Short-range plasma model for intermediate spectral statistics

We propose a plasma model for spectral statistics displaying level repulsion without long-range spectral rigidity, i.e. statistics intermediate between random matrix and Poisson statistics similar to the ones found numerically at the critical point of the Anderson metal-insulator transition in disordered systems and in certain dynamical systems. The model emerges from Dysons one-dimensional gas corresponding to the eigenvalue distribution of the classical random matrix ensembles by restricting the logarithmic pair interaction to a finite number k of nearest neighbors. We calculate analytically the spacing distributions and the two-level statistics. In particular we show that the number variance has the asymptotic form Σ²(L) ∼χL for large L and the nearest-neighbor distribution decreases exponentially when s→∞, P(s) ∼ exp(- Λs) with Λ = 1/χ = kβ + 1, where β is the inverse temperature of the gas (β = 1, 2 and 4 for the orthogonal, unitary and symplectic symmetry class respectively). In the simplest case of k = β = 1, the model leads to the so-called Semi-Poisson statistics characterized by particular simple correlation functions e.g. P(s) = 4s exp(- 2s). Furthermore we investigate the spectral statistics of several pseudointegrable quantum billiards numerically and compare them to the Semi-Poisson statistics. Received 13 September 2000     

Finite-size scaling of the level compressibility at the Anderson transition

We compute the number level variance Σ ₂ and the level compressibility χ from high precision data for the Anderson model of localization and show that they can be used in order to estimate the critical properties at the metal-insulator transition by means of finite-size scaling. With N, W, and L denoting, respectively, linear system size, disorder strength, and the average number of levels in units of the mean level spacing, we find that both χ(N, W) and the integrated Σ ₂ obey finite-size scaling. The high precision data was obtained for an anisotropic three-dimensional Anderson model with disorder given by a box distribution of width W/2. We compute the critical exponent as ν≈ 1.45±0.12 and the critical disorder as W _c≈ 8.59±0.05 in agreement with previous transfer-matrix studies in the anisotropic model. Furthermore, we find χ≈ 0.28±0.06 at the metal-insulator transition in very close agreement with previous results. Received 1st November 2001 and Received in final form 8 March 2002 Published online 6 June 2002     

Local magnetism of Ce in CeNi2B2C: a PAC study

By measuring the local susceptibility χ_loc(T) of ¹⁴⁰Ce using TDPAC method, we have studied magnetism and valence fluctuation behaviour of Ce in the quaternary borocarbide system CeNi₂B₂C. The magnitude of the measured χ_loc along with the observed temperature dependence indicates non-integral valence of Ce ions. As a new feature, the average valence of Ce derived from our χ_loc data shows large variation with temperature. This revised version was published online in August 2006 with corrections to the Cover Date.     

The phase diagram of (NH4I)x(KI)1−x

The χ,T phase diagram of (NH₄I)_x(KI)_1−x has been determined using neutron diffraction experiments and dielectric spectroscopy. At low temperatures and with decreasing χ, the sequence γ, β, ε and glass phase has been detected. The critical concentration χ_c≈0.55 separates the glassy phase with frozen-in orientational disorder from the ε phase which reveals long-range orientational order. Close to χ_c our experiments reveal evidence for two subsequent glass transitions.     

The emergence of coordination in public good games

In physical models it is well understood that the aggregate behaviour of a system is not in one to one correspondence with the behaviour of the average individual element of that system. Yet, in many economic models the behaviour of aggregates is thought of as corresponding to that of an individual. A typical example is that of public goods experiments. A systematic feature of such experiments is that, with repetition, people contribute less to public goods. A typical explanation is that people “learn to play Nash” or something approaching it. To justify such an explanation, an individual learning model is tested on average or aggregate data. In this paper we will examine this idea by analysing average and individual behaviour in a series of public goods experiments. We analyse data from a series of games of contributions to public goods and as is usual, we test a learning model on the average data. We then look at individual data, examine the changes that this produces and see if some general model such as the EWA (Expected Weighted Attraction) with varying parameters can account for individual behaviour. We find that once we disaggregate data such models have poor explanatory power. Groups do not learn as supposed, their behaviour differs markedly from one group to another, and the behaviour of the individuals who make up the groups also varies within groups. The decline in aggregate contributions cannot be explained by resorting to a uniform model of individual behaviour. However, the Nash equilibrium of such a game is a total payment for all the individuals and there is some convergence of the group in this respect. Yet the individual contributions do not converge. How the individuals “self-organsise” to coordinate, even in this limited way remains to be explained.     

