Landau criterion of superfluidity

F.W. Cummings, James R. Johnston

Walter F Wreszinski

The two-fluid and Landau criteria for superfluidity are compared for trapped Bose gases. While the two-fluid criterion predicts translational superfluidity, it is suggested, on the basis of the homogeneous Gross–Pitaevski limit, that a necessary part of Landau's criterion, adequate for non-translationally invariant systems, does not hold for trapped Bose gases in the GP limit. As a consequence, if the compressibility is detected to be very large (infinite by experimental standards), the two-fluid criterion is seen to be the relevant one in case the system is a translational superfluid, while the Landau criterion is the relevant one if translational superfluidity is absent.

Nobuyuki Fukuda, Kenji Fukushima, Tadasi Inagaki

Landau's criterion for superfluidity is re-examined by taking into account the interaction between the system and the wall explicitly. Provided that the excitation of the system at rest is described in terms of the quasiparticle with the spectrum ε(k), the system which is now moving below the critical velocity, min {ε(k)/k}, can never lose its velocity by creating quasiparticles. In order to obtain this result, we apply the Galilei transformation which brings the system to rest. Then the wall is moving and its moving field can transfer to the system not only the momentum but also the energy. The new form of the conservation law of energy leads to Landau's criterion.

Nikolay N. Bogolubov

Yusuke S. Kato, Shohei Watabe

We propose a stability criterion of superfluids in condensed Bose-Einstein systems, which incorporates the spectral function or the autocorrelation function of the local density. Within the Gross-Pitaevskii-Bogoliubov theory, we demonstrate the validity of our criterion for the soliton-emission instability, with use of explicit forms of zero modes of the Bogoliubov equation and a dynamical scaling near the saddle-node bifurcation. We also show that the criterion is applicable to the Landau phonon instability and the Landau roton instability within the single-mode approximation.

Yongle Yu