Current distributions in a two-dimensional random-resistor network

The current and logarithm-of-the-current distributionsn(i) andn(ln i) on bond diluted two-dimensional random-resistor networks at the percolation threshold are studied by a modified transfer matrix method. Thek th moment (–9k8) of n(ln i) i.e., ln i&^k, is found to scale with the linear sizeL as (InL)^(k). The exponents (k) are not inconsistent with the recent theoretical prediction (k)=k, with deviations which may be attributed to severe finitesize effects. For small currents, ln n(y)–, yielding information on the threshold below which the multifractality of (i) breaks down. Our numerical results for the moments of the currents are consistent with other available results.     

On a regularity problem occurring in connection with Anosov diffeomorphisms

Let be aC -manifold and _s and _u be two Hölder foliations, transverse, and with uniformlyC leaves. If a functionf is uniformlyC along the leaves of the two foliations, then it isC on . The proof is elementary.     

On the asymptotic behaviour of infinite gradient systems

We consider gradient systems of infinitely many particles in one-dimensional space interacting via a positive invariant pair potential with a hard core. The main assumption is that is strictly convex within the rangeR of (whereR is a fixed number ). Under some technical conditions we prove the following theorems: Let the initial distribution be given by a translation invariant point process onR ¹. Then there exists only one extreme equilibrium state with a given intensityI() satisfyingI()R ^–1, and all ergodic initial distributions with an intensityI()R ^–1 converge weakly ast to the extreme equilibrium state with the same intensity.     

Adjoint solutions of the Brans-Dicke equations

It is shown that if the Brans-Dicke equations have the solution,g _ij generated by the trace free sourceT _n (T-O) then there exists an adjoint solution ^–1, ²g_ij of these equations generated by the source ^-2 T _u. An example is considered.     

Upper critical fields of single-crystalline and polycrystalline Ca-Sr-Bi-Cu-O compounds

The ac resistivity of a 110 K phase multiphase polycrystalline Ca-Sr-Bi-Cu-O compound and an 85 K phase single-crystalline Ca_0.9Sr_2.1Cu_2.0O_{8 +} has been measured in various magnetic fields up to 8 T. Values forB _c ^2/ (0) of 71.5 T and forB _c2 (0) of 542 T are found for the 85 K phase sample. A value forB _c2(0) of 57.9 T is estimated for the 110K phase compound.     

Влияние сильного выс окочастотного поля на расслоение положи тельного столба постоянного тлеющег о разряда

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The influence of a strong high-frequency field on the stratification of the positive column of a D-C glow discharge

An experimental study is made of the damping of moving striations in a d-c glow discharge by a strong high-frequency field. The results of measurement are in agreement with existing conceptions on the production and mechanism of propagation of moving striations. Apart from the process of damping the paper also describes the standing stratification of the positive column of a d-c discharge as a result of a superposed high-frequency discharge.

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Hamiltonian formulation of general relativity in terms of Dirac spinors

The Dirac spinors and matrices are used in combination with the Arnowitt-Deser-Misner formalism in order to obtain yet another formulation of Hamiltonian general relativity, together with a new form of the Gauss-Codazzi equations. The relation with Ashtekar's variables is analyzed; it is shown, for instance, that the matrices are equivalent to the electric field variable. The electric and magnetic decomposition of the gravitational field is also studie using Dirac matrices.     

Large-Deviation Principle for One-Dimensional Vector Spin Models with Kac Potentials

We consider the one-dimensional planar rotator and classical Heisenberg models with a ferromagnetic Kac potential J (r)=J(yr), J with compact support. Below the Lebowitz-Penrose critical temperature the limit (mean-field) theory exhibits a phase transition with a continuum of equilibrium states, indexed by the magnetization vectors m s, s any unit vector and m the Curie–Weiss spontaneous magnetization. We prove a large-deviation principle for the associated Gibbs measures. Then we study the system in the limit 0 below the above critical temperature. We prove that the norm of the empirical spin average in blocks of order ^–1 converges to m , uniformly in intervals of order ^–p , for any p 1. We also give a lower bound to the scale on which the change of phase occurs, by showing that the empirical spin average is approximately constant on intervals having length of order ^-1-with (0,1) small enough.     