Nonlinear-optical and structural properties of nanocrystalline silicon carbide films

The aim of this study is to investigate the nonlinearity of refraction in nanostructured silicon carbide films depending on their structural features (synthesis conditions for such films, substrate temperature during their deposition, concentration of the crystalline phase in the film, Si/C ratio of atomic concentrations in the film, and size of SiC nanocrystals formed in the film). The corresponding dependences are obtained, as well as the values of nonlinear-optical third-order susceptibility χ⁽³⁾(ω; ω, −ω, ω) for various silicon polytypes (3C, 21R, and 27R) which exceed the value of χ⁽³⁾ in bulk silicon carbide single crystals by four orders of magnitude.     

Temperature dependent properties of metallic clusters containing magnetic impurities

The properties of magnetic impurities in small metallic clusters are investigated in the framework of the Anderson model by using exact diagonalization methods. Parameters representative of the Kondo limit are considered. The spin gap ΔE = E(S=1, 3/2) - E(S=0, 1/2) shows a remarkable band-filling dependence that can be interpreted in terms of the cluster-specific conduction-electron spectrum. Finite-temperature properties such as the magnetic susceptibility and specific heat are calculated exactly in the canonical and grand canonical ensembles. The structural dependence is illustrated. Received 30 November 2000     

Discrete gap solitons in a diffraction-managed waveguide array

A model including two nonlinear chains with linear and nonlinear couplings between them, and opposite signs of the discrete diffraction inside the chains, is introduced. In the case of the cubic [ χ⁽³⁾] nonlinearity, the model finds two different interpretations in terms of optical waveguide arrays, based on the diffraction-management concept. A continuum limit of the model is tantamount to a dual-core nonlinear optical fiber with opposite signs of dispersions in the two cores. Simultaneously, the system is equivalent to a formal discretization of the standard model of nonlinear optical fibers equipped with the Bragg grating. A straightforward discrete second-harmonic-generation [ χ⁽²⁾] model, with opposite signs of the diffraction at the fundamental and second harmonics, is introduced too. Starting from the anti-continuum (AC) limit, soliton solutions in the χ⁽³⁾ model are found, both above the phonon band and inside the gap. Solitons above the gap may be stable as long as they exist, but in the transition to the continuum limit they inevitably disappear. On the contrary, solitons inside the gap persist all the way up to the continuum limit. In the zero-mismatch case, they lose their stability long before reaching the continuum limit, but finite mismatch can have a stabilizing effect on them. A special procedure is developed to find discrete counterparts of the Bragg-grating gap solitons. It is concluded that they exist at all the values of the coupling constant, but are stable only in the AC and continuum limits. Solitons are also found in the χ⁽²⁾ model. They start as stable solutions, but then lose their stability. Direct numerical simulations in the cases of instability reveal a variety of scenarios, including spontaneous transformation of the solitons into breather-like states, destruction of one of the components (in favor of the other), and symmetry-breaking effects. Quasi-periodic, as well as more complex, time dependences of the soliton amplitudes are also observed as a result of the instability development. Received 14 September 2002 / Received in final form 4 February 2003 Published online 24 April 2003 RID="a" ID="a"e-mail: malomed@eng.tau.ac.il     

Bilinear optical susceptibilities of potassium dihydrogen phosphate and of III–V,II–VI and I–VII semiconductors

The approximate orbital-approach of Jha and Bloembergen is used to calculate the non-dispersive part of the bilinear optical susceptibility,χ ⁽²⁾, for various compounds. Using bonding and antibonding states of the molecular orbital theory it is shown thatχ ⁽²⁾ satisfies a simple relation in terms of other measurable physical quantities. This relation is used to calculateχ ⁽²⁾ for various III–V, II–VI and I–VII semiconductors, both with cubic zinc blende structure and with hexagonal wurtzite structure. The same procedure is used to obtainχ ⁽²⁾ for potassium dihydrogen phosphate (KDP). The calculated values are compared with the experimentally observed values and it is found that the present model gives excellent results for II–VI compounds and for KDP.     

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.     

Nonresonance spin-lattice absorption of ultrasound in Ising magnets

A theory of nonresonant acoustic absorption in Ising magnets is constructed by the nonequilibrium statistical operator method. It is assumed that the spins are coupled with the sound via modulation of the Ising exchange integral, and the nonresonant absorption is due to the interaction of the spin system with the thermal vibrations of the lattice. The frequency dependence of the absorption χ″(ω), which has an analytical form different from that of the well-known Debye function, is determined. The temperature dependence of χ″(ω), which is made up of 1) the averages of the vibrational variables and 2) the temperature dependence of the spin correlation functions of the linear Ising model, is analyzed. It is shown that the cross-coupling of the two subsystems (Ising and Zeeman) produces a second absorption peak at low frequencies together with the peak characteristic of the Debye curve. Fiz. Tverd. Tela (St. Petersburg) 39, 516–521 (March 1997)     

