Superfluid Bose Liquid Research Articles

Acoustic metric and Planck constants

Based on Akama–Diakonov (AD) theory of emergent tetrads, it was suggested that one can introduce two Planck constants,and, which are the parameters of the corresponding components of Minkowski metric,. In the Akama–Diakonov theory, the intervalis dimensionless, as a result the metric elements and thus the Planck constants have nonzero dimensions. The Planck constanthas dimension of time, and the Planck constanthas dimension of length. It is natural to comparewith the Planck length. However, this connection remains an open question, because the microscopic (trans-Planckian) physics of the quantum vacuum is not known. Here we study this question using the effective gravity emerging for sound wave quanta (phonons) in superfluid Bose liquid, where the microscopic physics is known, and the elements of the effective acoustic metric are determined by the parameters of the Bose liquid. Since the acoustic interval is dimensionless, one may introduce the effective “acoustic Planck constants.” The acoustic Planck constanthas dimension of length and is on the order of the interatomic distance. This supports the scenario in which. We also use the acoustic metric for consideration of dependence ofon the Hubble parameter in expanding Universe.

Acoustic Metric and Planck Constants

Based on Akama–Diakonov (AD) theory of emergent tetrads, it was suggested that one can introduce two Planck constants, hbar and not h , which are the parameters of the corresponding components of Minkowski metric, g_{text{Mink}}^{mu nu }=text{diag}(-{{hbar }^{2}},{{not h }^{2}},{{not h }^{2}},{{not h }^{2}}). In the Akama–Diakonov theory, the interval ds is dimensionless, as a result the metric elements and thus the Planck constants have nonzero dimensions. The Planck constant hbar has dimension of time, and the Planck constant not h has dimension of length. It is natural to compare not h with the Planck length {{l}_{{text{P}}}}. However, this connection remains an open question, because the microscopic (trans-Planckian) physics of the quantum vacuum is not known. Here we study this question using the effective gravity emerging for sound wave quanta (phonons) in superfluid Bose liquid, where the microscopic physics is known, and the elements of the effective acoustic metric are determined by the parameters of the Bose liquid. Since the acoustic interval is dimensionless, one may introduce the effective “acoustic Planck constants.” The acoustic Planck constant {{not h }_{text{ac}}} has dimension of length and is on the order of the interatomic distance. This supports the scenario in which not h sim {{l}_{text{P}}}. We also use the acoustic metric for consideration of dependence of hbar on the Hubble parameter in expanding Universe.

Two distinctive temperature dependences of the London penetration depth in high-Tc cuprate superconductors as support for the theory of Bose-liquid superconductivity

In the framework of the theory of Bose-liquid superconductivity, we show that in high-Tc cuprate superconductors the magnetic field penetration depth (known as the London penetration depth λL(T)) decreases first exponentially below the superconducting transition temperature Tc with decreasing the temperature T and then λL(T) decreases like a certain power of T at lower temperatures due to the vanishing of the energy gap Δg(T) in the excitation spectrum of a superfluid Bose-liquid at a characteristic temperature Tc⁎ lower than Tc. Below Tc, the London penetration depth λL(T) has an exponential temperature dependence down to Tc⁎, which is different from a BCS- like exponential temperature dependence, and then λL(T) will follow a power law temperature dependence down to T=0, which is also different from power-law temperature dependences predicted by some BCS-like (d-wave) pairing theories. In unconventional (bosonic) cuprate superconductors characterized by the strong interboson coupling constant (γB≳1), λL(T) exhibits the distinctly different temperature dependences in different temperature intervals 0≤T≤Tc⁎<<Tc and Tc⁎<T<Tc when the energy gap Δg(T) vanishes at a temperature Tc⁎ well below Tc. In the weak interboson coupling (γB<<1) the energy gap Δg(T) vanishes at a temperature Tc⁎ close to Tc and the reduced London penetration depth λL(T)/λL(0) has an unusual Tn power-law temperature dependence in a wide temperature range 0<T<Tc⁎ below Tc, i.e. the expression λL(T)/λL(0)≃[1−aL(T)(T/Tc)n]−1/2 (where n≳4 and aL(T)≲1) is valid only below Tc⁎ and is similar to the well-known empirical Gorter-Casimir law. Our theoretical predictions of the distinctive power-law and exponential temperature dependences of λL(T)/λL(0) are in good agreement with the experimental results reported for GdBa2Cu3O7−δ ceramics and YBa2Cu3O7−δ films. The peculiar temperature dependences of λL(T)/λL(0) observed in these high-Tc materials at low and high temperatures do not follow the predictions of the s- and d-wave BCS-like theories of Fermi-liquid superconductivity and give evidence for the predictions of the theory of Bose-liquid superconductivity.

