Discontinuity Evolution and Sonic Propagation for Superfluidity Hydrodynamics with Small Superfluid Entropy

In this paper, we have studied discontinuity evolution and sonic propagation for the two-fluid model with small superfluid entropy in the framework of hydrodynamics. General features of the transverse mode and the longitudinal mode are provided. The fourth sound and the sixth sound are identified as the propagation of discontinuity, in agreement with earlier theoretical studies. Moreover, the growth equation is obtained to describe the decay and growth of the discontinuity propagating along its normal trajectory. The solution is in an integral form and various cases are discussed. Important discriminations between the case of fourth sound and that of sixth sound are also presented, which may be meaningful for future's experiments to identify the sixth sound and the small superfluid entropy.     

二分量玻色-爱因斯坦凝聚中的二超流体模型

4He超流体在一定温度下可用二流体模型描述,包括常规流体和超流体两种成分.用这种二流体模型来描述二分量玻色爱因斯坦凝聚时叫做二超流体模型,是从耦合Gross-Pitaevskii方程出发推导得到的.二超流体模型与4He超流体中的二流体模型非常相近.在特定条件下,二超流体中的两个波模行为非常接近4He超流体中二流体模型中...     

Hydrodynamics of superfluid helium in a single nanohole

The flow of liquid helium through a single nanohole with radius smaller than 25 nm was studied. Mass flow was induced by applying a pressure difference of up to 1.4 bar across a 50 nm thick Si(3)N(4) membrane and was measured directly by means of mass spectrometry. In liquid He I, we experimentally show that the fluid is not clamped by the short pipe with diameter-to-length ratio D/L?1, despite the small diameter of the nanohole. This viscous flow is quantitatively understood by making use of a model of flow in short pipes. In liquid He II, a two-fluid model for mass flow is used to extract the superfluid velocity in the nanohole for different pressure heads at temperatures close to the superfluid transition. These velocities compare well to existing data for the critical superflow of liquid helium in other confined systems.     

On the dynamics of superfluid vorticity in non-dissipative processes

We investigate the consequences of the possible existence of superfluid vorticity on the Landau two-fluid equations. Assuming a conservation law for superfluid circulation, we show that in non-dissipative situations, the superfluid vorticity is swept along by the normal fluid.     

First and second sound in cylindrically trapped gases

We investigate the propagation of density and temperature waves in a cylindrically trapped gas with radial harmonic confinement. Starting from two-fluid hydrodynamic theory we derive effective 1D equations for the chemical potential and the temperature which explicitly account for the effects of viscosity and thermal conductivity. Differently from quantum fluids confined by rigid walls, the harmonic confinement allows for the propagation of both first and second sound in the long wavelength limit. We provide quantitative predictions for the two sound velocities of a superfluid Fermi gas at unitarity. For shorter wavelengths we discover a new surprising class of excitations continuously spread over a finite interval of frequencies. This results in a nondissipative damping in the response function which is analytically calculated in the limiting case of a classical ideal gas.     

First and second sound in a two-dimensional harmonically trapped Bose gas across the Berezinskii–Kosterlitz–Thouless transition

We theoretically investigate first and second sound of a two-dimensional (2D) atomic Bose gas in harmonic traps by solving Landau’s two-fluid hydrodynamic equations. For an isotropic trap, we find that first and second sound modes become degenerate at certain temperatures and exhibit typical avoided crossings in mode frequencies. At these temperatures, second sound has significant density fluctuation due to its hybridization with first sound and has a divergent mode frequency towards the Berezinskii–Kosterlitz–Thouless (BKT) transition. For a highly anisotropic trap, we derive the simplified one-dimensional hydrodynamic equations and discuss the sound-wave propagation along the weakly confined direction. Due to the universal jump of the superfluid density inherent to the BKT transition, we show that the first sound velocity exhibits a kink across the transition. These predictions might be readily examined in current experimental setups for 2D dilute Bose gases with a sufficiently large number of atoms, where the finite-size effect due to harmonic traps is relatively weak.     