Cascaded χ(2) nonlinearity in QND measurement

 QND measurement schemes often use Kerr nonlinearity to couple the intensity fluctuations of the signal beam to the phase fluctuations of the probe beam by means of the cross-phase modulation effect. Such schemes use materials with intrinsic χ⁽³⁾nonlinearity. However, it has already been shown that Kerr-effect-like correlation between two light waves may be achieved through cascaded χ⁽²⁾: χ⁽²⁾ processes. The value of the nonlinearity induced by cascading χ⁽²⁾ can, in many cases, be much higher than fibre χ⁽³⁾. The authors point out the possibility of using the cascaded χ⁽²⁾ nonlinearity instead of intrinsic χ⁽³⁾ nonlinearity in the scheme which resembles the well-known photon number QND measurement scheme. The non-degenerate second-harmonic generation (SHG) with a large phase mismatch is considered. The harmonic wave influence on the measurements is shown. High QND measurement characteristics can be achieved with the use of an appropriate set of parameters. Received: 6 April 1996     

Experimental observation of the interference of three-and five-wave mixing processes in optical second harmonic generation in a solution of bacteriorhodopsin

The generation of a femptosecond second harmonic in a bacterior-hodopsin solution is investigated. It is shown that the behavior of the harmonic can be explained by the coherent interference of several contributions from three-and five-wave mixing processes (χ ⁽²⁾ and χ ⁽⁴⁾). The magnitude and phase of the fourth-order electronic susceptibility χ ⁽⁴⁾ of the medium with respect to χ ⁽²⁾ are determined. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 10, 668–673 (25 November 1996)     

Monte Carlo test of the Goldstone mode singularity in 3D XY model

Monte Carlo simulations of magnetization and susceptibility in the 3D XY model are performed for system sizes up to L=384 (significantly exceeding the largest size L=160 considered in work published previously), and fields h ≥ 0.0003125 at two different coupling constants β=0.5, and β=0.55 in the ordered phase. We examine the prediction of the standard theory that the longitudinal susceptibility χ_∥ has a Goldstone mode singularity such that χ_∥ ∝h^-1/2 holds when h↦0. Most of our results, however, support another theoretical prediction that the singularity is of a more general form χ_∥ ∝h^ρ-1, where 1/2<ρ<1 is a universal exponent related to the ∼h^ρ variation of the magnetization.     

Physical property characterization of bulk MgB<Subscript>2</Subscript> superconductor

We report synthesis, structure/micro-structure, resistivity under magnetic field [ρ(T)H], Raman spectra, thermoelectric power S(T), thermal conductivity κ(T), and magnetization of ambient pressure argon annealed polycrystalline bulk samples of MgB₂, processed under identical conditions. The compound crystallizes in hexagonal structure with space group P6/mmm. Transmission electron microscopy (TEM) reveals electron micrographs showing various types of defect features along with the presence of 3–4 nm thick amorphous layers forming the grain boundaries of otherwise crystalline MgB₂. Raman spectra of the compound at room temperature exhibited characteristic phonon peak at 600 cm^-1. Superconductivity is observed at 37.2 K by magnetic susceptibility χ(T), resistivity ρ(T), thermoelectric power S(T), and thermal conductivity κ(T) measurements. The power law fitting of ρ(T) give rise to Debye temperature (Θ_D) at 1400 K which is found consistent with the theoretical fitting of S(T), exhibiting Θ _D of 1410 K and carrier density of 3.81 × 10²⁸/m³. Thermal conductivity κ(T) shows a jump at 38 K, i.e., at T_c, which was missing in some earlier reports. Critical current density (J_c) of up to 10⁵ A/cm² in 1–2 T (Tesla) fields at temperatures (T) of up to 10 K is seen from magnetization measurements. The irreversibility field, defined as the field related to merging of M(H) loops is found to be 78, 68 and 42 kOe at 4, 10 and 20 K respectively. The superconducting performance parameters viz. irreversibility field (H_irr) and critical current density J_c(H) of the studied MgB₂ are improved profoundly with addition of nano-SiC and nano-diamond. The physical property parameters measured for polycrystalline MgB₂ are compared with earlier reports and a consolidated insight of various physical properties is presented.     

