Exchange statistics in 1D: from the viewpoint of exact solution

We show that the exchange statistics have consequences in 1D systems with compact topology, contrary to the common opinion that exchange statistics is arbitrary in 1D. As examples of non-trivial statistical behavior we exactly calculate the partition function and correlators for systems of free q-particles on compactified chains using functional integral techniques and the supersymmetric trick. In particular we consider a spin 1/2 XY-chain with periodic boundary conditions that corresponds to the case of q=-1.Comment: A few formulae are corrected. A new formula for the generation function is adde

On the cosmological constant in quantum cosmology

Quantization of a dust-like closed isotropic cosmological model with a cosmological constant is realized by the method of B. DeWitt \cite{1}. It is shown that such quantization leads to interesting results, in particular, to a finite lifetime of the system, and appearance of the Universe in our world as penetration via the barrier. These purely quantum effects appear when $\Lambda>0$.Comment: This paper was published originally in "Problems of Gravitational Theory and Particle Theory", VNIIFTRI Proceedings, Moscow, 1972. v. 16(46), pp. 43-48 (in Russian). The English version was published in the journal "Gravitation & Cosmology" in 200

The Condition for the Onset of High Temperature Superconductivity

In this work the long-wave limit of electron-electron interaction arising from the exchange of virtual phonons in an approximation close to "jelly" model is considered. It is shown that the interaction through the exchange of virtual phonons is actually not screened in contrast to the Coulomb one; this just leads to instability relative to the formation of pairs near the Fermi surface. The consequences of this approach are examined with respect to high-temperature superconducting materials that have recently been synthesized. An approximate relationship connecting sound and Fermi velocities for these materials is obtained.Comment: 18 page

New approach to the superconductivity problem

In this work, a question is tackled concerning the formation of a superconducting condensate in an earlier proposed model of "elastic jelly", in which phonons of the ion system play the part of initiating ones. It was shown that in distinction from the BCS theory, the momenta of forming electron pairs are different from zero. This fact changes the pattern of the description of the superconductivity phenomenon in the proposed model. First, the gap in the one-electron spectrum appears due to the effect of a "mean field" on the energy of electron state from the side of occupied states, the nearest neighbors over the momenta grid. Second, the condensate is formed by electron states with energies below that of the gap edge, this is why the Fermi-condensation arises in the system. Third, anomalous expectation values are strictly equal to zero in the proposed model.Comment: 8 pages, 1 figur

Superconductivity in the Model of Elastic Jelly

In this work, a question is tackled concerning the formation of a superconducting condensate in an earlier proposed model of "elastic jelly", in which phonons of the valent skeleton play the part of initiating ones. It was shown that in distinction from the BCS theory, the momenta of forming electron couples are different from zero. This fact changes the pattern of the description of the superconductivity phenomenon in the proposed model. First, the gap in the one-electron spectrum appears due to the effect of a "mean field" on the energy of one-electron state from the side of occupied states, the nearest neighbors over the momenta grid. Second, the condensate is formed by one-electron states with energies below that of the gap edge. This is why the Fermi-condensation arises in the system. Third, in the proposed theory the electron couples appear in the form of low-energy excitations, i.e., as those with the minimum amount of energy per excitation electron. Hence, their role is minimized to that of low-energy excitation with the minimum energy per electron, and they are no more "bricks" the superconducting condensate is made of, as the case is in the BCS theory.Comment: 8 pages, 1 figur

Quantization of K\"ahler manifolds admitting HH-projective mappings

We discuss the quantization of mechanical systems for which the Hamiltonian vector fields of observables form the deformation of $n$-dimensional oscilator algebra. Because of this fact these systems can be considered as "deformations" of the harmonic oscillator. The set of abovementioned mechanical systems are realized at the classical level in the form of K\"ahler manifolds of constant holomorphic curvature. Such mechanical systems are quantized later with the help of the geometric quantization approach. We also discuss the quantization of more general K\"ahler manifolds (not necessarily of constant holomorphic curvature) admitting $H$-projective mappings.Comment: 11 pages, LaTe

New index formulas as a meromorphic generalization of the Chern-Gauss-Bonnet theorem

Laplace operators perturbed by meromorphic potential on the Riemann and separated type Klein surfaces are constructed and their indices are calculated by two different ways. The topological expressions for the indices are obtained from the study of spectral properties of the operators. Analytical expressions are provided by the Heat Kernel approach in terms of the functional integrals. As a result two formulae connecting characteristics of meromorphic (real meromorphic) functions and topological properties of Riemann (separated type Klein) surfaces are derived.Comment: LATEX, 14 page

Electrochemical Strain Microscopy with Blocking Electrodes: The Role of Electromigration and Diffusion

Electrochemical strains are a ubiquitous feature of solid state ionic devices ranging from ion batteries and fuel cells to electroresistive and memristive memories. Recently, we proposed a scanning probe microscopy (SPM) based approach, referred as electrochemical strain microscopy (ESM), for probing local ionic flows and electrochemical reactions in solids based on bias-strain coupling. In ESM, the sharp SPM tip concentrates the electric field in a small (10-50 nm) region of material, inducing interfacial electrochemical processes and ionic flows. The resultant electrochemical strains are determined from dynamic surface displacement and provide information on local electrochemical functionality. Here, we analyze image formation mechanism in ESM for a special case of mixed electronic-ionic conductor with blocking tip electrode, and determine frequency dependence of response, role of diffusion and electromigration effects, and resolution and detection limits.Comment: 41 pages, 10 figures, 3 appendices, accepted to J. Appl. Phy

Effective piezoelectric response of twin walls in ferroelectrics

The effective piezoelectric coefficients of twin walls in tetragonal ferroelectric are calculated in the framework of decoupling approximation and Landau-Ginzburg-Devonshire theory allowing for polarization gradient terms, electrostriction and flexoelectric coupling. Using an example of piezoelectric response of a1-a2 twins to a homogeneous electric field, we show that the response is almost independent on the flexoelectric coupling, but is very sensitive to the values of polarization gradient coefficients. This behavior originates from the strong coupling between local dielectric susceptibility and the gradient coefficients. The enhancement of piezoelectric response from 10% up to a factor of 103 times is predicted. The local electromechanical response of the domain walls can thus provide information on the gradient terms in GLD expansion and pinning mechanisms of the ferroelectric domain walls. The observability of these effects by the piezoresponse force microscopy of electroded structures and impact on the functional properties of the systems with dense domain structures is analyzedComment: 20 pages, 4 figures, 5 appendices, to be submitted to J. Appl. Phy

Exact results on linear response of cyclic molecular aggregates

Basing on the picture of Frenkel excitons in molecular crystals described by the XY-model we consider the linear response of linear cyclic aggregates at finite temperature. The exact results for characteristics of the response are obtained. In particular, we calculate time-dependent two-point correlation functions at finite temperature for the cyclic 1-D XY-model.Comment: LaTeX, 23 pages. few misprints were correcte