Dynamic scaling for spin glasses near the de Almeida-Thouless line

We calculate the dynamic local susceptibility () of an Ising spin glass near the de Almeida-Thouless (AT) line within the soft spin dynamics for the Sherrington-Kirkpatrick model. We find a crossover from analytic behaviour of () at =0 above the AT line to a power law behaviour ()(–i) ^v on the AT line and discuss the analytic properties of the crossover function. The frequencyscale is proportional to ^1/v , where measures the distance from the AT line. We determine the spectrum of relaxation times which diverge as ^1–1/v . The average relaxation time diverges as ^–1/v wherev1/2. In addition we determine the absolute frequency scale and prove the consistency of the ansatz of Sompolinsky and Zippelius ()–(0)(–i) ^v at and below the AT line.     

Inequalities for the Schattenp-norm. III

We present some inequalities for the Schattenp-norm of operators on a Hilbert space. It is shown, among other things, that ifA is an operator such that ReAa0, then for any operatorX, AX+XA* _p 2aX _p . Also, for any two operatorsA andB, A–B ₂ ² +A*B* ₂ ² 2A–B ₂ ² .     

Symmetry vector fields and similarity solutions of a nonlinear field equation describing the relaxation to a maxwell distribution

In the study of the formulation of Maxwellian tails the nonlinear partial differential equation ² u/x +u/x+u ²=0 arises. We determine the Lie point symmetry vector fields and calculate the similarity ansätze. Then we discuss the resulting ordinary differential equations. Finally, the existence of Lie Bäcklund vector fields is studied and a Painlevé analysis is performed.     

The ground state energy of Sdhrödinger operators

We studye()=inf spec(-+V) and examine whene()<0 for all 0. We prove thatc ²e()–d ² for suitableV and all small ||.Research partially funded under NSF grant number DMS-9101716.     

Self-gravitating three-dimensional solitons in nonlinear scale-invariant electrodynamics

A scale-invariant nonlinear modification of Maxwellian electrodynamics within general relativity is proposed. The starting point is the Mie model and its scale-invariant generalization in flat space-timeE ₄. We prove that all static, spherically symmetrical regular field configurations in this new theory, as well as those in the Mie model, possess negative energy. In search of solitonlike solutions with positive masses, we take into account their proper gravitational fields. We show first that in Riemannian space any gauge-invariant electrodynamic theory does not admit regular solutions. Supposing the gauge invariance to be broken inside the particle, we prove the existence of static particlelike solutions with spherical symmetry and positive energy in the scale-invariant electrodynamics described by a Lagrangian density of the form =-Y(I)R/(2)-W(I)F F _u/2+2X(I)R A A , withY, W, andX arbitrary functions of the invariantI=A A . The correspondence with the Maxwellian theory is required.     

Logical independence in quantum logic

The projection latticesP(₁),P(₂) of two von Neumann subalgebras ₁, ₂ of the von Neumann algebra are defined to be logically independent if A B0 for any 0AP(₁), 0BP(₂). After motivating this notion in independence, it is shown thatP(₁),P(₂) are logically independent if ₁ is a subfactor in a finite factor andP(₁),P(₂ commute. Also, logical independence is related to the statistical independence conditions called C^*-independence W^*-independence, and strict locality. Logical independence ofP(₁,P(₂ turns out to be equivalent to the C^*-independence of (₁,₂) for mutually commuting ₁,₂ and it is shown that if (₁,₂) is a pair of (not necessarily commuting) von Neumann subalgebras, thenP(₁,P(₂ are logically independent in the following cases: is a finite-dimensional full-matrix algebra and ₁,₂ are C^*-independent; (₁,₂) is a W^*-independent pair; ₁,₂ have the property of strict locality.     

