Thermodynamic Stability of Superfluid Flow Through a Channel

The limit of metastable existence of parallel superflow through channels is found by examining the second variation of the free energy. The corresponding critical velocity $V_{c1\mathrm{}}$ is calculated with the quasiparticle model and with the Ginzburg-Pitaevskii theory. $V_{c1\mathrm{}}$ reduces to the Landau velocity for $T\to 0$ and tends to zero for $T\to T_{\lambda }$. The behavior of the system above $V_{c1\mathrm{}}$ is discussed. There is qualitative agreement with experiments on hot ions drifting through He II.