How to measure subdiffusion parameters

We propose a method to measure the subdiffusion parameter alpha and subdiffusion coefficient Dalpha which are defined by means of the relation chi2 = 2Dalpha / Gamma(1+alpha)(t alpha), where chi2 denotes a mean square displacement of a random walker starting from x = 0 at the initial time t = 0. The method exploits a membrane system where a substance of interest is transported in a solvent from one vessel to another across a thin membrane which plays here only an auxiliary role. We experimentally study a diffusion of glucose and sucrose in a gel solvent, and we precisely determine the parameters alpha and Dalpha, using a fully analytic solution of the fractional subdiffusion equation.     

Activated scaling of classical and quantum spin glasses

A model for thermally activated dynamics in disordered systems shows that the linear and nonlinear susceptibility follows a generic exponential form with a "critical rounding," chi(1) proportional to chi(3) proportional to [T ln(t/tau(0)')/K](gamma/b phi) exp - [Tt(g)(phi b)ln(t/tau(0)'/K)](nu/b) (T=temperature, t=time, K=barrier constant, t(g) = 1 - T(SG)/T, and T(SG) = transition temperature; gamma>0 for chi(3) and <0 for chi(1)). This model, also valid in the presence of resonant tunneling states at energies K(0) < K [provided that K is replaced by K(0)+2T ln (1/Gamma(0)), where Gamma(0)(2) proportional, variant tunnel splitting of a spin S=1], is potentially applicable to a wide variety of systems opening the way for the study of thermally activated quantum phase transitions. The famous spin-glass system LiHo(x)Y(1-x) seems to follow this model.     

Rotators with long-range interactions: connection with the mean-field approximation

We analyze the equilibrium properties of a chain of ferromagnetically coupled rotators which interact through a force that decays as r(-alpha) where r is the interparticle distance and alpha>/=0. By integrating the equations of motion we obtain the microcanonical time averages of both the magnetization and the kinetic energy. We detect three different regimes depending on whether alpha belongs to the intervals [0,1), (1,2), or (2,infinity). For 0相似文献   

Multispecies pair annihilation reactions

We consider diffusion-limited reactions A(i)+A(j)--> (1< or =i2 and d> or =2, we argue that the asymptotic density decay for such mutual annihilation processes with equal rates and initial densities is the same as for single-species pair annihilation A+A-->. In d=1, however, particle segregation occurs for all q< infinity. The total density decays according to a q dependent power law, rho(t) approximately t(-alpha(q)). Within a simplified version of the model alpha(q)=(q-1)/2q can be determined exactly. Our findings are supported through Monte Carlo simulations.     

Random walks on a ( 2+1)-dimensional deformable medium

A model of random walks on a deformable medium is proposed in 2+1 dimensions. The behavior of the walk is characterized by the stability parameter beta and the stiffness exponent alpha. The average square end-to-end distance l approximately equals (2nu) and the average number of visited sites approximately equals (k) are calculated. As beta increases, for each alpha there exists a critical transition point beta(c) from purely random walks ( nu = 1/2 and k approximate to 1) to compact growth ( nu = 1/3 and k = 2/3). The relationship between beta(c) and alpha can be expressed as beta(c) = e(alpha). The landscape generated by a walk is also investigated by means of the visit-number distribution N(n)(beta). There exists a scaling relationship of the form N(n)(beta)approximately n(-2)f(n/beta(z)).     

Resonant excitations of the 't Hooft-Polyakov monopole

The spherically symmetric magnetic monopole in an SU(2) gauge theory coupled to a massless Higgs field is shown to possess an infinite number of resonances or quasinormal modes. These modes are eigenfunctions of the isospin 1 perturbation equations with complex eigenvalues, E(n)=omega(n)-igamma(n), satisfying the outgoing radiation condition. For n--> infinity, their frequencies omega(n) approach the mass of the vector boson, M(W), while their lifetimes 1/gamma(n) tend to infinity. The response of the monopole to an arbitrary initial perturbation is largely determined by these resonant modes, whose collective effect leads to the formation of a long living breatherlike excitation with an amplitude decaying at late times as t(-5/6).     

