Theory Of Superfluidity Research Articles

Clarification of the Theory of Superconductivity and Superfluidity based on Scientific Philosophy

The development of the results of the theory of superconductivity (BCW) is based on the idea of a deep analogy between some ideas of quantum electrodynamics and quantum hydrodynamics. On the other hand, there are reasons to doubt the basic results of quantum electrodynamics. The reason is that in order to complete the development of quantum electrodynamics, it is necessary to supplement it with the results of reassignment operations. The founder of quantum electrodynamics, Dirac, believed that such a necessity arose because of the defects in this doctrine. In this article, the main results of quantum electrodynamics and quantum hydrodynamics are obtained quite correctly on the way, where the basic ideas of scientific philosophy are taken as a basis.

Nearly critical superfluids in Keldysh-Schwinger formalism

We examine the effective theory of critical dynamics near superfluid phase transitions in the framework of the Keldysh-Schwinger formalism. We focus on the sector capturing the dynamics of the complex order parameter and the conserved current corresponding to the broken global symmetry. After constructing the theory up to quadratic order in the a-fields, we compare the resulting stochastic system with Model F as well as with holography. We highlight the role of a time independent gauge symmetry of the effective theory also known as “chemical shift”. Finally, we consider the limiting behaviour at energies much lower than the gap of the amplitude mode by integrating out the high energy degrees of freedom to reproduce the effective theory of superfluids.

Baby skyrmion in two-component holographic superfluids

In the two-component Ginzburg-Landau theory of superfluidity, a pair of fractional vortices form a composite type of topological defect, usually referred to as a baby skyrmion. In this paper, we initiate the construction of such a baby skyrmion in the holographic model of two-component superfluids. As a result, two types of baby skyrmion configurations are found, where the monopole-type of one is constructed directly by solving the static equations of motion while the dipole-type of one is obtained by resorting to the time evolution method. In addition, we find that the existence of these two types of baby skyrmion depends on the inter-component coupling, reminiscent of the situation in the baby skyrmion model.

Current-density functional theory for bosonic superfluids

A finite-temperature current-density functional theory for bosonic superfluids (sf-CDFT) in the thermal equilibrium state is proposed herein. In the sf-CDFT, hydrodynamic physical quantities, such as particle number density, current density, and the order parameter of the Bose–Einstein condensation, are chosen as the basic variables. This theory enables the simultaneous reproduction of the particle number and current densities of both the superfluid and normal fluid components with incorporating effects of the interaction between these components. Specifically, these components are determined by solving two single-particle equations, i.e., the Gross–Pitaevskii–Kohn–Sham and Kohn–Sham equations. Furthermore, using the continuity equation of superfluids, we present the sum rule for the exchange-correlation energy functional of the sf-CDFT, which is useful for developing the approximate form.

Lev Petrovich Pitaevskii

Lev Petrovich Pitaevskii

Giant Vortices and the Regge Limit

In recent years it has been shown that strongly coupled systems become analytically tractable in the regime of large quantum numbers, such as large spin or large charge. The effective theories that emerge in these two limits are Regge theory and superfluid theory, respectively. Here we make a proposal for a new phase, the “giant vortex,” describing an intermediate regime with large spin and charge. The new phase connects superfluid theory with the large-spin expansion. The giant vortex admits a semi-classical effective theory description with peculiar chiral excitations (moving at the speed of light) and a Fock space of states that is reminiscent of the multi-twist operators in Regge theory, including the leading and daughter Regge trajectories. A similar giant vortex phase appears for Bose-Einstein condensates in a rotating trap, and our results should be applicable in that context as well. We show that the transition from the giant vortex to the Regge regime is accompanied by the scaling dimension turning from being larger than to being smaller than the mean field theory value, i.e. gravity switches from being the weakest force at small AdS distance to being the strongest force at large AdS distance.

