A. Yu. Zakharov

Exact calculation method of the partition function for one-component classical systems with two-body interactions

Abstract We give an exact procedure for the evaluation of the partition function of classical systems with arbitrary two-body interactions.

Classical statistics of one-component systems with model potentials

We obtain a functional integral representation on the configuration integral for one-component classical systems with two-particle potentials admitting the Fourier expansion. In this representation, the integrand is factored with respect to the atomic coordinates. The “monoatomic” factors are universal (i.e., independent of the explicit form of the interatomic potential). We obtain a sufficient condition for spontaneous symmetry breaking in continuous classical statistics models. We investigate the case of model potentials with a nonnegative Fourier transform. The functional integral for this class of potentials is calculated using the saddle-point method. We prove the existence of phase transitions for some model potentials.

Forbidden band width change in semiconductor substitution alloys

Abstract The present paper deals with the isovalent substitution impurity influence on the forbidden band width in semiconductors. The expression for the forbidden band width change due to impurity potential is obtained for two-band model. It is shown that regularities found experimentally are explained by this model.

Anomalous Properties of Crystalline Methane in the Range of 60-70 K

Mechanical, structural, thermal, and spectral properties of solid methane in the temperature range 0.5Ttr-Ttr (Ttr is the triple point) at the equilibrium vapor pressure have been analyzed. It has been shown that the totality of observed anomalies in the temperature range of 60–70 K can be explained by the existence of collective rotational degrees of freedom in solid methane.

Hysteresis curves for ferroelectric crystals in a varying external field. Relaxation model

We propose a description of switching in ferroelectric crystals using the equations of relaxation processes taking into account the action of a varying external electric field. Exact analytic solutions to these equations are obtained for an arbitrary dependence of the relaxation time on the external field and an arbitrary time dependence of the external field. The resultant solution forms the basis of numerical analysis of coupling between the frequency of the sinusoidal external field and the shape of the hysteresis curves. The results of calculations are in qualitative agreement with experimental data.

The concept of elementary excitations in classical statistical mechanics

Exact representations of the generating functional of one-component classical systems with a central interatomic interaction potential are obtained in terms of the functional integrals over auxiliary fields determined in the wavevector space. It is proved that the problem of calculating a classical partition function for a system of particles with an arbitrary interatomic interaction potential is equivalent to the problem of calculating a statistical integral for a system of interacting oscillators with a temperature-dependent Hamiltonian.

Conductivity of disordered structures

Abstract The theory of the disordered alloy conductivity on the basis of Kadanoff-Baym equations was constructed. In the case of the alloy with the short-range impurity potential the “tails” of density of states should appear at low temperatures and conductivity becomes proportional to [φ(T)/T] exp {−λ/T 3 2 } . The theory is applicable at arbitrary impurity concentrations and at any impurity potential strength.

Effect of dislocations on the structural order parameter in a crystal upon torsional strain

The interaction of the structural subsystem with dislocations upon applying an elastic torsional strain has been studied. The consideration is performed in the terms of the Landau phenomenological theory with the refusal from the approximation that the irreducible vector magnitudes are constant. It is shown that additional spatial amplitude and frequency oscillations related to the change in the magnitudes of the structural order parameter and the dislocation density appear.

Low-frequency internal friction as express-method for identification of cryocrystals in pores of the solids

Abstract We show that studying of low-frequency internal friction (LFIF) of solid samples at low temperatures allows determining the presence of various gases absorbed, for some reasons, in pores and caverns of the solids. The gases come over to a solid state (cryocrystals) and exist in the pores under corresponding thermodynamic conditions giving an additional contribution to the LFIF spectra. The spectra reflect the special points of the gases (temperatures of melting or phase transitions). This information gives a real opportunity for identification of gas in the matrix, i.e. the studied solids. This may be of great importance for investigations of cosmic or geological samples, for instance, asteroids, meteorites, rock formations, etc. The LFIF method allows identification of gas media surrounding the studied sample.

Simulation of hysteresis curves of crystalline ferroelectrics using the controlling electric field parameters

We propose a description of switching in crystalline ferroelectrics taking into account the action of a varying external electric field, based on the equations of relaxation processes. We suppose that the probability of switching of domains depends not only on the instantaneous value of the controlling field, but also on the rate of its variation. The time dependence of the controlling field is defined by an arbitrary periodic function. The equations of the domain switching processes in a ferroelectric are derived and the exact analytic solutions to these equations are obtained. Numerical analysis of the interrelation between the frequency of the sinusoidal external field and the shape of the hysteresis curves is carried out on the basis of the resultant solutions. It is shown that the inclusion of the dependence of relaxation time on the rate of the controlling field variation makes it possible to sufficiently improve the agreement between the results of simulation of the ferroelectric hysteresis curves and the experimental data.