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.     

Manley-Rowe relations for an arbitrary discrete system

Manley-Rowe relations are formulated for a discrete Hamiltonian system with an arbitrary number of resonances. Assuming that the resonances are defined as , where is an n×n integer matrix of rank r<n, and |ω〉≡T(ω₁,…,ωn) is the frequency vector, the projection of the action vector |J〉 on is an adiabatic invariant. Hence n−r independent integrals, from where the conventional Manley-Rowe relations for a single resonance follow as a particular case.     

Quantum tomograms from intermediate entangled states

We show that for quantum tomography there exist two mutually conjugating intermediate coordinate-momentum entangled states |η₁,η_2〉λ,ν and |?₁,?_2〉σ,τ. The Radon transforms of the Wigner operators are just the pure-state density matrices and , respectively. As a result, the tomogram of quantum states is the module-square of their wave function in these representations. A new convenient formalism of quantum tomogram is thus established.     

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?∞.     

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.     

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.     

Traffic dynamics in scale-free networks with limited packet-delivering capacity

We propose a limited packet-delivering capacity model for traffic dynamics in scale-free networks. In this model, the total node’s packet-delivering capacity is fixed, and the allocation of packet-delivering capacity on node i is proportional to , where k_i is the degree of node i and ? is a adjustable parameter. We have applied this model on the shortest path routing strategy as well as the local routing strategy, and found that there exists an optimal value of parameter ? leading to the maximal network capacity under both routing strategies. We provide some explanations for the emergence of optimal ?.     

Haldane's instanton in 2D Heisenberg model revisited: Along the avenue of topology

Deconfined quantum phase transition from Néel phase to valence bond crystal state in 2D Heisenberg model is under debate nowadays. One crucial issue is the suppression of Haldane's instanton on quantum critical point which drives the spinon deconfined. In this Letter, by making use of the ?-mapping topological current theory, we reexamine the Haldane's instanton in an alternative way along the direction of topology. We find that the monopole events are space-time singularities of Néel field , the corresponding topological charges are the wrapping number of around the singularities which can be expressed in terms of the Hopf indices and Brouwer degrees of ?-mapping. The suppression of the monopole events can only be guaranteed when the ?-field possesses no zero points. Moreover, the quadrapolarity of monopole events in the Heisenberg model due to the Berry phase is also reproduced in this topological argument.     

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.     

On singular Lagrangian underlying the Schrödinger equation

We analyze the properties that manifest Hamiltonian nature of the Schrödinger equation and show that it can be considered as originating from singular Lagrangian action (with two second class constraints presented in the Hamiltonian formulation). It is used to show that any solution of the Schrödinger equation with time independent potential can be presented in the form , where the real field ?(t,xi) is some solution of nonsingular Lagrangian theory being specified below. Preservation of probability turns out to be the energy conservation law for the field ?. After introduction the field into the formalism, its mathematical structure becomes analogous to those of electrodynamics.     

On the asymptotic behavior of average energy and enstrophy in 3D turbulent flows

Rigorous upper and lower bounds are proved for the Taylor and the Kolmogorov wavenumbers for the three-dimensional space periodic Navier-Stokes equations. Under the assumption that Kolmogorov’s two-thirds power law holds, the bounds sharpen to and respectively, where is the Grashof number. This provides a rigorous proof that the power law implies (1) the energy cascade, (2) Kolmogorov dissipation law, and (3) a connection between κ_T and κ_?. The portion of phase space where a key a priori estimate on the nonlinear term is sharp is shown to be significant by means of a lower bound on any probability measure associated with an infinite-time average.     

Ordered zinc-vacancy induced Zn0.75Ox nanophase structure

Using transmission electron microscopy, a new nano-phase structure of Zn_0.75O_x induced by Zn-vacancy has been discovered to grow on wurtzite ZnO nanobelts. The superstructure grows epitaxial from the surface of the wurtzite ZnO nanobelts and can be fitted as an orthorhombic structure, with lattice parameters a′=2a, and c′=c, where a and c are the lattice parameters of ZnO. The superstructured phase is resulted from high-density Zn vacancies orderly distributed in the ZnO matrix. This study provides direct observation about the existence of Zn-vacancies in ZnO.     

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.     

The magnetocaloric effect and low temperature specific heat of SmNi

The magnetocaloric effect (MCE) in a magnetic SmNi sample was evaluated from magnetization and heat capacity measurements. The MCE phenomena in the vicinity of magnetic phase transitions in terms of magnetic entropy change, , and adiabatic temperature change, , are reported. Isothermal magnetization measurements at several temperatures around the transition were carried out and used for versusT calculations. A similar dependence of the magnetic entropy change was evaluated from heat capacity C_p(T) measurements under zero field and 5 T. The SmNi system provides magnetic refrigerants that induce an adiabatic cooling of about during the magnetization process with a field of 5 T in the temperature range of 35-45 K. The temperature dependence of C_p(T) is analyzed in terms of the magnetic and the lattice contributions.     

Third and fourth order phase transitions: Exact solution for the Ising model on the Cayley tree

In this work we present the first exact solution of a system of interacting particles with phase transitions of order higher than two. The presented analytical derivation shows that the Ising model on the Cayley tree exhibits a line of third order phase transition points, between temperatures and , and a line of fourth order phase transitions between T_BP and ∞, where k_B is the Boltzmann constant, and J is the nearest-neighbor interaction parameter.     

Multiple superconducting gap and anisotropic spin fluctuations in iron arsenides: Comparison with nickel analog

We present extensive ⁷⁵As NMR and NQR data on the superconducting arsenides PrFeAs_0.89F_0.11, LaFeAsO_0.92F_0.08, LiFeAs and Ba_0.72K_0.28Fe₂As₂ single crystal, and compare with the nickel analog LaNiAsO_0.9F_0.1. In contrast to LaNiAsO_0.9F_0.1 where the superconducting gap is shown to be isotropic, the spin lattice relaxation rate 1/T₁ in the Fe-arsenides decreases below T_c with no coherence peak and shows a step-wise variation at low temperatures. The Knight shift decreases below T_c and shows a step-wise T variation as well. These results indicate spin-singlet superconductivity with multiple gaps in the Fe-arsenides. The Fe antiferromagnetic spin fluctuations are anisotropic and weaker compared to underdoped copper-oxides or cobalt-oxide superconductors, while there is no significant electron correlations in LaNiAsO_0.9F_0.1. We will discuss the implications of these results and highlight the importance of the Fermi surface topology.     

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.     

Thermal step bunching on the restricted solid-on-solid model with point contact inter-step attractions

We present the restricted solid-on-solid (RSOS) model with the inter-ledge interaction of the point contact type (p-RSOS model). We have made detailed calculation of the Andreev free energy , which is similar to the equilibrium crystal shape (ECS) z=z(x,y), and the surface gradient as the function of the Andreev field . From the calculated and , we have obtained the vicinal surface free energy . The inter-ledge attraction between adjacent steps affects the surface free energies in the equilibrium, and causes the first-order transition on the profile of ECS at low temperature. The inter-ledge attraction also destabilizes the regular train of steps. We also have obtained the thermal step bunching.