Crossover from BCS-superconductivity to Bose-condensation

Starting from a model of free Fermions in two dimensions with an arbitrary strong effective interaction, we derive a Ginzburg-Landau theory describing the crossover from BCS-superconductivity to Bose-condensation. We find a smooth crossover from the standard BCS-limit to a Gross-Pitaevski type equation for the order parameter in a Bose superfluid. The mean field transition temperature exhibits a maximum at a coupling strength, where the behaviour crosses over from BCS to Bose like with corresponding values of 2 Δ₀/T_c ≈ 5 which are characteristic for high T_c superconductors.     

Thermodynamics of two-parameter quantum group Bose and Fermi gases

The high and low temperature thermodynamical properties of the two-parameter deformed quantum group Bose and Fermi gases with SU _p/q (2) symmetry are studied. Starting with a SU _p/q (2)-invariant bosonic as well as fermionic Hamiltonian, several thermodynamical functions of the system such as the average number of particles, internal energy and equation of state are derived. The effects of two real independent deformation parameters p and q on the properties of the systems are discussed. Particular emphasis is given to a discussion of the Bose-Einstein condensation phenomenon for the two-parameter deformed quantum group Bose gas. The results are also compared with earlier undeformed and one-parameter deformed versions of Bose and Fermi gas models. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Dynamical conductivity of the two-dimensional Bose condensate: Superfluid-insulator transition for a long-range random potential

We calculate the dynamical conductivity of a disordered charged Bose condensate in two dimensions with a long-range random potential due to charged impurities with a large spacer width . Analytical results for the frequency-dependent conductivity for weak disorder are derived. For strong disorder the frequency-dependent conductivity is given in terms of a transcendental equation. The disorder-induced transition from a superfluid phase to an insulator phase is discussed. The density-density relaxation function and the screening properties of the disordered Bose gas are calculated. Experimental results for high-T _c superconductors are discussed.     

Bose-Einstein condensation at finite momentum and magnon condensation in thin film ferromagnets

We use the Gross-Pitaevskii equation to determine the spatial structure of the condensate density of interacting bosons whose energy dispersion ϵ _k has two degenerate minima at finite wave-vectors ± q. We show that in general the Fourier transform of the condensate density has finite amplitudes for all integer multiples of q. If the interaction is such that many Fourier components contribute, the Bose condensate is localized at the sites of a one-dimensional lattice with spacing 2 π/|q|; in this case Bose-Einstein condensation resembles the transition from a liquid to a crystalline solid. We use our results to investigate the spatial structure of the Bose condensate formed by magnons in thin films of ferromagnets with dipole-dipole interactions.     

Oscillating Casimir force between two slabs in a Fermi sea

The Casimir effect for two parallel slabs immersed in an ideal Fermi sea is investigated at both zero and nonzero temperatures. It is found that the Casimir effect in a Fermi gas is distinctly different from that in an electromagnetic field or a massive Bose gas. In contrast to the familiar result that the Casimir force decreases monotonically with the increase of the separation L between two slabs in an electromagnetic field and a massive Bose gas, the Casimir force in a Fermi gas oscillates as a function of L. The Casimir force can be either attractive or repulsive, depending sensitively on the magnitude of L. In addition, it is found that the amplitude of the Casimir force in a Fermi gas decreases with the increase of the temperature, which also is contrary to the case in a Bose gas, since the bosonic Casimir force increases linearly with the increase of the temperature in the region T < T_c, where T_c is the critical temperature of the Bose-Einstein condensation.     

On the superfluidity of classical liquid in nanotubes,IV

The problem involves a large parameter, the number N of particles (outside the condensate), and a small parameter, the Planck constant ħ (to be more exact, a dimensionless parameter containing ħ in the numerator). These parameters turn out to be related for Bose particles. The exact solution of the equation for the variations for the Bose system in a capillary enables one to obtain sharp criteria limiting the radius of the capillary. This paper is dedicated to the memory of Lionya Volevich, a dear friend of mine     

Quantum phase diagram for homogeneous Bose‐Einstein condensate

We calculate the quantum phase transition for a homogeneous Bose gas in the plane of s‐wave scattering length a_s and temperature T. This is done by improving a one‐loop result near the interaction‐free Bose‐Einstein critical temperature T_c⁽⁰⁾ with the help of recent high‐loop results on the shift of the critical temperature due to a weak atomic repulsion based on variational perturbation theory. The quantum phase diagram shows a nose above T_c⁽⁰⁾, so that we predict the existence of a reentrant transition above T_c⁽⁰⁾, where an increasing repulsion leads to the formation of a condensate.     

