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arXiv:0908.1002

Temperature dependence of critical velocities and long time decay of supercurrents

Y. C. Yu

Published Aug 7, 2009• 0 citations
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Abstract

We show that a microscopic theory of superfluidity, based on the properties of the many-body spectrum of a superfluid, can explain naturally the temperature dependence of critical velocities and the long time decay of supercurrents.
DOI
10.48550/arxiv.0908.1002

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The theory of superfluidity of bosons in narrow channels forming a network in space is constructed. It is shown that the temperature Tc of superfluidity transition, below which the system has a long-range order, is equal to h2n/Ml in order of magnitude (here, n is the one-dimensional density of bosons of mass M and l the characteristic length of a link in the network). A generalization of the Ginzburg–Gross–Pitaevskii (GGP) equation permitting an analysis of the decay of current state is proposed. The relaxation time τ for the current state at T > Tc is estimated. It is shown that for a flow velocity υ→0, the relaxation time τ ∝ exp (ħnc/T), where c is the velocity of sound. For ħnc ≫ T ≫ Tc, the supercurrent decay time is astronomically large and quasisuperfluidity cannot be distinguished from true superfluidity in spite of the absence of a long-range order.
We examine the superfluid properties of a one-dimensional (1D) Bose gas in a ring trap based on the model of Lieb and Liniger. While the 1D Bose gas has nonclassical rotational inertia and exhibits quantization of velocities, the metastability of currents depends sensitively on the strength of interactions in the gas: the stronger the interactions, the faster the current decays. It is shown that the Landau critical velocity is zero in the thermodynamic limit due to the first supercurrent state, which has zero energy and finite probability of excitation. We calculate the energy dissipation rate of ring currents in the presence of weak defects, which should be observable on experimental time scales.