[en] The equation-of-motion technique is used within the random-phase-approximation to calculate the plasma frequency of the electron gas at zero temperature in the finite layered model of Visscher and Falicov with free surfaces. The plasma frequencies are given by the eigenvalues of a Toeplitz matrix. This matrix describes the Coulomb coupling between the plasmons which propagate in different layers. It is shown that this matrix splits into two parts: one which corresponds to the cyclic boundary condition imposed on the system of double thickness and the other due to the presence of the surfaces. The first contribution can be exactly diagonalized and the other one can be treated as a small perturbation for a sufficiently large number of layers. The first-order perturbation theory is applied to obtain finite-size corrections to the plasma frequency. (author)

[en] A high-temperature mechanism of superconductivity is proposed for distorted perovskite-like structures of Ba_xLa_2-xCuO₄ type. For x close to unity it is shown that the Jahn-Teller effect of the CU²⁺ cations might bring about an attractive pairing interaction in the wavevector space. In the opposite limit x ∼ 0 it is argued that the Coulomb repulsion might cause a real-space electron pairing. In both cases optimal values of the concentration x are predicted above 1-1/π and below 1/π which agree with the experimental data. The corresponding critical temperatures are also estimated. (author). 15 refs

[en] A phase representation is given for two complex, canonical conjugate, classical fields in one dimension. These basic fields are used to analyze the one-dimensional classical sine-Gordon (SG) model and, in particular, its soliton solutions. First-order correlation functions (structure factors) are calculated within the one-soliton approximation and in the low temperature limit. Possible applications are discussed of the phase representation to estimate the thermodynamics of the classical SG model shedding some light on the relationship between its classical and quantum-mechanical versions.(author)

[en] The plasma frequency of a degenerate electron gas in the layer model of Visscher and Falicov is calculated by means of both the Bohm-Pines canonical transformation method and the equation-of-motion method in the RPA. The dispersion equation for plasmons is obtained in a finite system of n planes with both the cyclic condition and free ends. It is shown that the thermodynamic limit (n → infinite) of the plasma frequency is independent of the boundary conditions. The previous results obtained by various authors in different ways are shown to be certain limits of our result. (orig.)

[en] Highlights: • New method for rotation molecular spectra in high electric fields. • Parametric resonances – new features in spectra. • New elementary excitations in polar solids from dipolar interaction (“dipolons”). • Discussion about a possible origin of the ferroelectricity from dipolar interactions. - Abstract: Molecular rotation spectra, generated by the coupling of the molecular electric-dipole moments to an external time-dependent electric field, are discussed in a few particular conditions which can be of some experimental interest. First, the spherical-pendulum molecular model is reviewed, with the aim of introducing an approximate method which consists in the separation of the azimuthal and zenithal motions. Second, rotation spectra are considered in the presence of a static electric field. Two particular cases are analyzed, corresponding to strong and weak fields. In both cases the classical motion of the dipoles consists of rotations and vibrations about equilibrium positions; this motion may exhibit parametric resonances. For strong fields a large macroscopic electric polarization may appear. This situation may be relevant for polar matter (like pyroelectrics, ferroelectrics), or for heavy impurities embedded in a polar solid. The dipolar interaction is analyzed in polar condensed matter, where it is shown that new polarization modes appear for a spontaneous macroscopic electric polarization (these modes are tentatively called “dipolons”); one of the polarization modes is related to parametric resonances. The extension of these considerations to magnetic dipoles is briefly discussed. The treatment is extended to strong electric fields which oscillate with a high frequency, as those provided by high-power lasers. It is shown that the effect of such fields on molecular dynamics is governed by a much weaker, effective, renormalized, static electric field.

[en] The Ward identity is derived for non-relativistic fermions with two-body spin-independent interaction. Using this identity for the one-dimensional Fermi gas with backward scattering the equations of the perturbation theory are solved for the effective interaction and the collective excitations of the particle density fluctuations are obtained. (author)

[en] It is shown that the usual cut-off procedure (α cut-off parameter) employed in the boson representation of the fermion field opepators of the one-djmensional two-fermion model (TFM) is an incorrect one as the computator of the hermitean-conjugate field operators at the same space-point fails to fulfil a certain relationship which was pointed out long ago by Jordan. The complete form of the boson representation (including the zero-mode) of a single fermion field and the correct values of the cut-off parameter α is reviewed following Jordan and generalized to the TFM. The cut-off parameter α corresponds to a bandwidth cut-off and Jordan's boson representation is exact only in the limit α → 0. The additional zero-mode terms make the exact solution of the backscattering and umklapp scattering problem to be valid only if a supplementary condition is imposed on the coupling constants. Using the present bosonization technique all the inconsistencies of the TFM are removed. The one-particle Green's function and response functions of the Tomonaga-Luttinger model (TLM) are calculated and found to be identical with those obtained by direct diagram summation. The energy gap appearing in the spectrum of the TFM with backscattering and umklapp scattering for certain values of the coupling constants is shown to be proportional to the momentum transfer cut-off γ^-1 which has to be kept finite while α goes to zero. Under such conditions the anticommunication relations and Jordan's commutator are invariant under the canonical transformation on the boson operators that diagonalizes the Hamiltonian of the TLM. The charge-density response function of the TFM with backscattering is perturbationally calculated up to the first order. The cut-off α^-1 applies in the same way to terms which differ only by their spin indices in the expression of this response function. The charge-density response function is also evaluated at low frequencies for the exactly soluble TFM with backscattering by using Jordan's cut-off procedure. (author)

No abstract available

[en] The operators of the particle-density fluctuations in two- and three-dimensional many-fermion systems are written down using polar coordinates in the wave-vector space. Assuming low-lying excited states only, the angular parts of these operators are expressed in terms of the Tomonaga boson operators. The decoupling of the Hamiltonian of the fermion-density oscillations is performed with respect to the angular coordinates by means of a simple orthogonal transform. The remaining one-dimensional boson Hamiltonian is diagonalized afterwards using the Mattis-Lieb canonical transform. In order to include higher-order effects in the frequency of the density waves, the Tomonaga one-dimensional model is generalized to two- and three-dimensional systems. The dispersion relation is derived by means of the equation-of-motion technique. (author)

[en] The Ward identity, relating the three-legged vertex function to the Green function, is derived for the one-dimensional normal many-fermion system making use of the equation of motion for the vertex function as well as by means of the gauge invariance of the system. The interaction of the system is taken either as a forward scattering or as a backward scattering. In the latter case only one momentum transfer is allowed. (author)