Structural stochastic multiresonance in the Ising model on scale-free networks

Stochastic resonance is investigated in the Ising model with ferromagnetic coupling on scale-free networks with various scaling exponents γ > 2 of the degree distributions p(k)∝k^-γ, subjected to a weak oscillating magnetic field. The cases of networks constructed using the Configuration Model algorithm, with fully developed power-law tails of the degree distribution, and the Uncorrelated Configuration Model algorithm, with arbitrary constraint on the maximum connectivity of nodes, are considered. In the former case, for 2 < γ < 3 stochastic multiresonance is observed in the Monte Carlo simulations of the system, with the spectral power amplification exhibiting two or three maxima as a function of the temperature. Otherwise, the spectral power amplification has one maximum as a function of temperature and stochastic multiresonance does not occur. These results are in qualitative agreement with predictions of the linear response theory in the mean-field approximation, and quantitative differences between numerical and theoretical results can be mainly attributed to the disassortative character of the networks constructed using the Configuration Model algorithm.     

κ-generalized statistics in personal income distribution

Starting from the generalized exponential function , with exp ₀(x)=exp (x), proposed in reference [G. Kaniadakis, Physica A 296, 405 (2001)], the survival function P_>(x)=exp _κ(-βx^α), where x∈R⁺, α,β>0, and , is considered in order to analyze the data on personal income distribution for Germany, Italy, and the United Kingdom. The above defined distribution is a continuous one-parameter deformation of the stretched exponential function P_> ⁰(x)=exp (-βx^α) to which reduces as κ approaches zero behaving in very different way in the x→0 and x→∞ regions. Its bulk is very close to the stretched exponential one, whereas its tail decays following the power-law P_>(x)∼(2βκ)^-1/κx^-α/κ. This makes the κ-generalized function particularly suitable to describe simultaneously the income distribution among both the richest part and the vast majority of the population, generally fitting different curves. An excellent agreement is found between our theoretical model and the observational data on personal income over their entire range.     

Intrinsic degree-correlations in the static model of scale-free networks

We calculate the mean neighboring degree function and the mean clustering function C(k) of vertices with degree k as a function of k in finite scale-free random networks through the static model. While both are independent of k when the degree exponent γ≥3, they show the crossover behavior for 2 < γ< 3 from k-independent behavior for small k to k-dependent behavior for large k. The k-dependent behavior is analytically derived. Such a behavior arises from the prevention of self-loops and multiple edges between each pair of vertices. The analytic results are confirmed by numerical simulations. We also compare our results with those obtained from a growing network model, finding that they behave differently from each other.     

On the Instability Intervals of the Mathieu–Hill Operator

Consider the Mathieu–Hill operator

Dephasing in the semiclassical limit is system-dependent

Dephasing in open quantum chaotic systems has been investigated in the limit of large system sizes to the Fermi wavelength ratio, L/λ_F 〉 1. The weak localization correction g ^wl to the conductance for a quantum dot coupled to (i) an external closed dot and (ii) a dephasing voltage probe is calculated in the semiclassical approximation. In addition to the universal algebraic suppression g ^wl ∝ (1 + τ_D/τ_ϕ)⁻¹ with the dwell time τ_D through the cavity and the dephasing rate τ _ϕ ⁻¹ , we find an exponential suppression of weak localization by a factor of ∝ exp[− /τ_ϕ], where is the system-dependent parameter. In the dephasing probe model, coincides with the Ehrenfest time, ∝ ln[L/λ_F], for both perfectly and partially transparent dot-lead couplings. In contrast, when dephasing occurs due to the coupling to an external dot, ∝ ln[L/ξ] depends on the correlation length ξ of the coupling potential instead of λ_F. The text was submitted by the authors in English.     

Instability in degenerate two-photon running wave laser

The stability of the homogeneously broadened and degenerate two-photon running wave laser is analysed by using the full set of matter-field equations. The stability depends on the relative size of the relaxation constants. For 2k>1+r(k=/,r=/; is the cavity loss of the field and , are the longitudinal and transversal decay constants, respectively) no stable lasing state exists. Forr<k<(1+r)/2 an instability occurs. With the decrease in pumping the stable lasing state loses its stability due to Hopf-bifurcation.     

