Fluctuations and Landau-Devonshire expansion for barium titanate

The experimentally observed temperature dependence of the quartic coefficients in the Landau-Devonshire expansion for BaTiO_3 is naturally accounted for within a proper fluctuation model. It is explained, in particular, why one of the quartic coefficients varies with temperature above T_c while the second is constant. The tetragonal phase in BaTiO_3 is argued to exist essentially due to the thermal fluctuations, while the true Landau-Devonshire expansion with temperature-independent coefficients favours the rhombohedral ferroelectric phase. Certain conclusions concerning the temperature dependence of the sextic Landau-Devonshire coefficients are also made.Comment: Minor changes, 1 reference added, published versio

Renormalization group and nonlinear susceptibilities of cubic ferromagnets at criticality

For the three-dimensional cubic model, the nonlinear susceptibilities of the fourth, sixth, and eighth orders are analyzed and the parameters \delta^(i) characterizing their reduced anisotropy are evaluated at the cubic fixed point. In the course of this study, the renormalized sextic coupling constants entering the small-field equation of state are calculated in the four-loop approximation and the universal values of these couplings are estimated by means of the Pade-Borel-Leroy resummation of the series obtained. The anisotropy parameters are found to be: \delta^(4) = 0.054 +/- 0.012, \delta^(6) = 0.102 +/- 0.02, and \delta^(8) = 0.144 +/- 0.04, indicating that the anisotropic (cubic) critical behavior predicted by the advanced higher-order renormalization-group analysis should be, in principle, visible in physical and computer experiments.Comment: 10 pages, LaTeX, no figures, published versio

Light trapping in an ensemble of point-like impurity centers in Fabry-Perot cavity

We report the development of quantum microscopic theory of quasi-resonant dipole-dipole interaction in the ensembles of impurity atoms imbedded into transparent dielectric and located into Fabry-Perot cavity. On the basis of the general approach we study the simultaneous influence of the cavity and resonant dipole-dipole interaction on the shape of the line of atomic transition as well as on light trapping in dense impurity ensembles. We analyze this influence depending on the size of the ensemble, its density, as well as on r.m.s. deviation of the transition frequency shifts caused by the symmetry disturbance of the internal fields of the dielectric medium. Obtained results are compared with the case when the cavity is absent. We show that the cavity can essentially modify cooperative polyatomic effects.Comment: 11 pages, 4 figure

Paraelectric in a Strong High-Frequency Field

A change in the effective permittivity of a ferroelectric film in the paraelectric phase under the action of a strong high-frequency field (nonequilibrium soft mode heating) is considered. It is shown that this effect must be most clearly pronounced far from the resonance (\omega_0 << \omega_sm), rather than for the external field frequency \omega_0 close to the soft mode frequency \omega_sm. The effective permittivity as a function of the high-frequency field amplitude is calculated using the phenomenological approach and within the microscopic theory based on the simple model of a displacement-type ferroelectric.Comment: 3 two-column page

Small-World Rouse Networks as models of cross-linked polymers

We use the recently introduced small-world networks (SWN) to model cross-linked polymers, as an extension of the linear Rouse-chain. We study the SWN-dynamics under the influence of external forces. Our focus is on the structurally and thermally averaged SWN stretching, which we determine both numerically and analytically using a psudo-gap ansatz for the SWN-density of states. The SWN stretching is related to the probability of a random-walker to return to its origin on the SWN. We compare our results to the corresponding ones for Cayley trees.Comment: 14 pages, 4 figures. Preprint version, submitted to JC

Pseudo-epsilon expansion and the two-dimensional Ising model

Starting from the five-loop renormalization-group expansions for the two-dimensional Euclidean scalar \phi^4 field theory (field-theoretical version of two-dimensional Ising model), pseudo-\epsilon expansions for the Wilson fixed point coordinate g*, critical exponents, and the sextic effective coupling constant g_6 are obtained. Pseudo-\epsilon expansions for g*, inverse susceptibility exponent \gamma, and g_6 are found to possess a remarkable property - higher-order terms in these expansions turn out to be so small that accurate enough numerical estimates can be obtained using simple Pade approximants, i. e. without addressing resummation procedures based upon the Borel transformation.Comment: 4 pages, 4 tables, few misprints avoide

The Spectra of Large Toeplitz Band Matrices with a Randomly Perturbed Entry

This report is concerned with the union $sp_{\Omega}^{(j,k)}T_{n}(a)$ of all possible spectra that may emerge when perturbing a large $n \times n$ Toeplitz band matrix $T_{n}(a)$ in the $(j,k)$ site by a number randomly chosen from some set $\Omega$. The main results give descriptive bounds and, in several interesting situations, even provide complete identifications of the limit of $sp_{\Omega}^{(j,k)}T_{n}(a)$ as $n \to \infty$. Also discussed are the cases of small and large sets $\Omega$ as well as the "discontinuity of the infinite volume case", which means that in general $sp_{\Omega}^{(j,k)}T_{n}(a)$ does not converge to something close to $sp_{\Omega}^{(j,k)}T_{n}(a)$ as $n \to \infty$, where $T(a)$ is the corresponding infinite Toeplitz matrix. Illustrations are provided for tridiagonal Toeplitz matrices, a notable special case. \ud \ud The second author was supported by UK Enginering and Physical Sciences Research Council Grant GR/M1241

Synchrotron radiation by fast fermions in heavy-ion collisions

We study the synchrotron radiation of gluons by fast quarks in strong magnetic field produced by colliding relativistic heavy-ions. We argue that due to high electric conductivity of plasma, time variation of the magnetic field is slow and estimate its relaxation time. We calculate the energy loss due to synchrotron radiation of gluons by fast quarks. We find that the typical energy loss per unit length for a light quark at LHC is a few GeV per fm. This effect alone predicts quenching of jets with $p_\bot$ up to about 20 GeV. We also show that the spin-flip transition effect accompanying the synchrotron radiation leads to a strong polarization of quarks and leptons with respect to the direction of the magnetic field. Observation of the lepton polarization may provide a direct evidence of existence of strong magnetic field in heavy-ion collisions.Comment: 10 pages, 6 figures; v3: estimate of the relaxation time of magnetic field is revised, acknowledgment adde