Variational wavefunction for multi-species spinful fermionic superfluids and superconductors

We introduce a new fermionic variational wavefunction, generalizing the Bardeen–Cooper–Schrieffer (BCS) wavefunction, which is suitable for interacting multi-species spinful systems and sustaining superfluidity. Applications range from quark matter to the high temperature superconductors. A wide class of Hamiltonians, comprising interactions and hybridization of arbitrary momentum dependence between different fermion species, can be treated in a comprehensive manner. This is the case, as both the intra-species and the inter-species interactions are treated on equally rigorous footing, which is accomplished via the introduction of a new quantum index attached to the fermions. The index is consistent with known fermionic physics, and allows for heretofore unaccounted fermion–fermion correlations. We have derived the finite temperature version of the theory, thus obtaining the renormalized quasiparticle dispersion relations, and we discuss the appearance of charge and spin density wave order.     

Approximate solutions for half-dark solitons in spinor non-equilibrium Polariton condensates

In this work I generalize and apply an analytical approximation to analyze 1D states of non-equilibrium spinor polariton Bose–Einstein condensates (BEC). Solutions for the condensate wave functions carrying black solitons and half-dark solitons are presented. The derivation is based on the non-conservative Lagrangian formalism for complex Ginzburg–Landau type equations (cGLE), which provides ordinary differential equations for the parameters of the dark soliton solutions in their dynamic environment. Explicit expressions for the stationary dark soliton solution are stated. Subsequently the method is extended to spin sensitive polariton condensates, which yields ordinary differential equations for the parameters of half-dark solitons. Finally a stationary case with explicit expressions for half-dark solitons is presented.     

Attenuation of the fourth sound in liquid helium II via extended thermodynamics

This work continues a study begun in previous works, where a non-standard model of liquid helium II is proposed, in which a small entropy transfer is associated with the superfluid component. In this work the influence of this superfluid entropy on the propagation of the fourth sound is analyzed. From experimental data for velocities and attenuations of the first and second sound, the model provides speed and attenuation coefficient of the fourth sound in a porous medium as a function of the ratio s_s/s between the superfluid entropy s_s and the total entropy s. These values are determined in the two limiting cases s_s/s=0 and =0.02, for various values of temperature and pressure.     

Review: Luttinger or fermi liquids versus topological superconductivity

Superconductors, classified by materials, embrace at least four broad groups: (i) BCS metals and alloys; (ii) heavy Fermion materials; (iii) high- T c cuprates and (some) organic compounds, and (iv) fullerides. Broadly speaking, in classes (i) and (iv), with (i) possibly embracing the recent discovery of superconductivity in MgB 2 with T c ～ 40 K, electron liquids flow through essentially non-magnetic lattices and the electron-phonon interaction is a key component of the mechanism for Cooper pairing. In classes (ii) and (iii), plus the low- T c material Sr 2 RuO 4 , electron or hole liquids flow through assemblies with magnetic spin fluctuations. The nature of the normal state in class (iii) is not yet universally agreed, both Fermi or Luttinger liquids remaining viable to date, the former, however, with the formation of precursor 2 e Bosons somewhat above T c . Our own studies reveal some common ground between classes (ii) and (iii), involving coherence lengths and effective masses, as well as non- s -wave pairing, though the interactions leading to pairing almost certainly have different physical origins in these two groups. Finally, topological superconductivity is reviewed. It is argued that such a treatment of a topological superfluid could eventually deepen the understanding of the class (iv) fullerides. Resonating valence bond theory, used by Anderson and co-workers as an, of course, approximate strongly-correlated electron technique for high- T c cuprates, can itself be re-written in the form of topological superconductivity, as discussed especially by Wiegmann and collaborators.     

Relativistic kinetics of phonon gas in superfluids

The relativistic kinetic theory of the phonon gas in superfluids is developed. The technique of the derivation of macroscopic balance equations from microscopic equations of motion for individual particles is applied to an ensemble of quasi-particles. The necessary expressions are constructed in terms of a Hamilton function of a (quasi-)particle. A phonon contribution into superfluid dynamic parameters is obtained from energy-momentum balance equations for the phonon gas together with the conservation law for superfluids as a whole. Relations between dynamic flows being in agreement with results of relativistic hydrodynamic consideration are found. Based on the kinetic approach a problem of relativistic variation of the speed of sound under phonon influence at low temperature is solved.     

Some current issues concerning statics and dynamics of inhomogeneous superfluid gases

After a brief introduction to the static Gross–Pitaevskii (GP) differential equation for the ground state of a Bose–Einstein condensed gas and an example of its use in describing a vortex array in a trapped condensate, a recent generalization is reviewed. By starting from the Bogoliubov–de Gennes equations for superfluid fermions, an integral equation results. This is shown to contain the static GP equation as a limiting case, by means of a low-order gradient expansion of the order parameter.

The time-dependent GP approximation is then presented and illustrated by a numerical example concerning drop emission under gravity from a gaseous condensate in an optical lattice. Further selected topics of present interest relating more generally to the dynamics of trapped superfluid gases concern the effects of temperature on collective excitations in a Bose gas and the fingerprints that these excitations in a gas of paired fermions contain of the crossover from a Bardeen–Cooper–Schrieffer correlated assembly to a Bose–Einstein condensate of composite bosons. Finally, some directions are pointed in which interaction of first-principles theory with experiment should prove fruitful.