Aging in 1D discrete spin models and equivalent systems

We derive exact expressions for a number of aging functions that are scaling limits of nonequilibrium correlations, R(t(w),t(w)+t) as t(w)-->infinity, t/t(w)-->theta, in the 1D homogenous q-state Potts model for all q with T = 0 dynamics following a quench from T = infinity. One such quantity is (0)(t(w));sigma-->(n)(t(w)+t)> when n/square root of ([t(w))-->z. Exact, closed-form expressions are also obtained when an interlude of T = infinity dynamics occurs. Our derivations express the scaling limit via coalescing Brownian paths and a "Brownian space-time spanning tree," which also yields other aging functions, such as the persistence probability of no spin flip at 0 between t(w) and t(w)+t.     

Excitations of one-dimensional Bose-Einstein condensates in a random potential

We examine bosons hopping on a one-dimensional lattice in the presence of a random potential at zero temperature. Bogoliubov excitations of the Bose-Einstein condensate formed under such conditions are localized, with the localization length diverging at low frequency as l(omega) approximately 1/omega(alpha). We show that the well-known result alpha=2 applies only for sufficiently weak random potential. As the random potential is increased beyond a certain strength, alpha starts decreasing. At a critical strength of the potential, when the system of bosons is at the transition from a superfluid to an insulator, alpha=1. This result is relevant for understanding the behavior of the atomic Bose-Einstein condensates in the presence of random potential, and of the disordered Josephson junction arrays.     

Interfacial reactions: mixed order kinetics and segregation effects

We study A-B reaction kinetics at a fixed interface separating A and B bulks. Initially, the number of reactions R(t) approximately tn(infinity)(A)n(infinity)(B) is second order in the far-field densities n(infinity)(A), n(infinity)(B). First order kinetics, governed by diffusion from the dilute bulk, onset at long times: R(t) approximately x(t)n(infinity)(A), where x(t) approximately t(1/z) is the rms molecular displacement. Below a critical dimension, d0) leads to anomalous decay of interfacial densities. Numerical simulations for z = 2 support the theory.     

Stability of spikes in the shadow Gierer-Meinhardt system with Robin boundary conditions

We consider the shadow system of the Gierer-Meinhardt system in a smooth bounded domain Omega subset R(N),A(t)=epsilon(2)DeltaA-A+A(p)/xi(q),x is element of Omega, t>0, tau/Omega/xi(t)=-/Omega/xi+1/xi(s) integral(Omega)A(r)dx, t>0 with the Robin boundary condition epsilon partial differentialA/partial differentialnu+a(A)A=0, x is element of partial differentialOmega, where a(A)>0, the reaction rates (p,q,r,s) satisfy 10, r>0, s>or=0, 1or=0. We rigorously prove the following results on the stability of one-spike solutions: (i) If r=2 and 11 and tau sufficiently small the interior spike is stable. (ii) For N=1 if r=2 and 11 such that for a is element of (a(0),1) and mu=2q/(s+1)(p-1) is element of (1,mu(0)) the near-boundary spike solution is unstable. This instability is not present for the Neumann boundary condition but only arises for the Robin boundary condition. Furthermore, we show that the corresponding eigenvalue is of order O(1) as epsilon-->0.     

Saturated absorption and nonlinear refraction of silicate glasses doped with silver nanoparticles at 532 nm

The nonlinear optical characteristics of silicate glasses doped with silver nanoparticles are investigated by Z-scan technique using second harmonic radiation of picosecond Nd:YAG laser (=532 nm, =55 ps). The real and imaginary parts of third-order nonlinear susceptibility of silver-contained glasses were measured. It was found that the sign of Im ⁽³⁾was negative due to saturated absorption and the sign of Re ⁽³⁾ was changed from negative (self-defocusing) to positive (self-focusing) with growth of laser radiation intensity. The mechanisms responsible for saturated absorption and nonlinear refraction are discussed.     