Impurity scattering in superconductors revisited: Diagrammatic formulation of the supercurrent-supercurrent correlation and Higgs-mode damping

The diagrammatic formalism and transport equation are conventionally considered as separate but complementary techniques to tackle the impurity scattering effect. To compare with the previous studies from the gauge-invariant kinetic equation approach [F. Yang and M. W. Wu, Phys. Rev. B 98, 094507 (2018); 102, 144508 (2020)], we analytically perform a diagrammatic formulation of the impurity scattering in superconductors, with both transport and collective Higgs mode studied, in order to fill the long missing calculation of the Kubo current-current correlation in superconductors with impurity scattering and resolve the controversy (whether the impurity scattering can lead to the damping of Higgs mode) between gauge-invariant kinetic equation and Eilenberger equation. For transport behavior, through a special unitary transformation that is equivalent to the Wilson-line technique for the diamagnetic response, we derive the Meissner-supercurrent vertex. Then, by formulating the supercurrent-supercurrent correlation with Born and vertex corrections from impurity scattering, we recover the previously revealed microscopic momentum-relaxation rate of superfluid by gauge-invariant kinetic equation. This rate is finite only when the superconducting velocity is larger than a threshold, at which the normal fluid emerges and causes the friction with the superfluid current, similar to the Landau's superfluid theory of liquid helium. This derivation also provides a physical understanding of the relaxation-time approximation in the previous diagrammatic formulation in the literature, which leads to the friction resistance of the Meissner supercurrent. For the collective Higgs mode, we calculate the amplitude-amplitude correlation with Born and vertex corrections from impurity scattering. The vertex correction, which only emerges at nonequilibrium case, leads to a Higgs-mode damping, ......

Breakdown of the Migdal-Eliashberg theory and a theory of lattice-fermionic superfluidity

Superconductors become unstable at strong renormalized electron-phonon coupling which breaks the crystalline symmetry and gives rise to a new phase. Smoking-gun evidence for this instability is negative specific heat. The authors also predict an upper bound on the superconducting critical temperature and explain why and how a spurious lattice instability as a function of the bare electron-phonon coupling has been frequently mistaken for a genuine breakdown of the Migdal-Eliashberg theory.

Mean field versus random-phase approximation calculation of the energy of an impurity immersed in a spin-1/2 superfluid

In this article we calculate the energy of an impurity weakly coupled to a spin 1/2 fermionic superfluid. We show that the divergences resulting from three-body physics can only be cured using a proper description of the excitations of the many-body background. We highlight the crucial role played by interactions between quasiparticles which are overlooked within BCS (Bardeen-Cooper-Schrieffer) mean-field theory of fermionic superfluidity. By contrast, we prove that their addition using the Random Phase Approximation (RPA) allows us to regularize the energy of the impurity. Finally, we show that these beyond mean-field corrections should be observable by the analysis of the frequency shift of the impurity center of mass oscillations in an external confining potential.

Implementation of a Classical Theory for Superfluids

The superfluidity of helium-4 is explained until today by a quantum theory: the Bose-Einstein condensation. This theory is rather satisfactory in describing the superfluid state of helium-4 because this one is a system made up of bosons (particles of integer spin). However, the discovery of the superfluidity of helium-3 in 1971 called into question the veracity of this quantum theory. In fact, helium-3 being a system composed of fermions (particles of half-integer spin), it cannot be subject to Bose-Einstein condensation. It is to correct this deficiency that we introduce here a classical (non-quantum) theory of superfluids. This new theory makes no difference between the λ transition of bosons and that of fermions. It is based on a fundamental law: “in a superfluid, density is conserved”. In this work, we have shown that this simple law explains not only the zero viscosity of superfluids but also the surprising phenomena observed in the superfluid state, I quote the liquidity of helium at normal pressure down to 0 K, vaporization without boiling, high thermal conductivity, the fountain effect, the ability to go up one side of the wall of a container to come down on the other side and the existence of a critical velocity.

Solution of Abel’s integral equation by Kashuri Fundo transform

Integral equations can be defined as equations in which unknown function to be determined appears under the integral sign. These equations have been used in many problems occurring in different fields due to the connection they establish with differential equations. Abel?s integral equation is an important singular integral equation and Abel found this equation from a problem of mechanics, namely the tautochrone problem. This equation and some variants of it found applications in heat transfer between solids and gases under non-linear boundary conditions, theory of superfluidity, subsolutions of a non-linear diffusion problem, propagation of shock-waves in gas field tubes, microscopy, seismology, radio astronomy, satellite photometry of airglows, electron emission, atomic scattering, radar ranging, optical fiber evaluation, X-ray radiography, flame and plasma diagnostics. Integral transforms are widely used mathematical techniques for solving advanced problems of applied sciences. One of these transforms is the Kashuri Fundo transform. This transform was derived by Kashuri and Fundo to facilitate the solution processes of ODE and PDE. In some works, it has been seen that it provides great convenience in finding the unknown function in integral equations. In this work, our aim is to solve Abel?s integral equation by Kashuri Fundo transform and some applications are made to explain the solution procedure of Abel?s integral equation by Kashuri Fundo transform.

