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.     

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 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.     

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.     

Quantum dynamical phase transition in a system with many-body interactions

Recent experiments, [G.A. Álvarez, E.P. Danieli, P.R. Levstein, H.M. Pastawski, J. Chem. Phys. 124 (2006) 194507], have reported the observation of a quantum dynamical phase transition in the dynamics of a spin swapping gate. In order to explain this result from a microscopic perspective, we introduce a Hamiltonian model of a two level system with many-body interactions with an environment whose excitation dynamics is fully solved within the Keldysh formalism. If a particle starts in one of the states of the isolated system, the return probability oscillates with the Rabi frequency ω₀. For weak interactions with the environment , we find a slower oscillation whose amplitude decays with a rate . However, beyond a finite critical interaction with the environment, , the decay rate becomes . The oscillation period diverges showing a quantum dynamical phase transition to a Quantum Zeno phase consistent with the experimental observations.     

Repulsive and bound parts of the interatomic potentials of the lowest singlet electronic energy states of the MeRg complexes (Me = Zn, Cd; Rg = He, Ne, Ar, Kr, Xe)

Laser-induced fluorescence excitation spectra of MeRg (Me = Zn, Cd; Rg = He, Ne, Ar, Kr, Xe) complexes were recorded using the D¹ ← X¹ free ← bound transition. The complexes were produced in their ground state in a free-jet expansion beam and excited with a dye-laser beam directly to the excited state. Analysis of free ← bound unstructured profiles provided a shape of the repulsive part of the D¹-state potentials. Valence ab initio calculations of the ZnRg and CdRg ground- and excited-state potentials and electronic transition dipole moments for the studied transition were performed, taking scalar relativistic and spin-orbit effects into account. Results of the calculations show regularities and correlations in the repulsive branches and bound wells of the X¹- and D¹-state potentials as well as provide information on the bonding character in both electronic energy states. The trends were compared with available experimental results for ZnRg and CdRg as well as for MgRg and HgRg.     

Low-temperature magnetic structures in the DySi FeB-type compound 27.03.09

The low-temperature magnetic ordering of the dimorphic DySi compound has been studied at 1.5 K by neutron diffraction on two polycrystalline samples. The samples comprise various amounts of the two orthorhombic modifications: CrB-type (Cmcm Nr. 63, all atoms at 4c site: (0, y, )) and FeB-type (Pnma Nr. 62, all atoms at 4c site: (x, , z)), both order antiferromagnetically (T_N≈38 K). The CrB-type phase orders with a uniaxial structure with the wave vector q₁=(0, 0, ) requiring a doubling of the c-axis. The Dy moments point along the linear chain with the shortest distance c. At 1.5 K, the ordered moment value is 8.57(1) μ_B/Dy atom.Two symmetry independent wave vectors describe the 1.5 K magnetic ordering of the FeB-type phase: q₂=(0, , ) and q₃=(0, 0.484(1), 0.0892(1)), coexisting in form of domains. In both structures the magnetic moments are confined to the (0 0 1) plane at an angle of 2(2)° and 22(3)° from the shortest axis b, respectively. Both structures correspond to sine wave modulations. The amplitude of the q₂ wave is m_o=7.5(1) μ_B/Dy atom and that of q₃ 8.2(1) μ_B/Dy atom. The wave vector q₂ when referring to the (a, 2b, c) cell and the wave vector q=(0, 0, ) corresponds to a transversal modulation, which by a proper origin choice can be also described as an antiphase domain structure with two amplitudes. The moments point to the b-axis and are stacked in the sequence (+m_o/2, −m_o/2, −m_o, −m_o/2, +m_o/2, +m_o, …) along the c-direction, while t_b acts as an antitranslation. For the q₃ phase, the local moment value depends on the atom position in the wave. We also discuss the case where q₃ and q₂ act simultaneously in physical space.     

On short and semi-short representations for four-dimensional superconformal symmetry

Possible short and semi-short representations for and superconformal symmetry in four dimensions are discussed. For the well known short supermultiplets whose lowest dimension conformal primary operators correspond to -BPS or -BPS states and are scalar fields belonging to the SU(4) R-symmetry representations [0,p,0] and [q,p,q] and having scale dimension Δ=p and Δ=2q+p, respectively, are recovered. The representation content of semi-short multiplets, which arise at the unitarity threshold for long multiplets, is discussed. It is shown how, at the unitarity threshold, a long multiplet can be decomposed into four semi-short multiplets. If the conformal primary state is spinless one of these becomes a short multiplet. For a -BPS multiplet need not have a protected dimension unless the primary state belongs to a [1,p,1] representation.     

