Finite-Volume Glauber Dynamics in a Small Magnetic Field

We consider Glauber dynamics on a finite cube in d-dimensional lattice (d2), which is associated with basic Ising model at temperature T=1/1 under a magnetic field h > 0. We prove that if the effective magnetic field is positive, then the relaxation of the Glauber dynamics in the uniform norm is exponentially fast, uniformly over the size of underlying cube. The result covers the case of the free-boundary condition with arbitrarily small positive magnetic field. This paper is a continuation of an attempt initiated earlier by Schonmann and Yoshida to shed more light on the relaxation of the finite-volume Glauber dynamics when the thermodynamic parameter (, h) is so near the phase transition line, (, h); _c < &h = 0, that the Dobrushin–Shlosman mixing condition is no longer available.     

On the equivalence of the relativistic theories of gravitation

Einstein's equations are rewritten in terms of a certain torsionless linear connection which differs, in general, from the Levi-Civita metric connection . The torsionless connection appears in a natural way as the canonical momentum of the gravitational field g . Einstein's equations have a simple interpretation in terms of the connection . The equivalence of the so-calledpurely metric, purely affine, andmetricaffine theories of gravitation is proved.This work has been written under the financial support of Gruppo Nazionale per la Fisica Matematica of the Italian National Research Council.     

Gentle perturbations

By introducing a specific type of perturbation,A, in the Hamiltonian, we define a class of gently perturbed states, ,A, of a canonical ensemble, . The perturbations are chosen so as to preserve a relationship of the form ,A constant ×. Applications in ergodic theory and phase transitions are described.     

Four-parametric regular black hole solution

We present a regular class of exact black hole solutions of the Einstein equations coupled with a nonlinear electrodynamics source. For weak fields the nonlinear electrodynamics becomes the Maxwell theory, and asymptotically the solutions behave as the Reissner–Nordström one. The class is endowed with four parameters, which can be thought of as the mass m, charge q, and a sort of dipole and quadrupole moments and , respectively. For 3, 4, and |q|2s _c m the corresponding solutions are regular charged black holes. For = 3, they also satisfy the weak energy condition. For = = 0 we recover the Reissner–Nordström singular solution and for = 3, = 4 the family includes a previous regular black hole reported by the authors.     

Finite-size scaling for Potts models

Recently, Borgs and Kotecký developed a rigorous theory of finite-size effects near first-order phase transitions. Here we apply this theory to the ferromagneticq-state Potts model, which (forq large andd2) undergoes a first-order phase transition as the inverse temperature is varied. We prove a formula for the internal energy in a periodic cube of side lengthL which describes the rounding of the infinite-volume jumpE in terms of a hyperbolic tangent, and show that the position of the maximum of the specific heat is shifted by _m (L)=(Inq/E)L ^–d +O(L ^–2d ) with respect to the infinite-volume transition point _t . We also propose an alternative definition of the finite-volume transition temperature _t (L) which might be useful for numerical calculations because it differs only by exponentially small corrections from _t .     

Higher quantum conserved current in a new completely integrable model

The first higher local quantum conserved current in the recently proposed new completely integrable (2 e+e^-2)₂ model is explicitly constructed thus proving absence of particle production and factorization of multiparticle scattering.     

Decay of the Bethe–Salpeter Kernel and Bound States for Lattice Classical Ferromagnetic Spin Systems at High Temperature

We consider lattice classical ferromagnetic spin systems at high temperature (1) with nearest neighbor interactions and even single-spin distributions (ssd). Associated with each system is an imaginary time lattice quantum field theory. It is known that there is a particle of mass m–ln in the energy-momentum spectrum. If s ⁴–3s ²²<0, where s ^k is the kth moment of the ssd, and is sufficiently small, we show that in the two-particle subspace there is no mass spectrum up to 2m. For >0 we show that the only mass spectrum in (m, 2m) is a bound state of mass m _b=2m+ln(1–)+O(), where =(+2s ²²)^–1. A bound on the decay of the kernel of a Bethe–Salpeter equation is obtained and used to prove these results.     

Probabilistic approach to homoclinic chaos

Three-dimensional systems possessing a homoclinic orbit associated to a saddle focus with eigenvalues ±i, – and giving rise to homoclinic chaos when the Shil'nikov condition < is satisfied are studied. The 2D Poincaré map and its 1D contractions capturing the essential features of the flow are given. At homoclinicity, these 1D maps are found to be piecewise linear. This property allows one to reduce the Frobenius—Perron equation to a master equation whose solution is analytically known. The probabilistic properties such as the time autocorrelation function of the state variablex are explicitly derived.     

Systems Approach to Optimization of the Regimen of Photodynamic Therapy of Solid Sarcoma M-1 Using the “Fotosens” Preparation as Example

A systems analysis of the interaction between objects (tumor, healthy tissue, radiation, and photosensitizer of the singlet state of oxygen) involved in photodynamic therapy was carried out. A schematic diagram of the biologically significative processes proceeding under these circumstances was proposed. This schematic diagram can serve as a basis for a systems approach to the optimization of photodynamic therapy. The efficiency of the systems approach in photodynamic therapy was demonstrated using Fotosens and Khlorin S preparations, carotene, and dodecaprene -carotene in biological experiments on Wistar rats and mouses inoculated for the solid sarcoma M-1.     

The strength of Einstein's equations

The strength of Einstein's empty-space field equations is computed anew and shown to be equal to the amount of initial data required for a local solution of the equations. This same amount of initial data is shown to be precisely that required for a set of 16 unknown first-order differential equations containing 10 field variables and having six identities of second order. The 10 field variables must be functions of second order in the metric coefficients. The 16 field equationsC , = 0 whereC is Weyl's conformal tensor, are shown to have the same properties as those of the unknown equations, suggesting thatC = 0 is a satisfactory local first-order formulation of Einstein's second-order empty-space field equations.     