A holographic superfluid symphony

We study the hydrodynamic excitations of backreacted holographic superfluids by computing the full set of quasinormal modes (QNMs) at finite momentum and matching them to the existing hydrodynamic theory of superfluids. Additionally, we analyze the behavior of the low-energy excitations in real frequency and complex momentum, going beyond the standard QNM picture. Finally, we carry out a novel type of study of the model by computing the support of the hydrodynamic modes across the phase diagram. We achieve this by determining the support of the corresponding QNMs on the different operators in the dual theory, both in complex frequency and complex momentum space. From the support, we are able to reconstruct the hydrodynamic dispersion relations using the hydrodynamic constitutive relations. Our analysis rules out a role-reversal phenomenon between first and second sound in this model, contrary to results obtained in a weakly coupled field theory framework.

On Asymptotic Behavior of Galactic Rotation Curves in Superfluid Vacuum Theory

The logarithmic superfluid theory of physical vacuum predicts that gravity is an induced phenomenon, which has a multiple-scale structure. At astronomical scales, as the distance from a gravitating center increases, gravitational potential and corresponding spacetime metric are dominated by a Newtonian (Schwarzschild) term, followed by a logarithmic term, finally by linear and quadratic (de Sitter) terms. Correspondingly, rotation curves are predicted to be Keplerian in the inner regions of galaxies, mostly flat in the outer regions, and non-flat in the utmost outer regions. We compare theory's predictions with the furthest rotation curves data points available for a number of galaxies: using a two-parameter fit, we perform a preliminary estimate which disregards the combined effect of gas and stellar disc, but is relatively simple and uses minimal assumptions for galactic luminous matter. The data strongly points out at the existence of a crossover transition from flat to non-flat regimes at galactic outskirts.

Inverse Faraday Effect for Superconducting Condensates.

The Cooper pairs in superconducting condensates are shown to acquire a temperature-dependent dc magnetic moment under the effect of the circularly polarized electromagnetic radiation. The mechanisms of this inverse Faraday effect are investigated within the simplest version of the phenomenological dynamic theory for superfluids, namely, the time-dependent Ginzburg-Landau (GL) model. The light-induced magnetic moment is shown to be strongly affected by the nondissipative oscillatory contribution to the superconducting order parameter dynamics, which appears due to the nonzero imaginary part of the GL relaxation time. The relevance of the latter quantity to the Hall effect in the superconducting state allows us to establish the connection between the direct and inverse Faraday phenomena.

Excitations in the Ultimate Quantum Fluid

Researchers have measured superfluid helium’s full dispersion spectrum, explaining discrepancies in previous studies and constraining theories of superfluidity.

Novel solitary wave solution of the nonlinear fractal Schrödinger equation and its fractal variational principle

PurposeThe nonlinear Schrödinger equation plays a vital role in wave mechanics and nonlinear optics. The purpose of this paper is the fractal paradigm of the nonlinear Schrödinger equation for the calculation of novel solitary solutions through the variational principle.Design/methodology/approachAppropriate traveling wave transform is used to convert a partial differential equation into a dimensionless nonlinear ordinary differential equation that is handled by a semi-inverse variational technique.FindingsThis paper sets out the Schrödinger equation fractal model and its variational principle. The results of the solitary solutions have shown that the proposed approach is very accurate and effective and is almost suitable for use in such problems.Practical implicationsNonlinear Schrödinger equation is an important application of a variety of various situations in nonlinear science and physics, such as photonics, the theory of superfluidity, quantum gravity, quantum mechanics, plasma physics, neutron diffraction, nonlinear optics, fiber-optic communication, capillary fluids, Bose–Einstein condensation, magma transport and open quantum systems.Originality/valueThe variational principle of the Schrödinger equation without the Lagrange multiplier method in the sense of the fractal calculus is developed for the first time in the literature to the best of the author's understanding.