Controlling subluminal to superluminal behavior of group velocity in an f-deformed Bose-Einstein condensate beyond the rotating wave approximation

In this paper, we investigate tunable control of the group velocity of a weak probe field propagating through an f-deformed Bose-Einstein condensate of Λ-type three-level atoms beyond the rotating wave approximation. For this purpose, we use an f-deformed generalization of an effective two-level quantum model of the three-level Λ-configuration without the rotating wave approximation in which the Gardiner’s phonon operators for Bose-Einstein condensate are deformed by an operator-valued function, , of the particle-number operator . We consider the collisions between the atoms as a special kind of f-deformation where the collision rate κ is regarded as the deformation parameter. We demonstrate the enhanced effect of subluminal and superluminal propagation based on electromagnetically induced transparency and electromagnetically induced absorption, respectively. In particular, we find that (i) the absorptive and dispersive properties of the deformed condensate can be controlled effectively in the absence of the rotating wave approximation by changing the deformation parameter κ, the total number of atoms and the counter-rotating terms parameter λ, (ii) by increasing the values of λ, κ and η = 1/N, the group velocity of the probe pulse changes, from subluminal to superluminal and (iii) beyond the rotating wave approximation, the subluminal and superluminal behaviors of the probe field are enhanced.     

Convergent iterative solutions for a Sombrero-shaped potential in any space dimension and arbitrary angular momentum

We present an explicit convergent iterative solution for the lowest energy state of the Schroedinger equation with an N-dimensional radial potential and an angular momentum l. For g large, the rate of convergence is similar to a power series in g⁻¹.     

On the partial trace over collective spin degrees of freedom

We derive analytical properties for the degeneracy ν(N,j) occurring in the decomposition of the state space C2⊗N. We also investigate the dynamics of two qubits coupled via Ising interactions to separate spin baths, and we study the thermodynamic limit.     

Anomalous thermostat and intraband discrete breathers

We investigate the dynamics of a macroscopic system which consists of an anharmonic subsystem embedded in an arbitrary harmonic lattice, including quenched disorder. The coupling between both parts is bilinear. Elimination of the harmonic degrees of freedom leads to a nonlinear Langevin equation with memory kernels and noise term for the anharmonic coordinates . For zero temperature, i.e. for , we prove that the support of the Fourier transform of and of the time averaged velocity-velocity correlation functions of the anharmonic system cannot overlap. As a consequence, the asymptotic solutions can be constant, periodic, quasiperiodic or almost periodic, and possibly weakly chaotic. For a sinusoidal trajectory with frequency we find that the energy E_T transferred to the harmonic system up to time T is proportional to T^α. If equals one of the phonon frequencies ω_ν, it is α=2. We prove that there is a zero measure set L such that for in its full measure complement R?L, it is α=0, i.e. there is no energy dissipation. Under certain conditions L contains a subset L^′ such that for the dissipation rate is nonzero and may be subdissipative (0≤α<1) or superdissipative (1<α≤2), compared to ordinary dissipation (α=1). Consequently, the harmonic bath does act as an anomalous thermostat, in variance with the common belief that elimination of a macroscopically large number of degrees of freedom always generates dissipation, forcing convergence to equilibrium. Intraband discrete breathers are such solutions which do not relax. We prove for arbitrary anharmonicity and small but finite coupling that intraband discrete breathers with frequency exist for all in a Cantor set C(k) of finite Lebesgue measure. This is achieved by estimating the contribution of small denominators appearing for , related to . For the small denominators do not lead to divergencies such that is a smooth and bounded function in t.     

Electro-optic behavior of lithium niobate at cryogenic temperatures

The unclamped relative permittivity, , and the Pockels coefficient, , of congruent lithium niobate at a frequency f = 5760 Hz have been determined at low temperatures (7 K < T < 300 K). A He cryostat setup mounted to one arm of an electronically phase-stabilized Michelson interferometer was utilized for the measurement of . A continuous decrease in both parameters was observed as T → 0 K with limiting values of and , respectively.     

Some characteristics in the interaction of slow highly charged I ions with a Si(1 1 1) 1 × 1-H surface

We have observed secondary particles and photons emitted from hydrogen terminated Si(1 1 1) 1 × 1 surfaces in the interactions with highly charged ions (HCIs) of iodine having a wide range of charge state, q, from I¹⁷⁺ up to I⁵³⁺, fully stripped iodine ion. A TOF-SIMS (time-of-flight secondary ion mass spectrometry) apparatus has been used to investigate secondary emissions where protons are dominant signals in the TOF spectra. Measured yields of H⁺ and show strong q-dependences, proportional to q^3.4 and q⁵, respectively. For Si⁺, while the yield remains constant for q < ∼ 25, it begins increasing with q^1.4 at higher q (∼25). The mechanism of secondary emissions is briefly discussed.