Power law scaling of the top Lyapunov exponent of a Product of Random Matrices

A sequence of i.i.d. matrix-valued random variables with probabilityp and with probability 1–p is considered. Leta() = a ₀ + O(), c() = c ₀ + O() lim ₀ b() = Oa ₀,c ₀, >0, andb()>0 for all >0. It is shown show that the top Lyapunov exponent of the matrix productX _n X _n-1...X ₁, = lim_n (1/n) n X _n X _n-1...X ₁ satisfies a power law with an exponent 1/2. That is, lim ₀(ln /ln ) = 1/2.     

A generalized representation for dielectric dispersion

The generalized formulation for dielectric dispersion is extended for dielectrics exhibiting strongly overlapping arcs in the- complex plane. Subsequently, a novel network representation is developed whereby Negative Impedance Converters (NICs) are employed along with passive R-C elements. Satisfactory agreement is obtained in comparing the experimental results with those calculated using the new formulation.     

Ising-Type and Other Transitions in One-Dimensional Coupled Map Lattices with Sign Symmetry

We consider a one-dimensional lattice of expanding antisymmetric maps [–1, 1][–1, 1] with nearest neighbor diffusive coupling. For such systems it is known that if the coupling parameter is small there is unique stationary (in time) state, which is chaotic in space-time. A disputed question is whether such systems can exhibit Ising-type phase transitions as grows beyond some critical value _c. We present results from computer experiments which give definite indication that such a transition takes place: the mean square magnetization appears to diverge as approaches some critical value, with a critical exponent around 0.9. We also study other properties of the coupled map system.     

Effective Potential for \mathcal{P}\mathcal{T}-Symmetric Quantum Field Theories

Recently, a class of -invariant scalar quantum field theories described by the non-Hermitian Lagrangian = () ² +g ² (i) was studied. It was found that there are two regions of . For <0 the -invariance of the Lagrangian is spontaneously broken, and as a consequence, all but the lowest-lying energy levels are complex. For 0 the -invariance of the Lagrangian is unbroken, and the entire energy spectrum is real and positive. The subtle transition at =0 is not well understood. In this paper we initiate an investigation of this transition by carrying out a detailed numerical study of the effective potential V _eff (_c) in zero-dimensional spacetime. Although this numerical work reveals some differences between the <0 and the >0 regimes, we cannot yet see convincing evidence of the transition at =0 in the structure of the effective potential for -symmetric quantum field theories.     

Continuity of type-I intermittency from a measure-theoretical point of view

We study a simple dynamical system which displays a so-called type-I intermittency bifurcation. We determine the Bowen-Ruelle measure and prove that the expectation (g) of any continuous functiong and the Kolmogoroff-Sinai entropyh() are continuous functions of the bifurcation parameter. Therefore the transition is continuous from a measure-theoretical point of view. Those results could be generalized to any similar dynamical system.     

Collision Integrals for Attractive Potentials

Motivated by previous discussions of particle interactions under the Manev potential U(r)=–/r–/r ², we construct the collision integrals for attractive potentials U(r) satisfying the condition U(r) r ²– as r0 with 0. For =0, we obtain a Boltzmann-type integral with a collision law allowing spiral interactions and nonunique correspondence between impact parameter and scattering angle. For >0, an additional Smoluchowski-type coagulation integral arises. All these integrals are derived and possible applications are discussed.     

Fine Structures of the Permittivity and Characteristic Losses of Electrons in Fluorite

Experimental-computational spectra of the permittivity and characteristic losses –Im^–1 for energies in the range 5–21 eV at a temperature of 4.2 K and theoretical spectra of and –Im^–1 of a fluorite crystal are resolved into elementary transition bands. The parameters of transition bands (energies of their maxima E _i, band halfwidths H _i and areas S _i, and oscillator forces f _i) are determined. A correlation of the spectral bands of and –Im^–1is established, and their specific features are elucidated.     