Localization transition of biased random walks on random networks

We study random walks on large random graphs that are biased towards a randomly chosen but fixed target node. We show that a critical bias strength bc exists such that most walks find the target within a finite time when b > bc. For b < bc, a finite fraction of walks drift off to infinity before hitting the target. The phase transition at b=bc is a critical point in the sense that quantities such as the return probability P(t) show power laws, but finite-size behavior is complex and does not obey the usual finite-size scaling ansatz. By extending rigorous results for biased walks on Galton-Watson trees, we give the exact analytical value for bc and verify it by large scale simulations.     

Qualitative modification of the high energy atomic photoionization cross section

It is demonstrated that the nonrelativistic high energy omega-->infinity behavior of the photoionization cross section of an nl atomic subshell, sigma(nl)(omega), for l>0 is independent of l and is given by sigma(nl)(omega) approximately 1/omega(9/2), rather than the previously generally accepted sigma(nl)(omega) approximately 1/omega(l+7/2). Furthermore, for l = 1, although the exponent does not change, the coefficient is significantly altered. This modification of sigma(nl)(omega) is due to the interchannel interaction between ns photoionization channels and l not equal0 channels in the atom. As a result, for the photoionization of l not equal0 electrons, the single-particle approximation is never correct in the omega-->infinity limit. This has important consequences for sum rule calculations.     

Dynamics of the chain of forced oscillators with long-range interaction: from synchronization to chaos

We consider a chain of nonlinear oscillators with long-range interaction of the type 1l(1+alpha), where l is a distance between oscillators and 0相似文献   

Photoassisted poling of azo dye doped polymeric films at room temperature

The reversible cis-trans photoisomerization of disperse red 1 (DR1) in PMMA thin films has been demonstrated to be strongly polarization sensitive [1]. In this communication two mechanisms are identified: the angular hole burning and the angular redistribution of molecules. It is shown that, in the presence of a DC electric field, the redistribution is not centrosymmetric and produces a poling of the film. The evolution of the second-order nonlinear susceptibility, ⁽²⁾, is monitored by measuring the electro-optic effect by attenuated total reflection and by second-harmonic generation.     

Method for solving moving boundary value problems for linear evolution equations

We introduce a method of solving initial boundary value problems for linear evolution equations in a time-dependent domain, and we apply it to an equation with dispersion relation omega(k), in the domain l(t)相似文献   

Autocorrelation exponent of conserved spin systems in the scaling regime following a critical quench

We study the autocorrelation function of a conserved spin system following a quench at the critical temperature. Defining the correlation length L(t) approximately t(1/z), we find that for times t' and t satisfying L(t')infinity limit, we show that lambda(')(c)=d+2 and phi=z/2. We give a heuristic argument suggesting that this result is, in fact, valid for any dimension d and spin vector dimension n. We present numerical simulations for the conserved Ising model in d=1 and d=2, which are fully consistent with the present theory.     

Electrooptical Kerr constant and third-order susceptibility measurements in nematic liquid crystals and their mixtures

We report for the first time the determination of the real part of the third order nonlinear susceptibilities ⁽³⁾ (–, , 0, 0) in the isotropic phase of two nematic liquid crystalsp-(ethoxybenzylidine)-p-butylaniline (EBBA) andp-(methoxybenzylidene)-p-butylaniline (MBBA) from electrooptic Kerr effect experiments. The highest value of ⁽³⁾ observed near nematic-to-isotropic transition temperature, at 632.8 nm is found to be 1.067×10^–20 m²V^–2 for EBBA and 6.602×10^–20 m²V^–2 for MBBA.     

Fractional dynamics of coupled oscillators with long-range interaction

We consider a one-dimensional chain of coupled linear and nonlinear oscillators with long-range powerwise interaction. The corresponding term in dynamical equations is proportional to 1//n-m/alpha+1. It is shown that the equation of motion in the infrared limit can be transformed into the medium equation with the Riesz fractional derivative of order alpha, when 0相似文献