The potts glass in uniform and random fields: a monte carlo investigation

As a simple model of an anisotropic orientational glass with short range forces, the 3-state Potts model on the simple cubic lattice with nearest neighbor interactions drawn from a Gaussian distribution is considered. With Monte Carlo methods we study the response of the system to a uniform “field” which favors one of the states. This is motivated by experiments which apply stress that favors one molecular orientation of the quadrupolar glass. The responsem to that fieldh=H/k _BT is analyzed in terms of an expansionm= χ₁ h+χ₁ h ²+χ₁ h ³+..., where χ₁ is the linear susceptibility, and χ₂,χ₁₃ are nonlinear susceptibilities. Unlike the case of spin glasses, where the spin inversion symmetry of the system in the absence of fields implies χ₂≡0,χ₂ is nonzero here and diverges to −∞ at the zero temperature transition of the model, while χ₃ diverges to +∞ as in spin glasses. At inifinite temperature, however, χ₁=1/3, χ₂=1/18 and χ₃=-1/54, i.e. the nonlinear susceptibilities have a different sign as at low temperature. In contrast, a random field does not induce a uniform order parameterm but only a glass order parameterq. The temperature dependence of this glass order parameterq(T) shows for intermediate field strength order parameterq(T) shows for intermediate field strength a maximum of the slopedq(T)/dT very similar to corresponding experiments.     

Wavevector-Dependent Susceptibility in <Emphasis Type="Italic">Z</Emphasis>-Invariant Pentagrid Ising Model

We study the q-dependent susceptibility χ(q) of a Z-invariant ferromagnetic Ising model on a Penrose tiling, as first introduced by Korepin using de Bruijn's pentagrid for the rapidity lines. The pair-correlation function for this model can be calculated exactly using the quadratic difference equations from our previous papers. Its Fourier transform χ(q) is studied using a novel way to calculate the joint probability for the pentagrid neighborhoods of the two spins, reducing this calculation to linear programming. Since the lattice is quasiperiodic, we find that χ(q) is aperiodic and has everywhere dense peaks, which are not all visible at very low or high temperatures. More and more peaks become visible as the correlation length increases—that is, as the temperature approaches the critical temperature. Supported in part by NSF Grant No. PHY 01-00041.     

Photophoresis of coarse aerosol particles with nonuniform thermal conductivity

The photophoresis of a coarse solid spherical aerosol particle in a one-component gas of nonuniform temperature is examined with consideration of the inertial effects in the hydrodynamic equations and the temperature jump in the Knudsen layer. The problem is solved in the spherical coordinates r, Θ, and ϕ. The photophoresis of a homogeneous particle is considered first. Then the results are generalized to an inhomogeneous particle. A particle whose thermal conductivity χ _i varies as a function of r is chosen as a model which describes a broad class of natural and artificially produced aerosol particles. It is shown that the error can be significant if the variable internal thermal conductivity χ _i =χ _i (r) of the particle is ignored and only the value of the thermal conductivity on its surface χ _i (a) is considered, on the assumption that the particle is homogeneous. It is also shown that a particle with a variable internal thermal conductivity χ _i =χ _i (r) and a density of heat sources within it q _i (r,Θ) can be regarded as a homogeneous particle with a thermal conductivity γχ _i (a) and a heat-source density m(r)q _i (r,Θ). Recurrence formulas for gand m(r) in the general case are presented. Analytical expressions for γ and m(r) are found for a model particle with pronounced inhomogeneity. Zh. Tekh. Fiz. 68, 1–6 (April 1998)     

Quark-antiquark states and their radiative transitions in terms of the spectral integral equation: Charmonia

Earlier by the authors (Yad. Fiz. 70, 68 (2007)), the bƃ states were treated in the framework of the spectral integral equation, together with simultaneous calculations of radiative decays of the considered bottomonia. In the present paper, such a study is carried out for the charmonium states. We reconstruct the interaction in the c-c sector on the basis of the data for the charmonium levels with J _PC = 0⁻⁺, 1⁻⁻, 0⁺⁺, 1⁺⁺, 2⁺⁺, 1⁺⁻ and radiative transitions ψ(2S) → γχ _c0(1P), γχ _c1(1P), γχ _c2(1P), γχ _c(1S) and χ _c0(1P), χ _c1(1P), χ _c2(1P) → γJ/ψ. The c-c levels and their wave functions are calculated for the radial excitations with n ≤ 6. Also, we determine the c-c component of the photon wave function using the e ⁺ e ⁻-annihilation data: e ⁺ e ⁻ → J/ψ(3097), ψ(3686), ψ(3770), ψ(4040), ψ(4160), ψ(4415) and perform the calculations of the partial widths of the two-photon decays for the n = 1 states η _c0(1S), χ _c0(1P), χ _c2(1P) → γγ and n = 2 states η _c0(2S) → γγ, χ _c0(2P) → γγ. We discuss the status of the recently observed c-c states X(3872) and Y(3941): according to our results, the X(3872) can be either χ _c1(2P) or η _c2(1D), while Y(3941) is χ _c2(2P). The text was submitted by the authors in English.