A simple mathematical model for anomalous diffusion via Fisher's information theory

Starting with the relative entropy based on a previously proposed entropy function , we find the corresponding Fisher's information measure. After function redefinition we then maximize the Fisher information measure with respect to the new function and obtain a differential operator that reduces to a space coordinate second derivative in the q→1 limit. We then propose a simple differential equation for anomalous diffusion and show that its solutions are a generalization of the functions in the Barenblatt-Pattle solution. We find that the mean squared displacement, up to a q-dependent constant, has a time dependence according to 〈x²〉∼K1/qt1/q, where the parameter q takes values (superdiffusion) and (subdiffusion), ∀n?1.     

Sufficient and necessary condition of separability for generalized Werner states

In a celebrated paper [Optics Communications 179, 447, 2000], A.O. Pittenger and M.H. Rubin presented for the first time a sufficient and necessary condition of separability for the generalized Werner states. Inspired by their ideas, we generalized their method to a more general case. We obtain a sufficient and necessary condition for the separability of a specific class of N d-dimensional system (qudits) states, namely special generalized Werner state (SGWS): , where is an entangled pure state of N qudits system and α_i satisfies two restrictions: (i) ; (ii) Matrix , where , is a density matrix. Our condition gives quite a simple and efficiently computable way to judge whether a given SGWS is separable or not and previously known separable conditions are shown to be special cases of our approach.     

Remarks on the star product of functions on finite and compact groups

We show that the characters of irreducible unitary representations of finite groups and compact Lie groups provide kernels of star-product on complex valued functions f(g) of the group elements g. Examples of permutation groups of two and three elements as well as SU(2) group are considered. The k-deformed star products of the functions of finite and compact Lie groups are presented. The explicit form of the quantizers and dequantizers as well as the duality symmetry of the considered star products of the functions on the finite and compact Lie groups are discussed.     

Random walks and diameter of finite scale-free networks

Dynamical scalings for the end-to-end distance R_ee and the number of distinct visited nodes N_v of random walks (RWs) on finite scale-free networks (SFNs) are studied numerically. 〈R_ee〉 shows the dynamical scaling behavior , where is the average minimum distance between all possible pairs of nodes in the network, N is the number of nodes, γ is the degree exponent of the SFN and t is the step number of RWs. Especially, in the limit t→∞ satisfies the relation , where d is the diameter of network with for γ≥3 or for γ<3. Based on the scaling relation 〈R_ee〉, we also find that the scaling behavior of the diameter of networks can be measured very efficiently by using RWs.     

Quantum mechanics of Klein-Gordon-type fields and quantum cosmology

With a view to address some of the basic problems of quantum cosmology, we formulate the quantum mechanics of the solutions of a Klein-Gordon-type field equation: (∂_t²+D)ψ(t)=0, where and D is a positive-definite operator acting in a Hilbert space . In particular, we determine all the positive-definite inner products on the space of the solutions of such an equation and establish their physical equivalence. This specifies the Hilbert space structure of uniquely. We use a simple realization of the latter to construct the observables of the theory explicitly. The field equation does not fix the choice of a Hamiltonian operator unless it is supplemented by an underlying classical system and a quantization scheme supported by a correspondence principle. In general, there are infinitely many choices for the Hamiltonian each leading to a different notion of time-evolution in . Among these is a particular choice that generates t-translations in and identifies t with time whenever D is t-independent. For a t-dependent D, we show that regardless of the choice of the inner product the t-translations do not correspond to unitary evolutions in , and t cannot be identified with time. We apply these ideas to develop a formulation of quantum cosmology based on the Wheeler-DeWitt equation for a Friedman-Robertson-Walker model coupled to a real scalar field with an arbitrary positive confining potential. In particular, we offer a complete solution of the Hilbert space problem, construct the observables, use a position-like observable to introduce the wave functions of the universe (which differ from the Wheeler-DeWitt fields), reformulate the corresponding quantum theory in terms of the latter, reduce the problem of the identification of time to the determination of a Hamiltonian operator acting in , show that the factor-ordering problem is irrelevant for the kinematics of the quantum theory, and propose a formulation of the dynamics. Our method is based on the central postulates of nonrelativistic quantum mechanics, especially the quest for a genuine probabilistic interpretation and a unitary Schrödinger time-evolution. It generalizes to arbitrary minisuperspace (spatially homogeneous) models and provides a way of unifying the two main approaches to the canonical quantum cosmology based on these models, namely quantization before and after imposing the Hamiltonian constraint.     

