state.
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