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Vortex Dynamics: Quantum versus Classical Regimes

For many years the classical Hall-Vinen-Iordanski (HVI) equation has been used to analyse vortex dynamics in superfluids. Here we discuss the extension of the theory of vortex dynamics to the quantum regime, in which the characteristic vortex frequency is higher than the temperature. At the same time we justify, in the low-frequency classical regime, the use of the HVI equation, provided an inertial mass term and a noise fluctuation term are added to it. The crossover to the quantum regime is discussed, and an intuitive picture is given of the vortex dynamics, which in general is described by 2 equations (one for the vortex coordinate, and one for its quantum fluctuations); we also discuss the simple equation of motion found in the extreme quantum regime.