On Conformal Field Theory of SLE(κ,ρ)

SLE(κ ρ), a generalization of chordal Schramm-Löwner evolution (SLE), is discussed from the point of view of statistical mechanics and conformal field theory (CFT). Certain ratios of CFT correlation functions are shown to be martingales. The interpretation is that SLE(κ ρ) describes an interface in a statistical mechanics model whose boundary conditions are created in the Coulomb gas formalism by vertex operators with charges α _j = $\alpha_j = \frac{\rho_j}{2 \sqrt{\kappa}}SLE(κ ρ), a generalization of chordal Schramm-Löwner evolution (SLE), is discussed from the point of view of statistical mechanics and conformal field theory (CFT). Certain ratios of CFT correlation functions are shown to be martingales. The interpretation is that SLE(κ ρ) describes an interface in a statistical mechanics model whose boundary conditions are created in the Coulomb gas formalism by vertex operators with charges α _j = $\alpha_j = \frac{\rho_j}{2 \sqrt{\kappa}}SLE(κ ρ), a generalization of chordal Schramm-L?wner evolution (SLE), is discussed from the point of view of statistical mechanics and conformal field theory (CFT). Certain ratios of CFT correlation functions are shown to be martingales. The interpretation is that SLE(κ ρ) describes an interface in a statistical mechanics model whose boundary conditions are created in the Coulomb gas formalism by vertex operators with charges α _j = . The total charge vanishes and therefore the partition function has a simple product form. We also suggest a generalization of SLE(κ ρ)     

Antiferromagnetic Ising model in scale-free networks

The antiferromagnetic Ising model in uncorrelated scale-free networks has been studied by means of Monte Carlo simulations. These networks are characterized by a connectivity (or degree) distribution P(k) ∼k^-γ. The disorder present in these complex networks frustrates the antiferromagnetic spin ordering, giving rise to a spin-glass (SG) phase at low temperature. The paramagnetic-SG transition temperature T_c has been studied as a function of the parameter γ and the minimum degree present in the networks. T_c is found to increase when the exponent γ is reduced, in line with a larger frustration caused by the presence of nodes with higher degree.     

Connectivity of growing networks with link constraints

We propose a growing network model with link constraint, in which new nodes are continuously introduced into the system and immediately connected to preexisting nodes, and any arbitrary node cannot receive new links when it reaches a maximum number of links k_m. The connectivity of the network model is then investigated by means of the rate equation approach. For the connection kernel A(k)=k^γ, the degree distribution n_k takes a power law if γ≥1 and decays stretched exponentially if 0≤γ< 1. We also consider a network system with the connection kernel A(k)=k^α(k_m-k)^β. It is found that n_k approaches a power law in the α> 1 case and has a stretched exponential decay in the 0≤α< 1 case, while it can take a power law with exponential truncation in the special α=β=1 case. Moreover, n_k may have a U-type structure if α> β.     

Reconstruction of Random Colourings

Reconstruction problems have been studied in a number of contexts including biology, information theory and statistical physics. We consider the reconstruction problem for random k-colourings on the Δ-ary tree for large k. Bhatnagar et al. [2] showed non-reconstruction when . We tighten this result and show non-reconstruction when , which is very close to the best known bound establishing reconstruction which is . Supported by NSF grants DMS-0528488 and DMS-0548249.     

Weak chaos and metastability in a symplectic system of many long-range-coupled standard maps

We introduce, and numerically study, a system of N symplectically and globally coupled standard maps localized in a d=1 lattice array. The global coupling is modulated through a factor r^-α, being r the distance between maps. Thus, interactions are long-range (nonintegrable) when 0≤α≤1, and short-range (integrable) when α>1. We verify that the largest Lyapunov exponent λ_M scales as λ_M ∝ N^-κ(α), where κ(α) is positive when interactions are long-range, yielding weak chaos in the thermodynamic limit N↦∞ (hence λ_M→0). In the short-range case, κ(α) appears to vanish, and the behaviour corresponds to strong chaos. We show that, for certain values of the control parameters of the system, long-lasting metastable states can be present. Their duration t_c scales as t_c ∝N^β(α), where β(α) appears to be numerically in agreement with the following behavior: β>0 for 0 ≤α< 1, and zero for α≥1. These results are consistent with features typically found in nonextensive statistical mechanics. Moreover, they exhibit strong similarity between the present discrete-time system, and the α-XY Hamiltonian ferromagnetic model.     

