The black-body radiation in Tsallis statistics

Some results for the black-body radiation obtained in the context of the $q$-thermostatistics are analyzed on both thermodynamical and statistical-mechanical levels. Since the thermodynamic potentials can be expressed in terms of the Wright's special function an useful asymptotic expansion can be obtained. This allows the consideration of the problem away from the Boltzmann-Gibbs limit $q=1$. The role of non-extensivity, $q<1$, on the possible deviation from the Stefan-Boltzmann $T^{4}$ behavior is considered. The application of some approximation schemes widely used in the literature to analyze the cosmic radiation is discussed.Comment: 11 pages, 1 figure. The present vesrion of the manuscript is larger. New references are adde

Casimir amplitudes in a quantum spherical model with long-range interaction

A $d$-dimensional quantum model system confined to a general hypercubical geometry with linear spatial size $L$ and ``temporal size'' $1/T$ ($T$ - temperature of the system) is considered in the spherical approximation under periodic boundary conditions. For a film geometry in different space dimensions $\frac 12\sigma <d<\frac 32\sigma$, where $0<\sigma \leq 2$ is a parameter controlling the decay of the long-range interaction, the free energy and the Casimir amplitudes are given. We have proven that, if $d=\sigma$, the Casimir amplitude of the model, characterizing the leading temperature corrections to its ground state, is $\Delta =-16\zeta(3)/[5\sigma(4\pi)^{\sigma/2}\Gamma (\sigma /2)]$. The last implies that the universal constant $\tilde{c}=4/5$ of the model remains the same for both short, as well as long-range interactions, if one takes the normalization factor for the Gaussian model to be such that $\tilde{c}=1$. This is a generalization to the case of long-range interaction of the well known result due to Sachdev. That constant differs from the corresponding one characterizing the leading finite-size corrections at zero temperature which for $d=\sigma=1$ is $\tilde c=0.606$.Comment: 10 pages latex, no figures, to appear in EPJB (2000

Algebraic techniques in designing quantum synchronizable codes

Quantum synchronizable codes are quantum error-correcting codes that can correct the effects of quantum noise as well as block synchronization errors. We improve the previously known general framework for designing quantum synchronizable codes through more extensive use of the theory of finite fields. This makes it possible to widen the range of tolerable magnitude of block synchronization errors while giving mathematical insight into the algebraic mechanism of synchronization recovery. Also given are families of quantum synchronizable codes based on punctured Reed-Muller codes and their ambient spaces.Comment: 9 pages, no figures. The framework presented in this article supersedes the one given in arXiv:1206.0260 by the first autho

Generalized Mittag-Leffler functions in the theory of finite-size scaling for systems with strong anisotropy and/or long-range interaction

The difficulties arising in the investigation of finite-size scaling in $d$--dimensional O(n) systems with strong anisotropy and/or long-range interaction, decaying with the interparticle distance $r$ as $r^{-d-\sigma}$ ($0<\sigma\leq2$), are discussed. Some integral representations aiming at the simplification of the investigations are presented for the classical and quantum lattice sums that take place in the theory. Special attention is paid to a more general form allowing to treat both cases on an equal footing and in addition cases with strong anisotropic interactions and different geometries. The analysis is simplified further by expressing this general form in terms of a generalization of the Mittag-Leffler special functions. This turned out to be very useful for the extraction of asymptotic finite-size behaviours of the thermodynamic functions.Comment: Accepted for publication in J. Phys. A: Math. and Gen.; 14 pages. The manuscript has been improved to help reader

Low-temperature regimes and finite-size scaling in a quantum spherical model

A $d$--dimensional quantum model in the spherical approximation confined to a general geometry of the form $L^{d-d^{\prime}} \times\infty^{d^{\prime}}\times L_{\tau}^{z}$ ($L$--linear space size and $L_{\tau}$--temporal size) and subjected to periodic boundary conditions is considered. Because of its close relation with the quantum rotors model it can be regarded as an effective model for studying the low-temperature behavior of the quantum Heisenberg antiferromagnets. Due to the remarkable opportunity it offers for rigorous study of finite-size effects at arbitrary dimensionality this model may play the same role in quantum critical phenomena as the popular Berlin-Kac spherical model in classical critical phenomena. Close to the zero-temperature quantum critical point, the ideas of finite-size scaling are utilized to the fullest extent for studying the critical behavior of the model. For different dimensions $1<d<3$ and $0\leq d^{\prime}\leq d$ a detailed analysis, in terms of the special functions of classical mathematics, for the free energy, the susceptibility and the equation of state is given. Particular attention is paid to the two-dimensional case.Comment: 36 pages, Revtex+epsf, 3 figures included. Some minor corrections are don