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We use a Langevin equation to examine the dynamics and
fluctuations of a flux line (FL) in the presence of an alternating
longitudinal current $J_{\|}( omega )$. The magnus and dissipative
forces are equated to those resulting from line tension,
confinement in a harmonic cage by neighboring FLs, parallel
current, and noise. The resulting mean-square FL fluctuations are
calculated exactly, and a Lindemann criterion is then used to
obtain a nonequilibrium "phase diagram" as a function of the
magnitude and frequency of $J_{\|}( omega )$. For zero frequency,
the melting temperature of the mixed phase (a lattice, or the
putative "Bose" or "Bragg glass") vanishes at a limiting current.
However, for any finite frequency, there is a nonzero melting
temperature.
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