Spin observables of the reactions NN → Δ N and pd → Δ( pp )(1 S 0) in collinear kinematics

A general formalism for double and triple spin correlations of the reaction is developed for the case of collinear kinematics. A complete polarization experiment allowing one to reconstruct all four amplitudes describing this process is suggested. Furthermore, the spin observables of the inelastic charge-exchange reaction (pp)(¹ S ₀ are analyzed in collinear kinematics within the single pN-scattering mechanism involving the subprocess pn → Δ⁰ p. The full set of spin observables, related to the polarization of one or two initial particles and one final particle, is obtained in terms of three invariant amplitudes of the reaction pd → Δ(pp)(¹ S ₀) and the transition form factor d → (pp)(¹ S ₀). A complete polarization experiment for the reaction (pp)(¹ S ₀) is suggested which allows one to determine three independent combinations of the four amplitudes of the elementary subprocess . The text was submitted by the authors in English.     

The Harmonic Oscillator on Three-Dimensional Spherical and Hyperbolic Spaces: Curvature Dependent Formalism and Quantization

A nonlinear model representing the quantum harmonic oscillator on the three-dimensional spherical and hyperbolic spaces, S_k³S_{\kappa }^{3} (κ>0) and H_k³H_{k}^{3} (κ<0), is studied using geodesic spherical coordinates (r,θ,φ). The curvature κ is considered as a parameter and the results are formulated in explicit dependence of κ. The first part of the paper is concerned with the existence of Killing vectors, the existence of Noether symmetries and the properties of the Noether momenta. The second part is devoted to the transition from classical to quantum mechanics. The classical system is quantized by obtaining a κ-dependent invariant measure dμ _κ and expressing the Hamiltonian as a function of the Noether momenta.     

Asymptotics for the Burgers Equation with Pumping

We consider the large time asymptotic behavior of solutions to the initial-boundary value problem We find large time asymptotic formulas of solutions for three different cases 1) a_±=±1, 2) a_±=1 and 3) a_±=0.     

Excitonic light-absorption and amplification bands in the presence of laser radiation

We examine the absorption and amplification bands of a weak probe signal in the presence of Bose-Einstein condensation of excitons that emerges in nonequilibrium conditions in the field of coherent laser radiation with a wave vector k ₀. We assume that the detuning from resonance between the energy ħω _ex (k ₀)+L ₀ of the exciton level, which is shifted because of exciton-exciton interaction, and the laser photon energy ħω _L , is generally nonzero. The elementary excitation spectrum consisting of the quasiexcitonic and quasienergy branches determines the optical properties of the system. When there is real induced Bose-Einstein condensation, at the two branches touch, as they do in spontaneous Bose-Einstein condensation. In virtual induced Bose-Einstein condensation, when , instabilities emerge in the spectrum in certain regions of the k-space. These instabilities are caused by a real transformation of two laser photons into two extracondensate particles. Nonequilibrium extracondensate excitons strongly affect the absorption and amplification of the probe light signal. We show that light absorption is due to the quantum transition from the ground state of the crystal to the quasiexcitonic branch of the spectrum. On the other hand, amplification of the signal is caused by the transition from the quasienergy branch to the ground state of the crystal. The same transition can be explained by a real transformation of two laser photons into a vacuum photon of frequency ħcq and a crystal exciton with a wave vector 2k ₀−q. Finally, we show that the excitonic absorption and light-amplification bands are essentially anisotropic at and depend on the orientation of the vectors q and k ₀. Zh. éksp. Teor. Fiz. 112, 167–179 (July 1997)     