Magnetic polarization of quantum vortices in He II

The weak magnetic polarization which a quantum vortex in a superfluid Bose liquid acquires as a result of the mutual electric polarization of atoms and the nonuniform distribution of the atomic density in its core is discussed. A rectilinear single-quantum vortex carries a magnetic moment directed along and proportional to the length of the vortex line. The magnetic moment density per unit length and the corresponding quantum of magnetic flux (vortex fluxoid) are directly related with the quantum circulation of the superfluid flow in the vortex. Numerical estimates of this effect are presented for vortices in He II.

“Infrared” singularities in the field theory of superfluidity and temperature corrections to the first and second sound velocities in helium II

Higher-order corrections to the self-energy parts of the field theory of superfluidity are obtained using V. N. Popov’s perturbation theory modified for a strongly interacting Bose system and free of infrared divergences. It is shown that the calculation of these corrections reduces to solving kinetic-type equations. Using these equations as a basis, the temperature corrections to the first and second sound velocities in the superfluid Bose liquid He4 are obtained. The temperature dependence of the density of the superfluid component of the Bose liquid He4 is calculated on the basis of a model of the superfluid component as a superposition of interaction-suppressed single-particle and intense pair condensates.

Effect of electric field on quantized vortices in HeII

A study is made of the electric polarization of quantized vortices in a superfluid Bose liquid and their interaction with electric field. Two types of vortex polarization are considered, both of which are due to the centrifugal forces exerted on the atoms of the liquid in their azimuthal motion around the vortex line. First, under the influence of these forces the atoms acquire dipole moments (inertial polarization in the absence of external field), and a nonuniform symmetric distribution of the polarization density arises around the vortex line. Here the vortex does not have an integral dipole moment, but each element of the vortex line possesses a quadrupole moment. Second, the centrifugal forces lead to a nonuniform distribution of the atomic density around the vortex line, and therefore the polarization density of the liquid in an external electric field is also nonuniform near the vortex line, and an individual element of the vortex line acquires an effective dipole moment proportional to the field (inductive polarization). Analytical expressions are obtained for the polarization density around rectilinear and ring-shaped vortex lines, and the effective dipole and quadrupole moments of such vortices are calculated. The distribution of ponderomotive forces acting on a superfluid liquid containing a quantized vortex in an electric field is analyzed, and the corrections to the vortex energy due to the field are found. Numerical estimates of these effects are made for the case of HeII.

A computer investigation of a superfluid Bose liquid with pair interaction and with a coherent condensate of boson pairs as a model of 4He quantum liquid

One considers a superfluid (SF) state of a Bose liquid with repulsion between bosons, in which at T = 0, along with a weak single-particle Bose-Einstein condensate (BEC), there exists an intensive pair coherent condensate (PCC), analogous to the Cooper condensate in a Fermi liquid with attraction between fermions. By iterations, one obtains a numerical solution of a closed system of nonlinear integral equations for the normal ∼ϵ 11 ( p , ω) and anomalous ∼ϵ 12( p, ω) self-energy parts in the framework of the model of “semi-transparent spheres”. A quasiparticle spectrum is then obtained, which is in good agreement with the experimental spectrum of elementary excitations in superfluid 4He.

Self-consistent calculation of the spectrum of quasiparticles in a superfluid Bose liquid with a quenched Bose–Einstein condensate

An iterative method is used in a self-consistent calculation, at T=0, of the normal Σ11 and anomalous Σ12 self-energy parts, the boson polarization operator Π on the “mass shell,” and the quasiparticle spectrum E(p) in a superfluid Bose liquid with an interaction-quenched single-particle Bose–Einstein condensate (BEC). The calculation is based on a system of “truncated” integral equations for Σ11 and Σ12 with allowance for terms of first order in the density n0/n≪1 of the BEC and with the “bare” interaction between bosons taken in the form of the repulsive pseudopotential in the “semitransparent spheres” model, for which the Fourier component of the pseudopotential is an oscillatory sign-varying function of the momentum transfer. By fitting with a single adjustable parameter—the amplitude of the initial repulsive pseudopotential—one can achieve completely satisfactory agreement of the theoretical quasiparticle spectrum E(p) with the measured spectrum of elementary excitations in superfluid helium from neutron-scattering experiments over a wide momentum range (0⩽p⩽pmax≃4 Å−1).