Hyperbolic initial-boundary-value problem for magnetic flux compression by plane liners

Based on the (relativistic) Maxwell equations with displacement current E/t, the initial-boundary-value problem for the compression of an initially homogeneous magnetic fieldB={0,B(x,t),0} between a fixed liner atx=0 and a detonation-driven liner atx=s(t) is solved analytically. By homogenizing the boundary conditions at the moving boundary, the transient electromagnetic fields are shown to be a superposition of quasistatic elliptic (E/t=0) and hyperbolic (E/t0) wave solutions. The wave equation is solved by a Fourier expansion in time-dependent eigenfunctionsf _n =f _n [nx/s(t)] for the variable region 0xs(t), where the Fourier amplitudes _n (t) are determined by coupled differential equations of second order. It is concluded that the conventional elliptic flux compression theories (E/t=0) hold approximately for nonrelativistic liner speeds , whereas the hyperbolic theory (E/t0) is valid for arbitrary liner speeds .     

Averaged electron Green function and CDW pinning in one-dimensional random potential

The averaged retarded electron Green functionG ⁺(,k) in 1d disordered metal is calculated using the Berezinsky diagram technique. Using the Gorkov's theory it is shown, that the substitution of inG ⁺ (,k) by the square of the external frequency atk=0 gives the dependence of Fröhlich conductivity _F(). This dependence describes the impurity pinning of CDW in 1d disordered metals. The good agreement of this dependence with experimental data Zeller et al. about _F() in quasi-1d conductor KCP is found     

Optical Spectra of Zinc Oxide in the Wide Energy Range 0–30 eV

A full set of spectra of the optical functions of a zinc oxide crystal in the range 0–30 eV has been calculated on the basis of the experimental spectrum of characteristic losses –Im ^–1. The ₂, ₁ and Im ^–1, Re ^–1 spectra were decomposed into elementary components. The most intense transverse and longitudinal components of transitions and their parameters have been determined. The data obtained were compared with theoretical calculations of the bands.     

Millimeter wave propagation through a chiral medium model of human trunk

That millimeter wave propagation through a chiral medium of human trunk has been discussed by obtaining the electromagnetic filed, absorbent power, specific absorption rate, temperature field and their distribution in a human trunk model with plane strati calate homogeneous tissues under a normal incidence plane wave. The chiral medium is described electromagnetically by the constitutive relationsD=E+B andB=H+E. The constants, and ate real and have values that are fixed by the size, the shape, and the spatial distribution of the elements that collectively compose the medium. Also, the principle of thermal therapeutics for millimeter wave is discussed preliminaryly.     

Сцинтилляционный сп ектрометр с сложение м импулъсов от двух кри сталлов

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A Local Quantum Version of the Kolmogorov Theorem

Consider in L²(^l) the operator family H():=P₀(,)+Q₀. P₀ is the quantum harmonic oscillator with diophantine frequency vector , Q₀ a bounded pseudodifferential operator with symbol holomorphic and decreasing to zero at infinity, and . Then there exists *>0 with the property that if ||<* there is a diophantine frequency () such that all eigenvalues E_n(,) of H() near 0 are given by the quantization formula where is an l-multi-index.Supported in part by NSF grant DMS-0204985.     

Semi-infinite Potts model and percolation at surfaces

The effects of surfaces on percolation are investigated near the bulk percolation threshold ind=6– dimensions. Using field-theoretic methods, this is done within the framework of a semi-infinite continuousq-state Potts model withq1. Renormalization-group equations are obtained which imply that the usual scaling laws for surface and bulk exponents are valid to all orders in , and the surface exponents at the ordinary and special transition are computed to order . Our result for ₁ ^ord is in conformity with the one by Carton.     