Damping of zero sound in Luttinger liquids

We calculate the damping γ_q of collective density oscillations (zero sound) in a one-dimensional Fermi gas with dimensionless forward scattering interaction F and quadratic energy dispersion k² / 2 m at zero temperature. Using standard many-body perturbation theory, we obtain γ_q from the expansion of the inverse irreducible polarization to first order in the effective screened (RPA) interaction. For wave-vectors | q| /k_F ≪F (where k_F = m v_F is the Fermi wave-vector) we find to leading order γ_q ∝| q |³ /(v_F m²). On the other hand, for F ≪| q| /k_F most of the spectral weight is carried by the particle-hole continuum, which is distributed over a frequency interval of the order of q²/m. We also show that zero sound damping leads to a finite maximum proportional to |k - k_F | ^{-2 + 2 η} of the charge peak in the single-particle spectral function, where η is the anomalous dimension. Our prediction agrees with photoemission data for the blue bronze K_0.3MoO₃. We comment on other recent calculations of γ_q.     

Ward's identity in critical dynamics

We consider the relaxation of an order-parameter fluctuation of wave numberk in a system undergoing a second-order phase transition. In general, close to the critical point, wherek ^{–1 –1} (the correlation length) the relaxation rate has a linear dependence on/k of the form (k, ) = (k, 0)x(1–a/k). In analogy with the use of Ward's identity in elementary particle physics, we show that the numerical coefficienta is readily calculated by means of a mass insertion. We demonstrate, furthermore, that this initial linear drop is the main feature of the full/k dependence of the scaling functionR ^–x (k,), wherex is the dynamic critical exponent andR=(k²+ ²)^1/2 is the distance variable.     

Quantum wire polaritons

Summary Using a nonlocal susceptibility with cilindrical symmetry as computed from the microscopic theory, we obtain the exciton-polariton modes in quantum wires, where the translational symmetry is preserved in one direction only. Resonant polaritons, with a finite radiative lifetime, result for , while wire polaritons with infinite radiative lifetime result fork _‖>k ₀. Dispersion laws and lifetimes are given for all values ofk _‖, and the separation between the longitudinal and the nonlongitudinal mode is obtained. Numerical examples are given for GaAs/Ga_1−x Al _x As quantum wires.     

Influence of gravity on surface melting

A chemical network system for use in the study of reaction cascades is described by the nonlinear rate equation , in which (x) is derived from the –G/x of Taylor's expansion of the order parameterx of the thermodynamic potential, Gibbs' functionG(T,P,x), at about the critical pointC(T _C ,P _C ) of the control variables (parameters)T andP. The behavior of the system around the stable pointx=0 is analyzed only with the sign ofk ₁(T, P), becausek ₂(T, P) is always positive. The system is not closed and is affected by physical and chemical changes in the neighbor systems. WhenT andP fluctuate ( ) through the changes andk ₁ passes zero, the system in the steady state becomes instable andk ₁ jumps at the reaction threshold. Then, the products are formed at the number of moleculesx=(|k ₁|/k ₂)^1/2. To describe such a transition,k ₁ giving theG curvature atx=0 is represented phenomenologically by an approximate function, tanh(G/RT), for a metastable state with a relatively smallk ₁(>0). The reaction takes place in a cascade in accordance with a cubic state equation obtained from tanh(G/RT), which describes a jump of the reaction energy G at the reaction threshold.     

Dynamics of low-energy nuclear forces for electromagnetic and weak reactions with the deuteron in the Nambu-Jona-Lasinio model of light nuclei

A dynamics of low-energy nuclear forces is investigated for low-energy electromagnetic and weak nuclear reactions with the deuteron in the Nambu-Jona-Lasinio model of light nuclei by example of the neutron-proton radiative capture (M1-capture) n + p → D + γ, the photomagnetic disintegration of the deuteron γ + D → n + p and weak reactions of astrophysical interest. These are the solar proton burning p + p → D + e⁺ + ν _e, the pep-process p + e⁻ + p → D + ν _e and the neutrino and antineutrino disintegration of the deuteron caused by charged ν _e + D → e⁻ + p + p, + D → e⁺ + n + n and neutral ν _e() + D → ν _e() + n + p weak currents.