Long-range correlations at depinning transitions

Semi-infinite systems are considered with long-range surface fields B _z ^–(1+r) for large distancesz from the surface. The influence of such fields on the global phase diagram and on the critical singularities of depinning transitions is studied within Landau theory. For |B|0, the correlation length diverges as b ^–1/2 withb=|Bln|B^–(1+r). For finiteB, t ^v withv =(2+r)/(2+2r) wheret measures the distance from bulk coexistence. In the latter case, a Ginzburg criterion leads to the upper critical dimensiond ^*=(2+3r)/(2+r).     

Enhancement of activated decay of metastable states by resonant pumping

We consider the effect of a high-frequency pumping cost on the escape rate of a classical underdamped Brownian particle out of a deep potential well. The energy dependence of the oscillation frequency(E) is assumed to be weak on the scale of thermal energy,_E(0)T(0)T/V₀ (0)[_E(0) is the derivative of(E) atE= 0,V ₀ is the barrier height,V ₀ T]. The quadratic-in- contribution to the decay rate is calculated in two different regimes: (1) for the case of resonance of the pumping frequency with the nth harmonic of the internal motion at an energye, when = n(e); (2) for a rollout region of the basic resonance near the bottom of the potential well, when ¦-(0)¦ and is the damping coefficient. In the latter case the absorption spectrum and the enhancement of the decay rate are calculated as functions of two reduced parameters, the anharmonicity of the potential,v _E (0)T/, and the resonance mismatch, [ —(0)]/. It is shown that the effect of the pumping increases with diminishing ¦v¦ and at small v is proportional tov ^–1. In this regime, the dependence on is stepwise: the pumping contribution is large for v > 0 and small for v < 0. In the frame of our theory, the decay rate is invariant against the simultaneous alternation of the signs of andv. The spectrum of the energy absorption has the standard Lorentzian shape in the absence of anharmonicity,v=0, and with increasing of ¦v¦ shifts and widens retaining its bell-shape form.     

Logically independent von Neumann lattices

Three definitions of logical independence of two von Neumann latticesP₁,P₂ of two sub-von Neumann algebras ₁, ₂ of a von Neumann algebra are given and the relations of the definitions clarified. It is shown that under weak assumptions the following notion, called logical independence is the strongest:A B 0 for any 0 A P₁, 0 B P₂. Propositions relating logical independence ofP₁,P₂ toC ^*-independence,W ^* independence, and strict locality of ₁, ₂ are presented.     

Bell's inequality forC *-algebras

Bell's inequality dealing with local hidden variables is given two formulations in terms ofC ^*-algebras. In particular, Bell's inequality holds for all states onAB wheneverA andB are unitalC ^*-algebras at least one of which is Abelian, i.e., at least one corresponds to a classical physical system.     

Second-order Zeeman effect of theX−B transition in molecular iodine

Saturated absorption spectroscopy was applied to study the line shape of the molecular iodineX( = 0,J = 13,15) B( = 43,J = 12, 16) transition ( = 514.5 nm) in a transversal magnetic field as high as 0.51 T. The Zeeman structure of several hyperfine structure (hfs) components was completely resolved and a detailed study of the second-order Zeeman shift and splitting was made. The anisotropic Magnetic Susceptibility (MS) of the molecular iodine both in theB(43) (X = 7.3 ± 1 × 10^–34 J/Oe²) and theX(0) [ = (0.6 ± 1) × 10^–34 J/Oe²] states as well as the isotropic MS difference [0 –o = (2 ± 0.2) × 10^–34 J/Oe²] was measured.     

Observed difference between the probabilities of recoilless resonance absorptionf′ and reemissionf″ of gamma-quanta in single crystals of Na2[Fe(CN)5NO]·2 H2O

The recoilless absorption probability factor,f, and recoilless reemission,f, both measured on Na₂[Fe(CN)₅NO]·2 H₂O single crystals using the black filter technique, were found to be different. Unexpectedly, the results found weref>f. In the calculation off, selfabsorption in the scatterer, non-ideality of the black filter and the influence of non-resonant scattering processes have all been taken into account. By varying the scattering geometry for the incoming and outgoing -beam relative to the crystallographic axes only a change in the reemitted valuesf _a, f_b, f_c could be detected because of the long lifetime of the excited nucleus (10^–7 s) relative to the lattice vibration frequencies (10¹² Hz).     