Structure of the superfluid component and spectrum of elementary excitations in the quantum Bose liquid He4

A self-consistent model is constructed for a superfluid Bose liquid in which the single-particle Bose–Einstein condensate (BEC) is suppressed on account of the strong interaction between bosons. The ratio of the density of the BEC to the total density of the Bose liquid is small, n0/n≪1, in contrast to the Bogolyubov theory for a nearly ideal Bose gas, in which the small parameter is the ratio of the number of overcondensate excitations to the number of particles in the intense BEC, (n−n0)/n0≪1. A closed system of nonlinear integral equations for the normal Σ̃11(p,ω) and anomalous Σ̃12(p,ω) self-energy parts is obtained in a renormalized perturbation theory constructed in the combined hydrodynamic (for p→0) and field (for p≠0) variables, the use of which ensures analyticity of the functions Σ̃ij(p,ε) for p→0 and ε→0 and a nonzero value of the superfluid order parameter Σ̃12(0,0)≠0 at T=0. It is shown that the structure of the quasiparticle spectrum E(p) and, in particular, the presence of a roton minimum are determined by the sign-varying and oscillatory behavior of the Fourier component of the pair interaction between bosons in the “hard spheres” model. An important role here is played by the renormalization (screening) of the pair interaction on account of many-particle (collective) effects, which are described by a polarization operator of the bosons on the “mass shell” and leads to enhancement of the effective attraction in certain regions of momentum space. It is shown that the superfluid component ρs at T→0 in this model is a superposition of the single-particle BEC and a pair coherent condensate, analogous to the condensate of Cooper pairs in superconductors. The structure of the superfluid state for T≠0 is also considered, with allowance for the appearance of a normal component ρn and a branch of second sound, the velocity of which goes to zero at the λ point. The applicability of the Landau superfluidity criterion is examined, and the question of the limiting permissible critical velocity of superfluid flow in the absence of quantum vortices is discussed.

Anomalous condensate fluctuations in strongly interacting superfluids

We show that the condensate occupation of a superfluid Bose liquid quite generally exhibits anomalously large fluctuations at finite temperatures. In three dimensions, the variance scales like T^2 V^{4/3} at low T, generalizing the result obtained by Giorgini, Pitaevskii, and Stringari for a weakly interacting Bose gas. In two dimensions there is only a quasicondensate, and the fluctuations are of the same order as the mean value.

The role of pair correlations in the formation of the ground state and the elementary excitation spectrum in a superfluid Bose liquid (A Review)