Microwave dielectric properties of Ti4+/MgO and Ni2+/MgO

The dielectric properties of titanium-doped magnesium oxide (Ti/MgO) and nickel-doped magnesium oxide (Ni/MgO) single crystals have been measured in the range of temperature from 300 to 450 K at the microwave frequency of 9.31 GHz. For both crystals the dielectric properties are found similar. From the conductivity data, the activation energy in the measured temperature region has been estimated to be 0.15 eV. The values of the temperature dependence (–1)^–1(+2)^–1 (/T) _p have been calculated. The data confirms the Bosmann and Havinga postulate that, for materials in which the dielectric constant; is less than 20 the temperature dependence should be positive.     

Geometric expansion of the boundary free energy of a dilute gas

We consider a dilute classical gas in a volume ^–1 which tends to ^d by dilation as 0. We prove that the pressurep(^–1) isC ^q in at =0 (thermodynamic limit), for anyq, provided the boundary isC ^q and provided the Ursell functionsu _n (x ₁, ...,x _n) admit moments of degreeq and have nice derivatives.     

Un phénomène de concentration évanescente pour des flots non-stationnaires incompressibles en dimension deux

We consider a sequencev of non-stationary solutions of the incompressible 2D-Euler equation, locally bounded inL ². We prove that if the defect measure is supported in a one-dimensional set (³) of some special type (which we call finite type), the weak limitv ofv is a solution of the Euler equations: our theorem is of the type concentration-cancellation.     

Construction of analytic KAM surfaces and effective stability bounds

A class of analytic (possibly) time-dependent Hamiltonian systems withd degrees of freedom and the corresponding class of area-preserving, twist diffeomorphisms of the plane are considered. Implementing a recent scheme due to Moser, Salamon and Zehnder, we provide a method that allows us to construct explicitly KAM surfaces and, hence, to give lower bounds on their breakdown thresholds. We, then, apply this method to the HamiltonianHy ²/2+(cosx+cos(x–t)) and to the map (y,x)(y+ sinx,x+y+ sinx) obtaining, with the aid of computer-assisted estimations, explicit approximations (within an error of 10^–5) of the golden-mean KAM surfaces for complex values of with || less or equal than, respectively, 0.015 and 0.65. (The experimental numerical values at which such surfaces are expected to disappear are about, respectively, 0.027 and 0.97.) A possible connection between break-down thresholds and singularities in the complex -plane is pointed out.To our friend and colleague Paola CalderoniSupported by Consiglio Nazionale delle Ricerche, Italy     

Renormalized field theory of the critical dynamics ofO(n)-symmetric systems

The critical dynamics of an-component order parameter of anO(n)-symmetric system is analyzed with a Gell'Mann-Low-type renormalization group equation ind=4– dimensions. Dynamical scaling holds forn>3/2+O(). Besides the dynamical exponentz=d/2 the correction exponents to order are found. To the same order the shape function of the dynamical order parameter correlation function is calculated which exhibits fluctuation induced peaks forn3 and extrapolated tod=3.     

Band-gap structure of the spectrum of periodic Maxwell operators

We investigate the band-gap structure of some second-order differential operators associated with the propagation of waves in periodic two-component media. Particularly, the operator associated with the Maxwell equations with position-dependent dielectric constant (x),xR ³, is considered. The medium is assumed to consist of two components: the background, where (x) = _b , and the embedded component composed of periodically positioned disjoint cubes, where (x) = _a . We show that the spectrum of the relevant operator has gaps provided some reasonable conditions are imposed on the parameters of the medium. Particularly, we show that one can open up at least one gap in the spectrum at any preassigned point provided that the size of cubesL, the distancel=L betwen them, and the contrast = _b / _a are chosen in such a way thatL ^–2, and quantities ^-1-3/2 and ² are small enough. If these conditions are satisfied, the spectrum is located in a vicinity of widthw(^3/2)^-1 of the set {² L ^-2 k ²:kZ³}. This means, in particular, that any finite number of gaps between the elements of this discrete set can be opened simultaneously, and the corresponding bands of the spectrum can be made arbitrarily narrow. The method developed shows that if the embedded component consists of periodically positioned balls or other domains which cannot pack the space without overlapping, one should expect pseudogaps rather than real gaps in the spectrum.