On the dynamics of excitations in disordered systems

A new, time-local (TL) reduced equation of motion for the probability distribution of excitations in a disordered system is developed. ToO(k²) the TL equation results in a Gaussian spatial probability distribution, i.e, P(r, t) = [(2)^1/2]^–dexp(-r²/2²), where = (t) is a correlation length, andr = ¦r¦. The corresponding distribution derived from the Hahn-Zwanzig (HZ) equation is more complicated and assumes the asymptotic (r ) form: P(r, s)(s ^d )^–1exp(–r/) · (r/)^(1-d)/2 where = (s),d is the space dimensionality, ands is the Laplace transform variable conjugate tot. The HZ distribution generalizes the scaling form suggested by Alexanderet al. ford= 1. In the Markov limit (t)t, (s)1/s, and the two distributions are identical (ordinary diffusion).     

High frequency gravitational radiation in Kerr-Schild space-times

Vaidya has obtained general solutions of the Einstein equationsR _ab= _{a b} by means of the Kerr-Schild metricsg _ab= _ab +H _{a b} . The vector field _a generates a shear free null geodetic congruence both in Minkowski space and in the Kerr-Schild space-time. If in addition it is hypersurface orthogonal, the Kerr-Schild metric may be interpreted as the background metric in a space-time perturbed by a high frequency gravitational wave. It is shown that Vaidya's solutions satisfying this additional condition are of only two types: (1) Kinnersley's accelerating point mass solution and (2) a similar solution where a space-like curve plays the role of the time-like curve describing the world line of the accelerating mass. The solution named by Vaidya as the radiating Kerr metric does not satisfy the hypersurface orthogonal condition.Supported in part by National Science Foundation Grant MPS 741029.     

Renormalization group equations with several length scales and crossover scaling functions for axial anisotropy

The critical behaviour of axially anisotropicn-vector models is characterized by two distinct length scales, the correlation lengths and for the easy and hard axes. In order to handle the full range of anisotropics from to partial differential renormalization group equations are derived, depending on and . The anisotropicX-Y model is studied in detail near four dimensions. The crossover scaling functions for the susceptibilities are calculated to first order in=4–d. Two distinct crossover regions are found for weak and dominant anisotropy, respectively.     

On the critical exponent for random walk intersections

The exponent _d for the probability of nonintersection of two random walks starting at the same point is considered. It is proved that 1/2<₂3/4. Monte Carlo simulations are done to suggest ₂=0.61 and ₃0.29.     

Functional Realization and Nonlinear Induced Representation in the Geometrodifferential Conception of Extended Particles

In a model of extended particles described by Minkowski space-time variables x, de Sitter internal variables , a physical wave _x () representing the proper characteristics of the particles, and a functional wave X [ ] giving previsions, we study functional propagation of X in the space of physical waves (as advocated by a quantum functional theory) as well as the nonlinear realization of the internal de Sitter group on its Lorentz subgroup (introduced by Drechsler). The first study is undertaken in a special instance _x () = (x), while in the second the general structure of the model is adopted and curved space-time treated, but the functional propagation is not considered. A fiber bundle structure and an induced representation method are used. Propagators are derived, a quantum version of a variant of Drechsler's theory is obtained, and a nonlinear version of our model is constructed.     

Spatial structure in diffusion-limited two-particle reactions

We analyze the limiting behavior of the densities _A(t) and _B(t), and the random spatial structure(r) = ( _A(t)., _B(t)), for the diffusion-controlled chemical reaction A+Binert. For equal initial densities _B(0) = _b(0) there is a change in behavior fromd 4, where _A(t) = _B(t) C/t^d/4, tod 4, where _A(t) = _b(t) C/t ast ; the termC depends on the initial densities and changes withd. There is a corresponding change in the spatial structure. Ind < 4, the particle types separate with only one type present locally, and , after suitable rescaling, tends to a random Gaussian process. Ind >4, both particle types are, after large times, present locally in concentrations not depending on type or location. Ind=4, both particle types are present locally, but with random concentrations, and the process tends to a limit.     