Origin of photoluminescence in nanocrystalline Si:H films

We have studied the origin of photoluminescence (PL) from hydrogenated nanocrystalline silicon (nc-Si:H) films produced by a plasma-enhanced chemical vapor deposition technique using SiF₄/SiH₄/H₂ gas mixtures. The nc-Si:H films were characterized using X-ray diffraction, infrared, Raman spectroscopy, optical absorption and stress, and were examined for PL by varying the deposition temperature (T_d) under two different hydrogen flow rate ([H₂]) conditions. The PL exhibited two peaks at around 1.7-1.75 and 2.2-2.3 eV. The peak energy, E_PL, of the 1.7-1.75-eV PL band was found to shift as T_d or [H₂] changes. It was found that the decrease in T_d acts to decrease the average grain size, 〈δ〉, and to increase both the optical band gap, , and the E_PL values. By contrast, the increase in [H₂] decreased the 〈δ〉 value, while increased the values of and E_PL. Thus, as either T_d decreases or [H₂] increases, it is found that a decrease in 〈δ〉 corresponds well with increases in and E_PL. As a consequence, it was suggested that an increase in E_PL of the 1.7-1.75-eV PL band can be connected with an increase in , through a decrease in 〈δ〉. However, the PL process cannot be connected with the transition between both the bands, related to formation of nanocrystals. Based on these results, it was proposed that the use of both low T_d and high [H₂] conditions would allow to grow nc-Si:H films with small grains.     

Computation of energy exchanges by combining information theory and a key thermodynamic relation: Physical applications

By considering a simple thermodynamic system, in thermal equilibrium at a temperature T and in the presence of an external parameter A, we focus our attention on the particular thermodynamic (macroscopic) relation . Using standard axioms from information theory and the fact that the microscopic energy levels depend upon the external parameter A, we show that all usual results of statistical mechanics for reversible processes follow straightforwardly, without invoking the Maximum Entropy principle. For the simple system considered herein, two distinct forms of heat contributions appear naturally in the Clausius definition of entropy, . We give a special attention to the amount of heat , associated with an infinitesimal variation at fixed temperature, for which a “generalized heat capacity”, , may be defined. The usefulness of these results is illustrated by considering some simple thermodynamic cycles.     

Optical phonon modes and structure of ZnGa2Se4 and ZnGa2S4

We present the infrared and Raman study of the optical phonon modes of the defective compounds ZnGa₂Se₄ and ZnGa₂S₄. Most of the compounds have been found to crystallize in the thiogallate structure (defect chalcopyrite) with space group where all cations and vacancies are ordered. For some Zinc compounds a partially disordered cationic sublattice with various degrees of cation and vacancy statistical distribution, which lead to the higher symmetry (defect stannite), has been reported. For ZnGa₂Se₄ we have found three modes of A symmetry, showing Raman activity only. In addition, we have observed each five modes of B and E symmetry, showing infrared as well as Raman activity. The number of modes and their symmetry assignment, based on polarized measurements, clearly indicate space group for the investigated crystals of ZnGa₂Se₄.Regarding ZnGa₂S₄ we have found three modes exclusively showing Raman activity (2A⊕1B₁), and only eight modes showing infrared as well as Raman activity (3B₂⊕5E). The assignment of the modes has been derived by analyzing the spectral positions of the vibrational modes in comparison to a number of compounds. From the number and symmetry assignment of the optical phonon modes we confirm that ZnGa₂S₄ most likely crystallizes in space group .     

