Zygmunt M. Galasiewicz

Microscopic theory of superfluid3He-superfluid4He solutions I. Derivation of hydrodynamic equations

The hydrodynamic equations for mixtures of superfluid3He and superfluid4He are derived on the basis of the microscopic theory proposed by Bogoliubov.

Onsager type relations for new-introduced kinetic coefficients connected with magnetic field in case of 3HeA, 3HeB

New terms describing dissipation are added to currents in the spin hydrodynamic equations for superfluid phases A and B of 3He. The terms contain kinetic coefficients connected with external magnetic field and nonconventional fields conjugated to the hydrodynamic variables describing suitable broken symmetries. Due to the Onsager type relations only two new coefficients in each phase (both connected with magnetic field) remain in the equations and can be expressed in terms of the “old” kinetic coefficients and some generalized susceptibilities. Experimental data for superfluid 3He may be able to provide information about “viscosity” of magnetic fields.

Enhancement of the Debye frequency due to a charged-boson exchange model of high temperature superconductors

Abstract A simple model of 1-2-3 superconductors in which electrons (holes) in CuO 2 planes interact via exchange with two kinds of bosons is considered. Namely, via one-phonon exchange (weak coupling-Cooper pairing), and via paired holes on oxygen O 0 from Cu-O chains. The mechanisms of paired holes exchange (“charged bosons”-“O 0 ” exchange) considered here in strong coupling leads to the enhancement of the Frohlich constant g f ( g 2 F → Kg 2 F ), and as a consequence to the enhancement of the Debye frequency ω D K = f K ω D , f K ≫ 1. In the proposed model the exact expression for the constant K is derived.

Microscopic theory of superfluid3He-superfluid4He solutions II. Acoustical approximation. Propagation of sounds

Linearized hydrodynamic equations for superfluid3He-superfluid4He solutions are examined. The addition of a new parameter, the velocity of the Fermi-pair condensate, increases the number of equations and, in consequence, the rank of the determinant of the equations. This leads to a new energy root of the determinant which describes an extra sound mode different from the first and second sound.

Remarks on the Uemura plot for weakly interacting charged Bose fluids

Abstract In the paper Enz and Galasiewicz [ Physica C 214 (1993) 239 ] one finds, for weakly repulsive Bose fluids the T c - n s relation which reproduces reasonably well the straight line part of “Uemura plot”. In the formula for superfluid density n s = n s ( t 1 , t ∼ 1) the integrals were presented as power series with respect to t 1 = t 1 ( t c ) ⪡ 1, where dimensionless parameters t 1 , t , t c describe interaction, temperature and critical temperature, respectively. Here, the integrals have been calculated numerically in a wider interval of parameters. Among new results we have found that, while for weak interaction t c > t c 0 ( t c 0 denotes critical temperature for free bosons), for the stronger one, like in superfluid helium 4, t c t c 0 . As concerns curves T c ( n s ) we find that in the “straight line” part the slight bending upward is local and very soon begins a much faster descent, like on the Uemura plot for type II high- T c superconductors. The lowest experimental data for carrier densities n s and m ★ = 5 m e lead to λ L ∼ 1000 A , ξ ∼ 1 A , T c ∼ 360 K .

STABILITY CONDITIONS FOR FERMION SYSTEMS

Abstract A new formulation of the generalized (Bogolyubov) Hartree-Fock variational principle is given. The functions which are subject to variations are quadratic forms in the functions which are varied in the method of Hartree-Fock or Bogolyubov. For the problem of nuclear matter the sign of the second variation of the average energy was examined for the solutions of the Hartree-Fock and Bogolyubov type.

KINETIC COEFFICIENTS CONNECTED WITH MAGNETIC FIELD IN CASE OF SUPERFLUID 3HE-B. II

The Onsager type relation show that it is necessary to introduce to the spin hydrodynamic equations for 3He B two new kinetic coefficients connected with magnetic field. The numerical values of necessary parameters have been found in Pleiners Doctoral Dissertation, Essen GHS (1977). The performed estimations give reasonable orders of magnitude for the magnetic field “viscosities”.

The influence of an external magnetic field and anisotropy on the “charge” Q(t, x) = divvs in 3He A

The normalization condition AijAij★ = 1 for the matrix order parameter describing 3He A leads to the relation dotAijAij★ + AijAij★ = 0, where dotAij denotes the equation of motion for Aij. It was shown that this relation is a condition for superfluid velocity vs of the form divvs = Q(t, x). If in the system the correlations and nonlocal dependences are important the “charge” Q(t, x) depends on the part of the density of magnetization m connected with the diffusive anisotropic mode and on an external magnetic field H.

Multi-time Green functions for systems evolving in time under unitary transformations. The linear, quadratic and higher order responses

Application of the unitary transformation, containing time dependent “external fields”, to the equation of motion for the density matrix and the Schrodinger equation leads to a self-consistent solution for the transformed density matrix and an expression for the transformed Hamiltonian. Knowing the change of the Hamiltonian and solving an integral equation we can get the equivalent solution for the density matrix. With help of this solution we can express changes of averages of suitable operators in terms of multi-time Green functions. Both equivalent, but of different form, solutions can be presented as infinite powre series in external fields (or a dimensionless parameter). Having two formulae for changes of averages we compare the coefficients of the nth power of the parameter. This gives us relations among multi-time Green functions. For superfluid 3He-B in the frame of linear response it is shown that the rotation of the spin system relative to the orbital one can be presented as rotation in the spin space. For the quadratic response all the basic equations containing the Green functions are written down explicitly.

Order parameter operator and equations of motion for quasi-conserved quantities for orbital 3He-A hydrodynamics

From the averaged order parameter operator equations of motion for unit vector l (describing broken rotational symmetry in real space) as well as for the local phase ϕ and superfluid velocity ν, were derived. Besides of the known condition for curl ν, the new condition for div ν, is derived.