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Progress of Theoretical Physics

On the Landau Theory of Superfluidity

Nobuyuki Fukuda, Kenji Fukushima, Tadasi Inagaki

Published Feb 1, 1963• 0 citations
Publisher

Abstract

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.

DOI
10.1143/ptp.29.206

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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.
We study the drag force on objects moving in a Fermi superfluid at velocities on the order of the Landau velocity vL{v}_{L}vL​. The expectation has been that vL{v}_{L}vL​ is the critical velocity beyond which the drag force starts to increase toward its normal-state value. This expectation is challenged by a recent experiment measuring the heat generated by a uniformly moving wire immersed in superfluid 3He^{3}\mathrm{He}3He. We introduce the basis for the calculation of the drag force on a macroscopic object using the Fermi-liquid theory of superfluidity. As a technical tool in the calculations, we propose a boundary condition that describes diffuse reflection of quasiparticles from a surface on a scale that is larger than the superfluid coherence length. We calculate the drag force on steadily moving objects of different sizes. For an object that is small compared to the coherence length, we find a drag force that is in accordance with the expectation. For a macroscopic object, we need to take into account the spatially varying flow field around the object. At low velocities, this arises from ideal flow of the superfluid. At higher velocities, the flow field is modified by excitations that are created when the flow velocity locally exceeds vL{v}_{L}vL​. The flow field causes Andreev reflection of quasiparticles and thus leads to change in the drag force. We calculate multiple limiting cases for a cylinder-shaped object. In the absence of quasiparticle-quasiparticle collisions, we find that the critical velocity is larger than vL{v}_{L}vL​ and the drag force (per cross-sectional area) at 2vL2{v}_{L}2vL​ is reduced by an order of magnitude compared to the case of a small object. In a collision-dominated limit, the flow shows signs of instability at a velocity below vL{v}_{L}vL​.
In this thesis we investigate the instabilities of superfluids at finite superflow by means of a hydrodynamical approach. We find that at a finite value of the background superfluid velocity a hydrodynamic collective mode crosses to the upper half complex frequency plane, thereby signalling a dynamical instability. At the same time, however, this instability is also thermodynamic, as its onset is controlled by one of the second derivatives of the free energy changing sign. We carry out our analysis in two main setups: the "probe limit", where the fluctuations of the temperature and the normal fluid's velocity are frozen, and a complete approach, which includes them. In both cases we test our results with the help of gauge-gravity duality, finding good agreement between the hydrodynamic modes of the boundary theory and the quasinormal modes of the gravity theory. Our criterion for the onset of the instability, which is formulated in a model-independent way, applies to interacting systems irrespective of the strength of interactions, does not rely on boost invariance and does not assume any specific quantum statistics. As a final check, we also show that it yields the Landau critical velocity for Galilean superfluids with Bose-Einstein quasiparticles.
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In this work we discuss the Landau criterion for anisotropic superfluidity. To this end we consider a pointlike impurity moving in a uniform Bose-Einstein condensate with either interparticle dipole-dipole interaction or Raman-induced spin-orbit coupling. In both cases we find that the Landau critical velocity vc{v}_{\mathrm{c}}vc​ is generally smaller than the sound velocity in the moving direction. Beyond vc{v}_{\mathrm{c}}vc​, the energy dissipation rate is explicitly calculated via a perturbation approach. In the plane-wave phase of a spin-orbit-coupled Bose gas, the dissipationless motion is suppressed by the Raman coupling even in the direction orthogonal to the recoil momentum. Our predictions can be tested in the experiments with ultracold atoms.