Percolation,fractals, and anomalous diffusion

Both the infinite cluster and its backbone are self-similar at the percolation threshold,p _c . This self-similarity also holds at concentrationsp nearp _c , for length scalesL which are smaller than the percolation connectedness length,. ForL<, the number of bonds on the infinite cluster scales asL ^D , where the fractal dimensionalityD is equal to(d-/v). Geometrical fractal models, which imitate the backbone and on which physical models are exactly solvable, are presented. Above six dimensions, one has D=4 and an additional scaling length must be included. The effects of the geometrical structure of the backbone on magnetic spin correlations and on diffusion at percolation are also discussed.     

Acoustomagnetoelectric effects at meso-ultrasonic frequencies in anisotropic semiconductors in arbitrary (classical) magnetic fields

Anisotropic acoustomagnetoelectric (AME) effects at meso-ultrasonic frequencies are calculated analytically in semiconductors with an anisotropic mobility () in arbitrary classical magnetic fields. For Bq(q is the ultrasonic wave vector) and an arbitrary direction of q two transverse components of the AME field (E ^B q E _y ^B ) occur in the crystal, and the longitudinal acoustoelectric field changes under the action of a longitudinal magnetic field (E _q ^B =E _q ^B -E _q ⁰ ),E ^B is even, and E ^B is odd in B; for B 1 the component E _y ^B E ^B /B, andE ^B and E _q ^B are independent of B and can be commensurate with the zero-field acoustoelectric field E _q ⁰ if the anisotropy of is large (hexagonal ZnS and ZnO or n-Ge highly compressed along [111]). The transverse AME field E _st ^B is calculated in the configuration E _st ^B qBE _st ^B (standard AMEeffect). For B >> 1 the field B 1E _st ^B B ^–3, so thatE ^B , E _y ^B , and _q ^B can be greater than E _st ^B here. The acoustoelectric analog of the Grabner effect (E _G ^B ), i.e., the component of the AME field along a transverse magnetic field (E _G ^B Bq) is also calculated. For pB > 1 the componentE _G ^B B ^–3.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 93–97, June, 1989.     

Classification of stationary space-times

A systematic approach to the geometric structure of stationary gravitational fields is presented. The algebraic type of the trace-free Ricci tensor together with the propagation properties of the eigenrays in the background 3-space defined by the Killing trajectories serve as a basis for classifying the solutions of the stationary field equations. The eigenrays are the integral curves belonging to the solutions _A of the eigenvalue problemG _A ^B _B=_A,G _A ^B spinor representing the gravitational field in the background space. Many of the already known stationary metrics can be derived in the present scheme but new solutions of the field equations are also obtained. The possible types of the vacuum and electrovac fields are discussed in their connection with the corresponding exact solutions.Work honoured by a Fifth Gravity Research Foundation Award in 1973.Leverhulme Visiting Fellow.     

The Countable Number of Models in the Cosmology with Nonminimal Coupling and Torsion

Cosmological models of flat space with a nonminimally coupled scalar field and ultrarelativistic gas are studied within the Einstein–Kartan theory. Exact general solutions are derived for two-component models and those containing only scalar field for an arbitrary coupling constant . It is shown that both singular and countable number of nonsingular models is possible depending on the type of scalar field and the sign of . The special values of and restrictions on are found for the above solutions. The role of relativistic gas in the evolution of models is revealed.     