The paradoxes and disparities in the contemporary microscopic theory of superfluid helium (He–II) are discussed along with possible ways of resolving them by taking pair correlations of He4 atoms into consideration. It is shown that most paradoxes are associated with the commonly accepted initial assumption concerning the dominating role of single-particle Bose condensate (SPBC) in the quantum microstructure of the superfluid component ρs. The existence of intensive SPBC leads to a strong hybridization of the elementary excitation branches and to a common dispersion law for all boson branches, which is identified with the quasiparticle spectrum E(p) observed experimentally from slow neutron scattering in liquid helium. However, the stability of this spectrum during a transition through the λ-point and the large value of the gap in the vicinity of the “rotonic” minimum contradict both the Landau theoretical criterion of superfluidity and the small value of experimentally measured critical velocity. At the same time, a strong interaction between particles in the Bose liquid He4 strongly suppresses the SPBC which amounts to less than 1% of all He4 atoms and hence cannot be the main constituent of the superfluid component, unlike the case of a weakly nonideal Bose gas. Moreover, for a quite strong attraction between particles in a certain region of the momentum space, bound pairs of bosons can be formed in the superfluid Bose liquid, and a coherent pair condensate (CPC) analogous to the Cooper pair condensate in superconductors may appear. Such a strong CPC may completely suppress the weak SPBC. In this case, the one-particle spectrum ε(p) of elementary excitations does not hybridize with the collective (two-particle) spectrum and does not appear in the structure of the dynamic form factor S(p,ε), i.e., does not coincide with the spectrum measured from neutron scattering. The dispersion of one-particle spectrum is defined by the momentum dependence of the pair order parameter Ψ̃(p) and may have a minimum or a point of inflection at p≠0. This peculiarity in the one-particle spectrum of a Bose liquid with CPC but without SPBC vanishes together with Ψ̃(p) at the temperature Tc=Tλ of the phase transition from the superfluid to the normal state (unlike the rotonic minimum in the collective spectrum), while the corresponding critical velocity vc=min[ε(p)/p] vanishes at the λ-point in accordance with the Landau criterion and the experimental data. The assumption that the strong “Cooper-like” CPC is responsible for the quantum structure of the superfluid component ρs is confirmed indirectly by the successful application of the Justrow approximation (based on strong pair correlations) for describing the properties of liquid He4 and quantum liquid mixtures He3–4He on one hand, and by an anomalously large effective mass of He3 impurity atoms in He4, which is approximately equal to total mass of He3 and He4 atoms, thus pointing to the existence of helium atoms in superfluid liquid He–II. The value of the superfluid velocity circulation quantum in the Onsager–Feynman vortices in a Bose liquid with CPC but without SPBC is discussed as well as the critical velocities of superfluid He4 in ultrathin films and channels in which the creation and motion of quantum vortices are ruled out, and the quasiparticle spectrum undergoes dimensional quantization.

Variational determination of multi-time Green's functions for degenerate bose systems and common pole structures of their hydrodynamic asymptotic behavior

Variational determination of n-time (n=2,3,...) retarded Green's functions of Bose systems, whose equilibrium state is noninvariant under the group of gauge transformations, is given. Based on Bogoliubov's ideas of a reduced description of nonequilibrium states, the mathematical method of studying the hydrodynamic asymptotic behavior of Green's functions is developed and their pole structures are analyzed. It is shown that qualitatively new results for nonlinear interaction processes of the first-and second-sound waves in the superfluid Bose liquid are determined in terms of the three-time Green's functions, and that the increase in singularities in n-time (n≥4) Green's functions is caused by virtual effects only.

The method of two-time Green's functions in the molecular hydrodynamics of a superfluid

For a system of interacting bosons at temperature below the critical temperature the single-particle functions as well as the Green's functions for the fluctuations of the density and the temperature are constructed on the basis of the hierarchy of equations for the irreducible Green's functions. In the limiting case of low frequency and small wave vectors a comparison is made with the results obtained on the basis of the two-fluid hydrodynamics of a superfluid Bose liquid. It is shown that the macroscopic parameters of the two-fluid hydrodynamics (the susceptibilities and the transport coefficients) are completely determined in the framework of the microscopic approach.

Hydrodynamics of a superfluid bose liquid with allowance for dissipative processes in a model with weak interaction

Hydrodynamics of a superfluid bose liquid with allowance for dissipative processes in a model with weak interaction

Equations of hydrodynamics and transport coefficients for a superfluid bose liquid

Equations of hydrodynamics and transport coefficients for a superfluid bose liquid

Elementary excitations in superfluid liquid helium based on the Bogoliubov-Zubarev formalism

The Bogoliubov-Zubarev (BZ) formulation of the superfluid Bose liquid in terms of density as a collective variable leads to a non-Hermitian Hamiltonian (${H}_{\mathrm{BZ}}$) for describing the elementary excitations. An appropriate mathematical framework for dealing with non-Hermitian operators is here employed for the first time to develop schemes for studying the elementary excitations of the Bose liquid. The energies of the ground and the first excited states associated with ${H}_{\mathrm{BZ}}$ in "perturbation" theory are derived. A consistent scattering theory appropriate to ${H}_{\mathrm{BZ}}$ is also given from which the two-roton scattering amplitude in the leading order of "perturbation" theory is explicitly deduced. A finite-temperature Green's-function theory is also presented. These results are shown to be equivalent to those based on the Sunakawa Hamiltonian. Results for the energy spectrum are also shown to be equivalent with those evaluated by means of a variation-perturbation procedure based on the method of correlated basis functions in the uniform limit.