The q-gamma and (q,q)-polygamma functions of Tsallis statistics

An axiomatic definition is given for the q-gamma function of Tsallis (non-extensive) statistical physics, the continuous analogue of the q-factorial of Suyari [H. Suyari, Physica A 368 (1) (2006) 63], and the q-analogue of the gamma function of Euler and Gauss. A working definition in closed form, based on the Hurwitz and Riemann zeta functions (including their analytic continuations), is shown to satisfy this definition. Several relations involving the q-gamma and other functions are obtained. The (q,q)-polygamma functions , defined by successive derivatives of , where ln_qa=(1−q)⁻¹(a^1−q−1),a>0 is the q-logarithmic function, are also reported. The new functions are used to calculate the inferred probabilities and multipliers for Tsallis systems with finite numbers of particles N?∞.     

A novel realization of the Virasoro algebra in number state space

The group of diffeomorphisms is crucial in quantum computing. Representing it by vector fields over a d-manifold, d?2, accounting for both projective action and conformal symmetry at the quantum mechanical level, requires the direct-sum decomposition of tensor product for non-compact algebras, viable only for su(1,1). As a step towards the solution, a realization of the (d=1) Virasoro algebra Vir∼Diff₊(S(1)) in the universal envelope of su(1,1) (and h(1)) is presented, which is simple in the discrete positive series irreducible unitary representation of su(1,1).     

Electronic structure of (0 0 1) AlN/GaN quantum wells by means of a spsd empirical tight-binding Hamiltonian

We have studied the electronic band structure of (0 0 1) AlN/GaN quantum wells by means of a sp³s^∗d⁵ empirical tight-binding Hamiltonian with nearest-neighbor interactions, including spin-orbit coupling and the effects of strain together with the surface Green function matching method. We have analyzed quantum wells with a thickness in the range 2 ? n ? 50, n being the number of principal layers of GaN in the well region. Results are presented for the point and the direction of the 2D Brillouin zone. The orbital character and the spatial localization of the different states have been also studied.     

Radiative corrections with 5D mixed position-/momentum-space propagators

In higher dimensional field theories with compactified dimensions there are three standard ways to do perturbative calculations: (i) by the summation over Kaluza-Klein towers; (ii) by the summation over winding numbers making use of the Poisson-resummation formula; and (iii) by using mixed propagators, where the coordinates of the four infinite dimensions are Fourier-transformed to momentum space while those of the compactified dimension are kept in configuration space. The third method is broadly used in finite temperature field theory calculations. One of its advantages is that one can easily separate the ultraviolet divergent terms of the uncompactified theory from the non-local finite corrections arising from windings around the compact dimensions. In this note we demonstrate the use of this formalism by calculating one-loop self-energy corrections in a 5D theory formulated on the manifold and on the orbifold .     

Magnetic states and exchange interaction in hexagonal MnFeAs: A first principles study

The electronic structure and magnetic states for hexagonal-MnFeAs have been studied by a first-principles density functional theory (DFT) calculation. The ground state is ferromagnetic and the calculated magnetic moments for Fe and Mn are 1.1 and 3.1μ_B, respectively, leading to a total magnetization of 4.1μ_B per formula unit due to the small negative moments of As atoms. The exchange interaction between Fe and Mn layers () is positive and tends to form the ferromagnetic ordering. On the other hand, the exchange interaction at the Fe-As₁ layer () is negative while that at the Mn-As₂ layer () is positive. The field induced first order magnetic transition at T_C is related to the competed exchange interaction in the compound.     

A relativistic wave equation for the Skyrmion

We propose a relativistically invariant wave equation for the Skyrme soliton. It is a differential equation on the space R^1,3×S³ which is invariant under the Lorentz group and isospin. The internal variable valued in SU(2)≡S³ describes the orientation of the soliton. The mass of a particle of spin and isospin both equal to is predicted to be which agrees with the known spectrum for low angular momentum. The iso-scalar magnetic moment is predicted to be , where Σ is the spin.