Fluctuation-enhanced conductivity and magnetoconductivity of high-quality YBa2Cu3O7−δ crystals

We present measurements of the in-plane resistivity _ab of YBa₂Cu₃O_7– single crystals withT _c 92 K and _ab (100 K)50 cm. The temperature dependence of the fluctuation conductivity and of the magnetoconductivity aboveT _c is analyzed in terms of direct and indirect fluctuation contributions for layered superconductors. The combination of fluctuation conductivity and magnetoconductivity allows to determine both coherence lengths _ab (0) and _c (0) as well as the phase-relaxation time of the pairs in an unequivocal manner. Evidence for clean limit type-II superconductivity in our crystals is given by large values of the mean free pathl _{ab ab} (0).Dedicated to Prof. Dr. F. Hund on the occasion of his 95th birthday     

Integration in the GHP Formalism IV: A New Lie Derivative Operator Leading to an Efficient Treatment of Killing Vectors

In order to achieve efficient calculations and easy interpretations of symmetries, a strategy for investigations in tetrad formalisms is outlined: work in an intrinsic tetrad using intrinsic coordinates. The key result is that a vector field is a Killing vector field if and only if there exists a tetrad which is Lie derived with respect to ; this result is translated into the GHP formalism using a new generalised Lie derivative operator with respect to a vector field . We identify a class of it intrinsic GHP tetrads, which belongs to the class of GHP tetrads which is generalised Lie derived by this new generalised Lie derivative operator in the presence of a Killing vector field . This new operator also has the important property that, with respect to an intrinsic GHP tetrad, it commutes with the usual GHP operators if and only if is a Killing vector field. Practically, this means, for any spacetime obtained by integration in the GHP formalism using an intrinsic GHP tetrad, that the Killing vector properties can be deduced from the tetrad or metric using the Lie-GHP commutator equations, without a detailed additional analysis. Killing vectors are found in this manner for a number of special spaces.     

Inertial effects on the escape rate of a particle driven by colored noise: An instanton approach

A recent calculation, in the weak-noise limit, of the rate of escape of a particle over a one-dimensional potential barrier is extended by including an inertial term in the Langevin equation. Specifically, we consider a system described by the Langevin equation , where is a Gaussian colored noise with mean zero and correlator (t)(t')=(D/)exp(–|t–t'|/). A pathintegral formulation is augmented by a steepest descent calculation valid in the weak-noise (D0) limit. This yields an escape rateexp(–S/D), where the actionS is the minimum, over paths characterizing escape over the barrier, of a generalized Onsager-Machlup functional, the extremal path being an instanton of the theory. The extremal actionS is calculated analytically for smallm and for general potentials, and numerical results forS are displayed for various ranges ofm and for the typical case of the quartic potentialV(x)=–x ₂/2+x ₄/4.     

Kinetics of random sequential parking on a line

We study the kinetics of irreversible random sequential parking of intervals of different sizes on an infinite line. For the simplest fixed-length parking distribution the model reduces to the known car-parking problem and we present an alternate solution to this problem. We also consider the general homogeneous case when the parking distribution varies asx ^–1 atx 1 with the lengthx of the filling interval. We develop a scaling theory describing such mixture-deposition processes and show that the scaled hole-size distribution(), with =xt ^z a scaling variable, decays with the scaled mass as ^–exp(—const·¹⁺) as . We determine scaling exponentsz and, and find that at large times the coverage(t) has a power-law form 1 – (t)t ^–v with nonuniversal exponent =(2–)/(1+) depending on the homogeneity index .     

Lorentzian Warped Products and Singularity

We show that to any convex function f: ⁿ there correspondinfinitely many geodesically complete metricsds² such that Ric() 0 for anynonspacelike vector . These metrics are constructedas the warped products of the natural metric in and the inner metric of a convexhyperface (the graph of f) in ^{n + 1}.     