A model for the λ-transition of helium

Summary Guided by the analogy to the Bose-Einstein condensation of the ideal Bose gas (IBG) we propose a new model for the λ-transition of liquid helium. Deviating from the IBG our model uses phase-ordered and localized single-particle functions. This means that finite groups of particles are assumed to be phase-locked. These phase correlations can be related to the singularity at the transition point and to the occurrence of the superfluid density. The model leads to the following results: 1) a possible explanation of the logarithmic singularity of the specific heat, 2) a characteristic functional form for the superfluid density which yield excellent fits to the experimental data, 3) a quantitative prediction of a small nonzero entropy content of the superfluid component.     

R-Charged Black Hole and Holographic Superfluid

In this paper we consider an interesting model of superfluid and use AdS/CFT correspondence to extract sound modes. We assume that dual picture of superfluid is the R-charged black hole with two equal charges. By using hydrodynamic variables of such a black hole we obtain first, second and fourth sound modes as a function of black hole charge.     

Relaxation and collective motion in superconductors: a two-fluid description

A simple, unified discussion of branch imbalance and gap relaxation in superconductors is presented. Both phenomena are treated within the framework of the ordinary Boltzmann equation, supplemented by the BCS gap equation. We show that the physics of the process commonly referred to as quasiparticle branch imbalance relaxation may be understood simply if one introduces a two-fluid model for the charge in the superconductor, and regards the process as one in which charge associated with the normal component is converted into charge associated with the superfluid. We derive in detail the exact solutions of the Boltzmann equation, which are valid near T_c, and allow for the effects of anisotropy. We discuss the comparison between relaxation rates measured in the superfluid and those obtained from normal state measurements and calculations. We then derive a set of two-fluid hydrodynamic equations based on the two-fluid model for the charge, and find that the current of charge associated with the normal component is not in general equal to the usual normal current. On the basis of these equations we derive expressions for the characteristic quasiparticle diffusion length near phase slip centers, and for the frequency of the recently observed collective mode. We compare our result with those of both microscopic and phenomenological calculations.     

Superfluid helium interferometry: an introduction

This article describes, at an introductory level, how superfluids can be used to measure absolute rotations. To make it self-contained to some degree, I first introduce briefly the two-fluid model for superfluid helium and the concept of superfluid order parameter. These ideas, which were put forward for the superfluid heliums, are now widely used, in particular for the BEC gases which are the main topic of this volume. They are presented in the somewhat different perspective of helium physics. The second part will deal with the Josephson effects, the real engine behind superfluid interferometry. These effects were predicted in the early sixties for superconductors and were promptly observed in the laboratory. It was quickly realised that they would also exist in superfluids but the search took longer and conclusive experiments were performed in the eighties only in the B-phase of superfluid ³He. How these experiments are done, and how they can be used to measure the rotation of the Earth by superfluid interferometry is surveyed in the last two sections.     

Inflation with multiple sound speeds: A model of multiple DBI type actions and non-Gaussianities

In this Letter we study adiabatic and isocurvature perturbations in the frame of inflation with multiple sound speeds involved. We suggest this scenario can be realized by a number of generalized scalar fields with arbitrary kinetic forms. These scalars have their own sound speeds respectively, so the propagations of field fluctuations are individual. Specifically, we study a model constructed by two DBI type actions. We find that the critical length scale for the freezing of perturbations corresponds to the maximum sound horizon. Moreover, if the mass term of one field is much lighter than that of the other, the entropy perturbation could be quite large and so may give rise to a growth outside sound horizon. At cubic order, we find that the non-Gaussianity of local type is possibly large when entropy perturbations are able to convert into curvature perturbations. We also calculate the non-Gaussianity of equilateral type approximately.     

Canonical form of generalised two-fluid equations for helium II

A canonical form of generalised two-fluid equations is derived. The Landau equations are contained as a special case. It turns out that superfluid vortices are transported with the mass velocity.     