Quaternion Algebra on 4D Superfluid Quantum Space-Time: Can Dark Matter Be a Manifestation of the Superfluid Ether?

Quaternions are a natural framework of 4D space-time, where the unit element relates to time, and three others relate to 3D space. We define a quaternion set of differential torsion operators (shifts with rotations) that act to the energy-momentum tensor written on the same quaternion basis. It results in the equations of gravity-torsion (gravitomagnetic) fields that are similar to Maxwell’s equations. These equations are parent equations, generating the following equations: (a) equations of the transverse gravity-torsion waves; (b) the vorticity equation describing vortices orbital speed of which grows monotonically in the vortex core but far from it, it goes to a permanent level; (c) the modified Navier–Stokes equation leading to the Schrödinger equation in the nonrelativistic limit and to the Dirac equation in the relativistic limit. The Ginsburg–Landau theory of superfluidity resulting from the Schrödinger equation shows the emergence of coupled proton-antiproton pairs forming the Bose–Einstein condensate. In the final part of the article, we describe Samokhvalov’s experiment with rotating nonelectric, nonferromagnetic massive disks in a vacuum. It demonstrates an unknown force transferring the rotational moment from the driving disk to a driven one. It can be a manifestation of the dark matter. For studying this phenomenon, we propose a neutron interference experiment that is like the Aharonov–Bohm one.

Resolving cosmological singularity problem in logarithmic superfluid theory of physical vacuum

A paradigm of the physical vacuum as a non-trivial quantum object, such as superfluid, opens an entirely new prospective upon origins and interpretations of Lorentz symmetry and spacetime, black holes, cosmological evolution and singularities. Using the logarithmic superfluid model, one can formulate a post-relativistic theory of superfluid vacuum, which is not only essentially quantum but also successfully recovers special and general relativity in the “phononic” (low-momenta) limit. Thus, it represents spacetime as an induced observer-dependent phenomenon. We focus on the cosmological aspects of the logarithmic superfluid vacuum theory and show how can the related singularity problem be resolved in this approach.

On effective theory of superfluid phonons

It is shown that the standard effective field theory of non-relativistic superfluids, which includes only the leading order action in derivative expansion, is in general inadequate for studying supersonic processes. Namely, for a proper treatment of the latter the phonons with momenta greater than mcs are relevant at times (with m being the mass of the superfluid constituent and cs denoting the sound-speed), which lie beyond the regime of validity of the naive effective theory mentioned above. This is demonstrated on a concrete example by recovering the known expression for the friction force as a process of radiating phonons by a supersonic perturber. In particular, when the impurity is heavier than superfluid constituents, it is indeed necessary to extend the non-relativistic effective theory of superfluids to include high-derivative corrections. For the light perturber, however, there is a window of velocities for which high-derivative corrections are irrelevant.

Viscoelastic hydrodynamics and holography

We formulate the theory of nonlinear viscoelastic hydrodynamics of anisotropic crystals in terms of dynamical Goldstone scalars of spontaneously broken translational symmetries, under the assumption of homogeneous lattices and absence of plastic deformations. We reformulate classical elasticity effective field theory using surface calculus in which the Goldstone scalars naturally define the position of higher-dimensional crystal cores, covering both elastic and smectic crystal phases. We systematically incorporate all dissipative effects in viscoelastic hydrodynamics at first order in a long-wavelength expansion and study the resulting rheology equations. In the process, we find the necessary conditions for equilibrium states of viscoelastic materials. In the linear regime and for isotropic crystals, the theory includes the description of Kelvin-Voigt materials. Furthermore, we provide an entirely equivalent description of viscoelastic hydrodynamics as a novel theory of higher-form superfluids in arbitrary dimensions where the Goldstone scalars of partially broken generalised global symmetries play an essential role. An exact map between the two formulations of viscoelastic hydrodynamics is given. Finally, we study holographic models dual to both these formulations and map them one-to-one via a careful analysis of boundary conditions. We propose a new simple holographic model of viscoelastic hydrodynamics by adopting an alternative quantisation for the scalar fields.