Theory of percolation in fluids of long molecules

We use the reference interaction site model (RISM) integral equation theory to study the percolation behavior of fluids composed of long molecules. We examine the roles of hard core size and of length-to-width ratio on the percolation threshold. The critical density _c is a nonmonotonic function of these parameters exhibiting competition of different effects. Comparisons with Monte Carlo calculations of others are reasonably good. For critical exponents, the theory yields =2=2 for molecules of any noninfinite lengthL. WhenL is very large, the theory yields _cL ^–2. These predictions compare favorably with observations of the conductivity for random assemblies of conductive fibers. The threshold region where asymptotic scaling holds requires the correlation length (/ _c ) ^–v to be much larger thanL. Evidently, the range of densities in this region diminishes asL increases, requiring that density deviations from _c be no larger thanL ^–2. Otherwise, crossover behavior will be observed.     

μ+SR in magnetically ordered BCC metals: Local fields, μ+ sites,quantum diffusion,and strain effects

The paper gives a critical discussion of the procedures for extracting from the ⁺SR signals obtainable on magnetically ordered metals information on ⁺ sites, on local lattice distortions induced by the ⁺, on the local magnetic fields felt by the ⁺, and on quantum diffusion. Results for-Fe are: ⁺ occupy O sites, the tetragonality of the elastic double-force tensor isA–B 2eV, the dipolar magnetic field acting on the ⁺ isB _dip=(0.66±0.02)T. Using this information ⁺ hopping rates and diffusivities in Fe are deduced and compared with diffusivities obtained for hydrogen and deuterium. From this it is concluded that hydrogen in Fe diffuses via the adiabatic mechanism. In addition, the paper contains a brief summary of the theoretical background required for taking advantage of the rather large ¦A– B¦ values expected for ⁺ at O sites in bcc metals in order to gain information on the effects of energy asymmetries between neighbouring ⁺ sites on the ⁺ hopping rates.     

Static and Vibrational Properties of Transition Metals

A model pseudopotential depending on an effective core radius but otherwise parameter free is proposed to study the equation of state by incorporating the s-d hybridization effects. Very recently proposed screening function due to Sarkar et al has been used to obtain the screened form factor. The equations of state for Cu, Ta, Mo, W and Pt have been studied up to the pressure of 1000 GPa. The vibrational properties such as phonon dispersion curves (in q and r space), phonon density of states, mode Grüneisen parameters, maximum frequency _max, mean frequency , ^21/2 = (/ ^-1)^1/2 and fundamental frequency ² and static properties such as dynamical elastic constants of rhodium and iridium are also calculated. The theoretical results are compared with experimental findings wherever possible. A good agreement between theoretical investigations and experimental findings has confirmed our formulation.     

Ballistic annihilation and deterministic surface growth

A model of deterministic surface growth studied by Krug and Spohn, a model of the annihilating reactionA+Binert studied by Elskens and Frisch, a one-dimensional three-color cyclic cellular automaton studied by Fisch, and a particular automaton that has the number 184 in the classification of Wolfram can be studied via a cellular automaton with stochastic initial data called ballistic annihilation. This automaton is defined by the following rules: At timet=0, one particle is put at each integer point of . To each particle, a velocity is assigned in such a way that it may be either +1 or –1 with probabilities 1/2, independent of the velocities of the other particles. As time goes on, each particle moves along at the velocity assigned to it and annihilates when it collides with another particle. In the present paper we compute the distribution of this automaton for each timet . We then use this result to obtain the hydrodynamic limit for the surface profile from the model of deterministic surface growth mentioned above. We also show the relation of this limit process to the process which we call moving local minimum of Brownian motion. The latter is the processB _x ^min ,x , defined byB _x ^min min{B _y ;x–1yx+1} for everyx , whereB _x ,x , is the standard Brownian motion withB ₀=0.     

Improved bounds for the transition temperature of directed polymers in a finite-dimensional random medium

We consider the problem of directed polymers in a random medium of a finitedimensional lattice. In the high-temperature phase of this system it is known that the annealed and quenched free energies coincide. Upper bounds on the transition temperature to a low-temperature phase had previously been obtained by calculating the first two moments Z and Z² of the partition function. We improve these bounds by estimating noninteger moments Z for 1<<2.     

An upper bound on the free energy for classical systems with Coulomb interactions in a varying external field

The thermodynamic limit is taken using a sequence of regions all the same shape as a given region of volume ||, with a specified distribution of normal field component on . We show that with magnetostatic interactions the limiting free energy density is bounded above by jhen where (,B) is the free energy density for a system of density in a uniform external fieldB and the inf is taken over all divergence-free fieldsB with given normal component on and all densities (x) compatible with particle number constraints of the form where _i is a sub-region of . A physical argument suggests that this upper bound is the true thermodynamic limit, and that it takes account demagnetization effects. Electrostatic interactions can be treated similarly.     