Spin excitons — a new mechanism of superconducting pairing in copper oxides

The Fermi and Bose quasiparticle spectrum in copper oxides is studied in a many-band p-d model taking account of the strong electronic correlations. It is shown that hole-doped systems possess a Bose mode — a spin exciton — which is associated with the singlet-triplet excitation of the two-hole ground-state term of CuO₄ clusters. Intercluster hopping leads to fermion-boson interaction with a spin exciton as the intermediate boson. Such a mechanism does not exist for n-type systems. Pis'ma Zh. éksp. Teor. Fiz. 64, No. 1, 23–28 (10 July 1996)     

Realisations of the representations of para-Fermi algebra in Fock space of Bose operators: part I

Using the matrix realisations of para-Fermi operators we find isomorphic mappings with respect to the Green product of the para-Fermi algebra into second-order polynomials of creation and annihilation para-Bose operators with arbitrary order of parastatistics. In the Fock space ℋ ₂ ¹ of two Bose operators all the irreducible representations of the para-Fermi algebra are realised. The spaces ofn-particle Bose statesn=1,2,..., from which ℋ ₂ ¹ is constructed as a direct sum, can be interpreted as spaces of para-Fermi states of para-statisticsn.     

Kinetic equation for a weakly nonideal Bose gas

A kinetic equation for a weakly nonideal Bose gas is derived in the range where the thermal wavelength (λ_T) is less than or on the order of the mean interatomic distance (r ₀). The case when λ_T > r ₀ is discussed.     

Bose-Einstein condensation in dense quark matter

We consider the problem of Bose condensation of charged pions in QCD at finite isospin chemical potential μ_I using the O(4)-symmetric linear sigma model as an effective field theory for two-flavor QCD. Using the 2PI 1/N-expansion, we determine the quasiparticle masses as well as the pion and chiral condensates as a function of the temperature and isospin chemical potential in the chiral limit and at the physical point. The calculations show that there is a competition between the condensates. At T=0, Bose condensation takes place for chemical potentials larger than μ_π. In the chiral limit, the chiral condensate vanishes for any finite value of μ_I.     

Transport properties of the disordered charged bose condensate in two dimensions

Analytical results for the frequency-dependent conductivity of a disordered two-dimensional interacting Bose condensate are presented. Charged and uncharged impurities are considered. We find that for weak disorder the condensate is a superfluid while for strong disorder it is an insulator (a Bose glass). At the superfluid-insulator transition point (at the critical boson densityN _c) the condensate exhibits metallic tranport properties. An loffe-Regel criterion for the transition point is derived. The conductivity at the transition point is of ordere ²/h (h is Planck's constant) and depends on the kind of disorder. For charged impurities (with impurity densityN _i) the conductivity (for a condensate of particles with charge 2e and forN _i=2N _c) at the transition point is given by _c =0.26x(2e)²/h. We discuss recent experiments on superconducting ultra-thin films and on high-T _c superconductors.     

Free Energies of Dilute Bose Gases: Upper Bound

We derive an upper bound on the free energy of a Bose gas at density ϱ and temperature T. In combination with the lower bound derived previously by Seiringer (Commun. Math. Phys. 279(3): 595–636, 2008), our result proves that in the low density limit, i.e., when a ³ ϱ≪1, where a denotes the scattering length of the pair-interaction potential, the leading term of Δf, the free energy difference per volume between interacting and ideal Bose gases, is equal to 4pa(2r²-[r-r_c]²₊)4\pi a(2\varrho^{2}-[\varrho-\varrho_{c}]^{2}_{+}). Here, ϱ _c (T) denotes the critical density for Bose–Einstein condensation (for the ideal Bose gas), and [⋅]₊=max {⋅,0} denotes the positive part.     

Dynamic d-symmetry Bose condensate of a planar-large-bipolaron liquid in cuprate superconductors

Abstract

Planar-large-bipolarons can form if the ratio of the surrounding mediums’ static to high-frequency dielectric constants is especially large, ε₀/ε_∞ >> 2. A large-bipolaron in p-doped La₂CuO₄ is modelled as two electrons being removed from the out-of-plane orbitals of four oxygen ions circumscribed by four copper ions of a CuO₂ layer. These oxygen dianions relax inwardly as they donate electrons to the surrounding outwardly relaxing copper cations. This charge transfer generates the strong in-plane electron–lattice interaction needed to stabilise a large-bipolaron with respect to decomposing into polarons. The lowest-energy radial in-plane optic vibration of a large-bipolaron’s four core oxygen ions with their associated electronic charges has d-symmetry. Electronic relaxation in response to multiple large-bipolarons’ atomic vibrations lowers their frequencies to generate a phonon-mediated attraction among them which fosters their condensation into a liquid. This liquid features distinctive transport and optical properties. A large-bipolaron liquid’s superconductivity can result when it undergoes a Bose condensation yielding macroscopic occupation of its ground state. The synchronised vibrations of large-bipolarons’ core-oxygen ions with their electronic charges generate this Bose condensate’s dynamic global d-symmetry.     