Hamiltonian and Thermodynamic Modeling of Quantum Turbulence

The state variables in the novel model introduced in this paper are the fields playing this role in the classical Landau-Tisza model and additional fields of mass, entropy (or temperature), superfluid velocity, and gradient of the superfluid velocity, all depending on the position vector and another tree dimensional vector labeling the scale, describing the small-scale structure developed in ⁴He superfluid experiencing turbulent motion. The fluxes of mass, momentum, energy, and entropy in the position space as well as the fluxes of energy and entropy in scales, appear in the time evolution equations as explicit functions of the state variables and of their conjugates. The fundamental thermodynamic relation relating the fields to their conjugates is left in this paper undetermined. The GENERIC structure of the equations serves two purposes: (i) it guarantees that solutions to the governing equations, independently of the choice of the fundamental thermodynamic relation, agree with the observed compatibility with thermodynamics, and (ii) it is used as a guide in the construction of the novel model.     

Dirac mechanics and Landau two-fluid model in4HE II

This paper is devoted to the development of the Dirac formalism for singular systems when applied to the Landau two-fluid model in superfluid helium. Notably, the Hamiltonian density is weakly zero (in the sense of Dirac). We obtain the physical and gauge variables, and show that all the constraints are of first class, and hence, that the Dirac bracket coincides with the Poisson bracket. We leave the quantization of this system for a later work.     

Holographic Superfluid and STU Model

In this study we consider STU model as dual picture of superfluid. By using AdS/CFT correspondence we obtain sound modes as a function of black hole charge and temperature. We find that the second sound has linear behavior with charge and fourth sound yields to one by increasing black hole charge.     

Quantum Statistical Entropy of Dielectric Black Hole

Using the new equation of state density from the generalized uncertainty principle in quantum gravity, we study statistical entropy of a dielectric black hole. When λ introduced in the generalized uncertainty principle takes a specific value, we find that the leading term of the statistical entropy of the dielectric black hole takes the Bekenstein-Hawking entropy form. In addition a finite correction term is also obtained. Comparing with the original brick-wall model, in our calculation there is no divergence and the small mass approximation is also not needed.     

Will a bose-condensed exciton gas be superfluid?

For a system of Bose-condensed Wannier excitons, the second reduced density matrix for electrons and holes is shown to have the property of off-diagonal long-range order (ODLRO). From the equation of motion for this density matrix, we derive the conservation laws which are relevant for a condensed exciton system. These equations are obtained by projecting the electron-hole density matrices into the exciton space. From the conservation laws, a two-fluid model follows, which describes the superfluid flow of the excitation energy.     

Anisotropic Superfluidity in a Weakly Interacting Condensate of Quasi‐2D Photons

The anisotropic superfluidity in a weakly interacting two‐dimensional Bose gas of photons in a dye‐filled optical microcavity is investigated, taking into account the dependence of the photon effective mass on the in‐plane coordinate. With the use of the generalized Gross–Pitaevskii equation and the Bogoliubov approach, it is shown that the modulation of the microcavity width leads to an effective periodic potential and the periodicity of the condensate wave function, and both the condensate energy and the spectrum of elementary excitations depend on the direction of motion. The anisotropic character of the dynamical and superfluid properties, such as helicity modulus, superfluid density, and sound velocity, as well as experimentally observable manifestations of their anisotropy are described.     

Energy spectra of quantum turbulence in He II and 3He-B: A unified view

Quantum turbulence in superfluid He II and in ³He-B that can be regarded as nearly isothermal, isotropic, and homogeneous is discussed within the two-fluid model. A general form of the 3D energy spectrum is proposed: at large length scales, where normal and superfluid eddies are locked together by the mutual friction force, the energy spectrum is essentially classical and includes an inertial range of a Kolmogorov K62 form. With increasing wavenumber k, the normal fluid part of the spectrum terminates due to finite viscosity, while the superfluid part of the spectral energy density changes towards k ⁻³ and then back into Kolmogorov-like k ^−5/3 again. Agreement with computer simulations and experiments is claimed if account is taken of the turbulent box size and of the energy decay rate. The text was submitted by the author in English.