Analyticity properties of the surface free energy of the Ising model

For an Ising ferromagnet with nearest-neighbour interactions of strengthK and surface magnetic fieldh, the surface free energy in the presence of a positively (or negatively) magnetized zero-field bulk phase is shown to be analytic inh for Reh<K–/, where =2.96 ... and is the inverse temperature. This puts the lower boundK–/ on the values ofh at which wetting and layering transitions can take place.     

Betatron-synchrotron resonance in free electron laser

In terms of Bogoliubov's nonlinear theory, the first five betatron-synchrotron resonances of _s=(p q)2K, p/q=1/2, 1, 3/2, 1/3, 2/3 which may occur during laser satulation establishing process have been generally examined. Contrast to previous studies we found that the most dangerous resonance does not take place in the vicinity of _s=2k, but in that of _s=k. The width of region of _s=k is proportional to with (k _w ² /k) remittance, the passing time over the region due to the laser field being amplified is only one pass over the undulator at most and depends on the gain, and the increment of synchrotron amplitude in passing time is proportional to .In summary we conclude that the betatron-synchrotron resonances do not have any significant effect for detrapping off-axis electrons in a practical case.     

Power-law falloff in the kosterlitz-Thouless phase of a two-dimensional lattice Coulomb gas

We give a rigorous proof of power-law falloff in the Kosterlitz-Thouless phase of a two-dimensional Coulomb gas in the sense that there exists a critical inverse temperaturegb and a constant >0 such that for all> and all external charges R we have , whereG (x) is the two-point external charges correlation function,=dist(, Z), and for 0$$ " align="middle" border="0"> . In the case of a hard-core or standard Coulomb gas with activityz, we may choose=(z) such that(z)24 asz0.     

One-dimensional harmonic lattice caricature of hydrodynamics: Second approximation

The long-time behavior of an infinite chain of coupled harmonic oscillators is studied. In addition to a limiting hydrodynamic (Euler-type) equation, the next approximation is investigated. The corresponding equation is derived.     

The temperature vibrations of urea molecules

The structural and dynamic parameters of urea at 112°K and 295°K were determined by the least squares method. The characteristic temperature of the torsional optical vibrations of a molecule about a C-O bond was determined and is in good agreement with the value determined by Raman scattering. The fractional X-coordinate of the nitrogen atom corrected for torsional vibrations was determined and it was found that the magnitude of the projection of the C-N bond in the given temperature range changes only within the limits of observational errors. A new method, called temperature difference synthesis, is described and it is shown that it is suitable for rapid qualitative determination of the thermal anisotropy of the vibrations of atoms in a crystal lattice.

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112°K 295°K. C-O , , . X- , C-N . , , , .

     

Relaxation Processes and Fractional Differential Equations

Relaxation properties of different media (dielectrics, semiconductors, ferromagnetics, and so on) are normally expressed in terms of response function f(t) or of real and imaginary components of its Fourier transform dependent on the frequency . It had been recently recognized that most of real materials show deviation from classical Debye process. There exist a few empirical approximations of non-Debye response functions. One of them is the two-power approximation containing and , where and belong to the interval (0, 1). This formula gives the basis for introducing of fractional differential equation considered in this paper. A stochastic interpretation of this equation is offered; its solution is found and investigated. The results are in agreement with experimental data.     

Analytic Properties of the Structure Function for the One-Dimensional One-Component Log–Gas

The structure function S(k; ) for the one-dimensional one-component log–gas is the Fourier transform of the charge–charge, or equivalently the density–density, correlation function. We show that for |k|j in the power series expansion of f(k; ) about k=0 is of the form of a polynomial in /2 of degree j divided by (/2)^j. The bulk of the paper is concerned with calculating these polynomials explicitly up to and including those of degree 9. It is remarked that the small k expansion of S(k; ) for the two-dimensional one-component plasma shares some properties in common with those of the one-dimensional one-component log–gas, but these break down at order k⁸.     

A dynamical phase transition in a caricature of a spin glass

This paper studies the rate of convergence to equilibrium of Glauber dynamics (Gibbs Sampler) for a system ofN Ising spins with random energy (at inverse temperature >0). For each of the 2 ^N spin configurations the energy is drawn independently from the values 0 and-logN with probabilities 1-N ^–7, resp.N ^– (>0), and is kept fixed during the evolution. The main result is an estimate of the coupling time of two Glauber dynamics starting from different configurations and coupled via the same updating noise. AsN the system exhibits two dynamical phase transitions: (1) at =1 the coupling time changes from polynomial (>1) to stretched exponential (<1) inN; (2) if <1, then at = the almost coupling time [i.e., the first time that the two dynamics are within distanceo(N)] changes from polynomial (<) to stretched exponential (>) inN. The techniques used to control the randomness in the coupling are static and dynamic large-deviation estimates and stochastic domination arguments.     

An Equation for the Dissipation Rate Correlation and Its Implications for the Intermittency Exponent μ in Turbulence

We derive an equation satisfied by the dissipation rate correlation function, for the homogeneous, isotropic state of fully-developed turbulence from the the Navier–Stokes equation. In the equal time limit we show that the equation leads directly to two intermittency exponents ₁=2– ₆ and ₂=z₄– ₄, where the 's are exponents of velocity structure functions and z₄ is a dynamical exponent characterizing the fourth order structure function. We discuss the contributions of the pressure terms to the equation and the consequences of hyperscaling.     

К ВОПРОСУ НЕОДНОРОДН ОСТИ РАЗМАГНИЧИВАЮЩ ИХ ПОЛЕИ ПРИ ФЕРРОМАГНИ ТНОМ РЕЗОНАНСЕ

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