Hydrodynamic Limit of Brownian Particles Interacting with Short- and Long-Range Forces

We investigate the time evolution of a model system of interacting particles moving in a d-dimensional torus. The microscopic dynamics is first order in time with velocities set equal to the negative gradient of a potential energy term plus independent Brownian motions: is the sum of pair potentials, V(r)+ ^d J(r); the second term has the form of a Kac potential with inverse range . Using diffusive hydrodynamic scaling (spatial scale ^–1, temporal scale ^–2) we obtain, in the limit 0, a diffusive-type integrodifferential equation describing the time evolution of the macroscopic density profile.     

Noncommutative Ricci Curvature and Dirac Operator on C q [SL2] at Roots of Unity

We find a unique torsion free Riemannian spin connection for the natural Killing metric on the quantum group C _q [ SL₂], using a recent frame bundle formulation. We find that its covariant Ricci curvature is essentially proportional to the metric (i.e. an Einstein space). We compute the Dirac operator and find for q an odd rth root of unity that its eigenvalues are given by q-integers [m] _q for m=0,1...,r–1 offset by the constant background curvature. We fully solve the Dirac equation for r=3.     

Analyticity of the density of states in the anderson model on the Bethe lattice

Let H=1/2+V on l²(B), whereB is the Bethe lattice andV(x),x B, are i.i.d.r.v.'s with common probability distribution. It is shown that for distributions sufficiently close to the Cauchy distribution, the density of states(E) is analytic in a strip about the real axis.     

First experiment to test whether space-time is flat. II. Effects of orbit

The gyroscope in an orbiting satellite will be acted on by additional gravitational fields due to the rotation of the earth and due to the orbital velocity of the satellite. According to special relativistic gravitational theory, we deduce _L ^(S) —the gyroscope's precession rate due to the orbital velocity—and _S ^(S) —the gyroscope's precession rate due to the earth's rotation in the polar orbit case. The results are _L ^(S) = (2/3) _L ^(G) , _S ^(S) = (3/2) cos (1 - sin² cos²)^1/2 _S ^(G) , where and are the gyroscope's polar angles, and _L ^(G) and _S ^(G) are the geodetic and frame-dragging precession rates predicted by general relativity, respectively.     

Spacetime dynamical entropy of quantum systems

The definition of the dynamical entropy for single automorphisms of nuclear C ^*-algebras is extended to groups of several commuting automorphisms. This entropy of a Z ^v-action is shown to be nonzero only if all the corresponding Z -subactions (0<<v) have infinite entropy. As a simple consequence, the spacetime entropy of quantum lattice spin systems, and of one-dimensional continuous systems with physically reasonable quasifree states, vanishes.     

The photomagneton B(3) and longitudinal ghost field B(3) of electromagnetism

The concepts are introduced of the longitudinal ghost fieldB ⁽³⁾ and photomagnetonB ⁽³⁾) of electromagnetism:B ⁽³⁾ = B⁽³⁾ =B⁽⁰⁾/, whereB ⁽⁰⁾ is the magnetic flux density amplitude and the angular momentum operator of a photon beam. The major implication is that the individual photon hasthree degrees of polarization, the longitudinal one being accompanied by the ghost fieldB ⁽³⁾ which has no energy or linear momentum, and is generated from the angular momentum of the photon.     

Quantum field theory and the coloring problem of graphs

The ^k theory is compared with the multilinear theory of scalar fields ₁, ₂, ..., _k having the same mass as that of . In particular, it is shown that Feynman integrals encountered in the ³ theory are not necessarily present also in the _{1 2 3} theory, but they are if they correspond to planar Feynman graphs having no tadpole part. Furthermore, a necessary and sufficient condition for the presence of a ³ Feynman integral in the _{1 2} ² theory is found. Those considerations are applications of graph theory, especially of the coloring problem of graphs, to Feynman graphs.     

Hausdorff dimension and fluctuations for the largest cluster at the two-dimensional percolation threshold

Monte Carlo simulation shows the average mass of the largest cluster to increase asL ^1.9 at the percolation threshold inL × L square lattices,L290. This fractal dimension agrees with the finite-size scaling prediction/v for this exponent, in contrast to results of Halley and Thang Mai. The mean-square fluctuations in the mass of the largest cluster diverge with the same exponent/v1.8 as the susceptibility.