International Journal of Modern Physics B

Collective modes of bilayered superconducting superlattices (e.g., YBCO) are investigated within the conserving gauge-invariant ladder diagram approximation including both the nearest interlayer single electron tunneling and the Josephson-type Cooper pair tunneling. By calculating the density–density response function including Coulomb and pairing interactions, we examine the two collective mode branches corresponding to the in-phase and out-of-phase charge fluctuations between the two layers in the unit cell. The out-of-phase collective mode develops a long wavelength plasmon gap whose magnitude depends on the tunneling strength with the mode dispersions being insensitive to the specific tunneling mechanism (i.e., single electron or Josephson). We also show that in the presence of tunneling the oscillator strength of the out-of-phase mode overwhelms that of the in-phase-mode at k_‖ = 0 and finite k_z, where k_z and k_‖ are respectively the mode wave vectors perpendicular and along the layer. We discuss the possible experimental observability of the phase fluctuation modes in the context of our theoretical results for the mode dispersion and spectral weight.

It is shown that Poincaré's recurrence theorem incorporates Loschmidt's requirement for velocity reversion in thermodynamic gas systems. It differs essentially from Hamiltonian dynamics from which Boltzmann's H-theorem follows. The inverse automorphism, T^-1, on which is based the demonstration of the recurrence theorem does not exist for atoms and molecule systems. Thermodynamic systems need not spontaneously return to states they occupied in the past and a Zermelo paradox has never existed for them. The same conclusion follows a fortiori for quantum systems in chrono-topology. Poincaré's recurrence theorem does not conflict with Boltzmann's H-theorem because they apply to systems described by quite different mathematical structures.

We derive a McBryan–Spencer bound to the correlation function of a one-dimensional array of quantum rotators in the Villain approximation of the cosine interaction. We obtain the partition function of the system in the gas representation and establish a lower bound on the external charges correlation function. We also discuss the possible existence of a Kosterlitz–Thouless phase for the quantum rotators in the Villain approximation.

A new nonperturbative method calculating the one-particle Green's function is introduced and applied to the Hubbard model. We show the metal–insulator transition in the paramagnetic ground state of the half-filled Hubbard model on a Bethe lattice with infinite connectivity. This method describes the transition regime appropriately. The analytic result using the continued fraction formalism which has a close relationship with present formalism is provided for comparison. As for the Hubbard model with doping, we obtain the optical conductivities and show the interesting features, such as midinfrared band and isobestic point. We also show that the sharp frequency-dependent behavior at large doping is the dispersed Drude type in this model.

A full three-band model for the CuO₂ plane of cuprates, which includes all the essential interaction — Cu-O and O-O hopping and the Coulomb repulsion on the Cu and O sites and between them, is considered. Its antiferromagnetic ground state for the half-filling is studied by using the mean field approximation. The electronic structure and the magnetic properties such as the densities of states, the energy spectra, the composition of holes (Cu or O character), the superexchange interaction and the magnetic moment are calculated and in general, our results are in agreement with the available experimental and other calculation results. Meanwhile, we find that the influence of the O-O hopping and Cu-O intrasite Coulomb repulsion on these properties is considerable. Our estimate of the energy of the spin singlet state above the antiferromagnetic background indicates that the lowest excitation state of the holes is the singlet state and give a charge-transfer energy in agreement with the experiment. We also discuss the hole-doping to the antiferromagnetic background and find the mean field approach invalid. Finally, based on the electronic structure at the half-filling, en effective one-band Hubbard model is presented and the effective parameters are close to the values given by the computation on the clusters.

The effects of aluminum substitution into the M-type Ba-hexaferrites on the saturation magnetization and Mossbauer spectrum of these ferrites are studied. The saturation magnetization M_s of the BaFe_12-xAl_xO₁₂ is seen to decrease linearly with increasing Al substitution. The Mossbauer spectrums for the x = 0.1, 0.2 and 0.6 specimens were all resolved as superpositions of four sub-spectrums (12k, 4f_iv+2a, 4f_vi and 4e). The half width of the Mossbauer lines of the 4f_iv+2a sextets is seen to broadening as Al ions are substituted into the ferrite. No broadening is seen in the lines of the other sextets. These behaviors (the line broadening and the linear decrease in M_s) are consistent with the Al³⁺ ions substituting preferentially into the 2a sites.

We write effective propagators associated to: (1) A quantum particle interacting with a classical gas and a quantum bosonic gas, modeling friction environments. (2) A noisy and quantum phonon field modeling friction environment at zero temperature. These studies are implemented by means of the Bell functional integrals representing these external dissipative environments.

We study the interatomic correlations and mean square relative displacements (MSRD) in anharmonic crystals on the basis of the correlative method of unsymmetrized self-consistent field (CUSF). Here we present general formulae for crystals with the anharmonicity, including the strong one, up to the fourth anharmonic terms and perform calculations of the quadratic correlation moments (QCM) in a crystal with face centered cubic lattice, namely in solid Ar. The second order of CUSF allows one to investigate correlations in this lattice between the nearest, second, third and fourth neighbors. The anharmonicity was demonstrated to have strong effect on the interatomic correlations at temperatures above 0.4 of the melting temperature causing a drastic rise near the spinodal point. The dependence of QCM on the distance between atoms and on the crystallographic direction is discussed.

A computational study of population dynamics in a primitive life form model is presented. The spatio-temporal dependencies of density were calculated for different values of the control parameters (birth and death rates). The calculations have shown that the dynamics of the investigated system lead to the formation of patterns and self-organization only for a certain dependence between the control parameters.