Experimental Test of a Time-Temperature Formulation of the Uncertainty Principle Via Nanoparticle Fluorescence

No Heading The uncertainty in the measured fluorescence decay lifetimes of 30 nm particles of YAG:Cc was used to evaluate the predictions of a novel form of the Heisenberg uncertainty principle suggested by de Sabbata and Sivaram, T t h/k. The worst-case uncertainty in temperature of 4.5 °K (as derived from the relationship between temperature and lifetime) and the measured uncertainty in decay lifetime, 0.45 ns, yielded an internal estimate of T t = 2.0 × 10^–9 °K s, which is 263 times larger than /k = 7.6 × 10^–12 °K s. An external estimate of T t = 4.5 × 10¹¹ °K s (which is = 6 times /k) is derived from the independently measured uncertainty in the temperature of the sample and the experimentally determined uncertainty in lifetime. These results could be low by a factor of 5.6 if signal averaging must be taken into account. If valid, the findings are consistent with the predictions of this version of the uncertainty principle and they imply the existence of a type of thermal quantum limit.     

Convergent perturbation expansions for Euclidean quantum field theory

Mayer perturbation theory is designed to provide computable convergent expansions which permit calculation of Greens functions in Euclidean quantum field theory to arbitrary accuracy, including nonper-turbative contributions from large field fluctuations. Here we describe the expansions at the example of 3-dimensional ⁴-theory (in continuous space). They are not essentially more complicated than standard perturbation theory. Then ^th order term is expressed in terms ofO(n)-dimensional integrals, and is of order ^k if 4k–3n4k.Dedicated to the memory of Kurt Symanzik     

Direct observation of the second-order Stark effect of theX-B transition in molecular iodine

The second-order Stark shift of the components of the hyperfine structure of the transition¹ _g ⁺ ( = 0,j = 13, 15) ³ _ou ⁺ ( = 43,j = 12, 16) (of molecular iodine have been studied by means of saturated absorption spectroscopy in an external cell with the I₂ vapour located in an electric field. The anisotropic polarizabilities of the upper and lower levels together with the difference between the isotropic polarizabilities of the levels of the transition have been obtained.     

Ground state of a spin-phonon system. II. Adiabatic limit

The phase transition for a spin in a magnetic fieldB coupled to acoustic phonons by a coupling constant is studied. The caseB1 with an upper cutoff of unity for the phonons is studied systematically by using an adiabatic canonical transformation. In leading order the transition line is at =2/B=1. In the normal phase (<1) the ground-state energy is –B/2 plus a function of that is given explicitly as the solution of a pair theory. In the broken symmetry phase (>1) the energy is the classical energy plus the same function of =1/². It is found that the first derivatives of the energy with respect to and with respect toB have finite jumps across the transition line. Quantum fluctuations in both phases are treated. Higher-order terms are a series of powers of 1/B times functions of . The case of a small transverse fieldB is also studied. The sharp transition disappears and is replaced by rapid variation in a region of order (B₁/B)^2/3 about =1.     

Phase Turbulence in the Complex Ginzburg-Landau Equation via Kuramoto–Sivashinsky Phase Dynamics

We study the Complex Ginzburg-Landau initial value problem for a complex field uC, with ,R. We consider the Benjamin–Feir linear instability region We show that for all and for all initial data u₀ sufficiently close to 1 (up to a global phase factor eⁱ₀,₀R) in the appropriate space, there exists a unique (spatially) periodic solution of space period L₀. These solutions are small even perturbations of the traveling wave solution, and s, have bounded norms in various L^p and Sobolev spaces. We prove that apart from corrections whenever the initial data satisfy this condition, and that in the linear instability range the dynamics is essentially determined by the motion of the phase alone, and so exhibits phase turbulence. Indeed, we prove that the phase satisfies the Kuramoto–Sivashinsky equation for times while the amplitude 1+² s is essentially constant.Supported in part by the Fonds National Suisse.     

Surviving extrema for the action on the twisted SU(∞) one point lattice

We give a simplified construction of twist eating configurations, based on a theorem due to Frobenius. These configurations are defined through the equation:U U U ⁺ U ⁺ =exp(2in /N) withU SU(N), =1 tod andn an antisymmetric matrix with integer entries. In the (Twisted)-Eguchi-Kawai model they yield extrema some of which survive forN. Comparison is made with the Monte Carlo data of the internal energy in the small coupling region.