Crossover finite-size scaling at first-order transitions

In a recent paper we developed a method which allows one to control rigorously the finite-size behavior in long cylinders near first-order phase transitions at low temperature. Here we apply this method to asymmetric transitions with two competing phases, and to theq-state Potts model as a typical model of a temperature-driven transition, whereq low-temperature phases compete with one high-temperature phase. We obtain the finite-size scaling of the firstN eigenvalues (whereN is the number of competing phases) of the transfer matrix in a periodic box of volumeL × ... ×L ×t, and, as a corollary, the finite-size scaling of the shape of the order parameter in a hypercubic box (t=L), the infinite cylinder (t=), and the crossover regime from hypercubic to cylindrical scaling. For the two-phase case (N=2 we find that the crossover length _L is given by O(L^w)exp(L^v), where is the inverse temperature, is the surface tension, and w=1/2 if v+1=2 whilew=0 if v+1 >2. For the standard Ising model we also consider free boundary conditions, showing that _L=exp[L^v+O(L^v– 1)] for any dimension v+12. For v+1=2 we finally discuss a class of boundary conditions which interpolate between free (corresponding to the interpolating parameter g=0) and periodic boundary conditions (corresponding to g=1), finding that _L=O(L^w)exp(L ^v) withw=0 forg=0 andw=1/2 for 0<g1.     

Nonlocal regularization and spontaneously broken abelian gauge theories for an arbitrary gauge parameter

We study the nonlocal regularization for the case of a spontaneously broken abelian gauge theory in the R-gauge with an arbitrary gauge parameter . We consider a simple abelian-Higgs model with chiral couplings as an example. We show that if we apply the nonlocal regularization procedure (to construct a nonlocal theory with FINITE mass parameter) to the spontaneously broken R-gauge Lagrangian, using the quadratic forms as appearing in this Lagrangian, we find that a physical observable in this model, an analogue of the muon anomalous magnetic moment, evaluated to order O [g²] does indeed show -dependence. We then apply the modified form of nonlocal regularization that was recently advanced and studied for the unbroken non-abelian gauge theories and discuss the resulting WT identities and -independence of the S-matrix elements.     

Attractor States and Quantum Instabilities in de Sitter Space

The asymptotic behavior of the energy–momentum tensor for a free quantized scalar field with mass m and curvature coupling in de Sitter space is investigated. It is shown that for an arbitrary, homogeneous, and isotropic, fourth-order adiabatic state for which the two-point function is infrared finite, T _ab approaches the Bunch–Davies de Sitter invariant value at late times if m ² + R > 0. In the case m = = 0, the energy–momentum tensor approaches the de Sitter invariant Allen–Folacci value for such a state. For m ² + R = 0 but m and not separately zero, it is shown that at late times T _ab grows linearly in terms of cosmic time leading to an instability of de Sitter space. The asymptotic behavior is again independent of the state of the field. For m ² + R < 0, it is shown that, for most values of m and , T _ab grows exponentially in terms of cosmic time at late times in a state dependent manner.     

Search for right-handed currents in muon decay

We report new limits on right-handed currents, based on precise measurements of the endpoint of the e⁺ spectrum from ⁺ decay. Highly polarized ⁺ from the TRIUMF surface beam were stopped in pure metal foils within either an 1.1-T spin-holding logitudinal field, or a 70-gauss spin-precessing transverse field. Decay e⁺ emitted within 200 mrad of the beam direction were momentum-analyzed to ±0.2%. For the spin-held data, decay via (V-A) currents requires the e⁺ rate to approach zero in the beam direction at the endpoint. Measurement of this rate sets the 90%-confidence limits P />0.9959 and M(W_R)>380 GeV, where W_R is the possible right-handed gauge boson. For the spin-precessed data we independently determine a 90% confidence limit P />0.9918.We are indebted to the entire TRIUMF management and staff for their splendid support of this experiment. In its early stages we benefited from discussion with J. Brewer, R. Cahn, K. Crowe, and W. Wenzel. Rapid commissioning of the polarimeter was made possible by the superb efforts of the LBL support staff. This research was supported in part by the U.S. Department of Energy, Division of Basic Energy Sciences, Office of Energy Research under contracts W-7405-ENG-48 and AC02-ER02289.     

Multiatom interactions,order and stability in binary transition metal alloys

Interface delocalization or depinning transitions such as wetting or surface induced disorder are considered. At these transitions, the correlation length for transverse correlations parallel to the surface diverges. These correlations are studied in the framework of Landau theory. It is shown the t^–1/2 at all types of transitions for systems with short-range forces wheret measures the distance from bulk coexistence.