Relaxation of the ideal Bose gas

For the ideal Bose gas we study the approach to equilibrium. Above the critical temperature we prove exponential behaviour, with a relaxation time of the order (T-T _c)^-2 around T _c. For T _c we find the t ^-1 law for the two-point function.     

Quantum limit for the atom-light interferometer

The standard quantum limit is calculated for the atom-light interferometer. It is shown that the smallest detectable phase is $$\delta \phi _{\min } = \frac{1}{2}[N_{atoms} + 4N_{photons} )/N_{atoms} N_{photons} ]^{1/2} .$$ Therefore, in practical experiments, the accuracy is limited by the square root of the number of atoms. We propose a novel correlated atom-photon state interferometer which makes a transition to the Heisenberg limit, δφ_min ∝ 1/N _atoms, as the atoms approach a Bose condensate. Such an interferometer may serve as a sensitive probe of the onset of Bose condensation. Finally, we point out that the correlated atom-photon state preparation scheme we propose may be used in a different way to approach the Heisenberg limit for non-Bose-condensed atoms.     

A symmetry relating certain processes in 2-and 4-dimensional space-times and the value α0 = 1/4π of the bare fine structure constant

The symmetry manifests itself in exact relations between the Bogoliubov coefficients for processes induced by an accelerated point mirror in 1 + 1 dimensional space and the current (charge) densities for the processes caused by an accelerated point charge in 3 + 1 dimensional space. The spectra of pairs of Bose (Fermi) massless quanta emitted by the mirror coincide with the spectra of photons (scalar quanta) emitted by the electric (scalar) charge up to the factor e ²/ħc. The integral relation between the propagator of a pair of oppositely directed massless particles in 1 + 1 dimensional space and the propagator of a single particle in 3 + 1 dimensional space leads to the equality of the vacuum-vacuum amplitudes for the charge and the mirror if the mean number of created particles is small and the charge e = √ħc. Due to the symmetry, the mass shifts of electric and scalar charges (the sources of Bose fields with spin 1 and 0 in 3 + 1 dimensional space) for the trajectories with a subluminal relative velocity β₁₂ of the ends and the maximum proper acceleration w ₀ are expressed in terms of the heat capacity (or energy) spectral densities of Bose and Fermi gases of massless particles with the temperature w ₀/2π in 1 + 1 dimensional space. Thus, the acceleration excites 1-dimensional oscillation in the proper field of a charge, and the energy of oscillation is partly deexcited in the form of real quanta and partly remains in the field. As a result, the mass shift of an accelerated electric charge is nonzero and negative, while that of a scalar charge is zero. The symmetry is extended to the mirror and charge interactions with the fields carrying spacelike momenta and defining the Bogoliubov coefficients α^B,F. The traces trα^B,F, which describe the vector and scalar interactions of the accelerated mirror with a uniformly moving detector, were found in analytic form for two mirror trajectories with subluminal velocities of the ends. The symmetry predicts one and the same value e ₀ = √ħc for the electric and scalar charges in 3 + 1 dimensional space. Arguments are adduced in favor of the conclusion that this value and the corresponding value α₀ = 1/4π of the fine structure constant are the bare, nonrenormalized values. The text was submitted by the author in English.     

Long Cycles in a Perturbed Mean Field Model of a Boson Gas

In this paper we give a precise mathematical formulation of the relation between Bose condensation and long cycles and prove its validity for the perturbed mean field model of a Bose gas. We decompose the total density ρ=ρ_short+ρ_long into the number density of particles belonging to cycles of finite length (ρ_short) and to infinitely long cycles (ρ_long) in the thermodynamic limit. For this model we prove that when there is Bose condensation, ρ_long is different from zero and identical to the condensate density. This is achieved through an application of the theory of large deviations. We discuss the possible equivalence of ρ_long≠ 0 with off-diagonal long range order and winding paths that occur in the path integral representation of the Bose gas     

Iterative Solutions of the Schrödinger Equation

In the first example containing a long ranged potential, the long range part of the solution is obtained by an iterative Born-series type method. The convergence is illustrated for a case with the long range part of the potential given by C ₆/r ⁶. Accuracies of 1 : 10⁸ are achieved after 8 iterations. The second example iteratively calculates the solution of a non-linear Gross–Pitaevskii equation for condensed Bose atoms contained in a trap at low temperature.