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.     

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.     

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.     

Isometric motions of a perfect charged fluid

Space-times with perfect charged fluids as sources, that admit groups G_r of isometric motions, are investigated. It is assumed that the velocity vector of the fluid is collinear to the timelike Killing vector ⁱ of group G_r. It is shown that the macroscopic motion of a perfect charged fluid can occur only in the direction of such a Killing vector ⁱ that defines an operator in an invariant subgroup or, in particular, an operator of the center of the group. Parametric representations of the generalized equations of state for the pressure p, the energy density of the fluid, , and the electric charge density are established. All these quantities are functions of the norm of the Killing vector ⁱ and the projection of the 4-potential of the electromagnetic field onto this vector ⁱ. In the approximation of the weak field in the coordinate system where ⁱ= ₄ ⁱ , these functional dependences imply that p, , and are functions of Newtonian and electrostatic potentials.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 25–29, October, 1987.     

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).     

Screening Effect Due to Heavy Lower Tails in One-Dimensional Parabolic Anderson Model

We consider the large-time behavior of the solution to the parabolic Anderson problem _tu=u+u with initial data u(0, ·)=1 and non-positive finite i.i.d. potentials . Unlike in dimensions d2, the almost-sure decay rate of u(t, 0) as t is not determined solely by the upper tails of (0); too heavy lower tails of (0) accelerate the decay. The interpretation is that sites x with large negative (x) hamper the mass flow and hence screen off the influence of more favorable regions of the potential. The phenomenon is unique to d=1. The result answers an open question from our previous study [BK00] of this model in general dimension.     

Yang-Lee theory and the conductor-insulator transition in asymmetric log-potential lattice gases

A feature of a conducting phase at low density is that there is a singularity in the fugacity expansion of the pressure, whereas the same expansion in the insulating phase gives an analytic series. The Yang-Lee characterization of a phase transition thus implies that in the conducting phase the zeros of the grand partition function must pinch the real axis in the complex scaled fugacity () plane at =0, whereas in the insulating phase a neighborhood of =0 must be zero free. Exact and numerical calculations are presented which suggest that for two-component log-potential lattice gases in one dimension with dimensionless coupling, the zeros pinch the point =0 for<2, while for2 a neighborhood of =0 is zero free. The conductor-insulator transition therefore takes place at=2 independent of the density and other parameters in the model.     

Algebraisch spezielle Einstein-Räume mit einer Bewegungsgruppe

In algebraically special Einstein spaces (R_v=0) with a hypersurfaceorthogonal spacelike Killing vector field _v, the trajectories of the multiple eigen null directions k lie — except one case — in the subspacesV ₃ orthogonal to _v (k=0) and are hypersurface-orthogonal. The solutions with vanishing expansion (k_,;=0, Kundt's class) can be determined explicitly.     

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.     

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.     

On ruelle's ξ-function for exponentially decreasing potentials

We show that Ruelle's generalised -function for a classical one-dimensional lattice spin system with two-body interaction (i) exp(-i )a(i) with >1 extends to a meromorphic function in the whole complex plane.     

Superconducting surface resistance of thin amorphous Ga films on metallic substrates

The surface resistance of a metal coated with amorphous superconducting films is investigated. With an improved microwave cryostat and a two layer model considering the influence of the substrate, much thinner films can be used than previously. As an example the surface resistance of amorphous Ga is determined. A set of parameters ₀/k _BT_c=2,27; _L=13,4 nm; ₀=223 nm andl=1,0 nm describes the temperature dependence independent of thickness. As expected a model of free electrons is in agreement with the experimental results. For crystalline-Ga ₀/k _B T _c =1,91; _L=24 nm; ₀=163 nm and a much larger mean free pathl=22 nm is found.     

On nonlinear stationary half-space problems in discrete kinetic theory

We show that every steady discrete velocity model of the Boltzmann equation on the real line, _i·(d/dx)f ⁱ=C ⁱ(f), which satisfies anH-theorem and for which all _i0, has solutions on the half-line (0, ) which take prescribed non-negativef ⁱ(O) if _i>0 and approach a certain manifold of Maxwellians asx. Such solutions give the density distribution in a Knudsen boundary layer in the discrete velocity case.     

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.     

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.     

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.     

Neutron scattering study of the two-dimensional spinS=1/2 square-lattice Heisenberg antiferromagnet Sr2CuO2Cl2

We have carried out a neutron scattering investigation of the static structure factorS(q _2D ) (q _2D is the in-plane wave vector) in the two-dimensional spinS=1/2 square-lattice Heisenberg antiferromagnet Sr₂CuO₂Cl₂. For the spin correlation length we find quantitative agreement with Monte Carlo results over a wide range of temperature. The combined Sr₂CuO₂Cl₂-Monte Carlo data, which cover the length scale from 1 to 200 lattice constants, are predicted without adjustable parameteres by renormalized classical theory for the quantum nonlinear sigma model. For the structure factor peakS(0), on the other hand, we findS(0) ² for the reduced temperature range 0.16<T/2 _s <0.36, whereas current theories predict that at low temperaturesS(0)T ^{2 2}. This discrepancy has important implications for the interpretation of many derivative quantities such as NMR relaxation rates. In the ordered phase, we have measured the temperature dependence of the out-of-plane spin-wave gap. Its low-temperature value of 5.0 meV corresponds to an XY anisotropyJ _XY /J=1.4×10^–4. From measurements of the sublattice mangetization we obtain =0.22±0.01 for the order parameter exponent. This may either reflect tricricality as in La₂CuO₄, or it may indicate finite-size two-dimensional XY behavior as suggested by Bramwell and Holdsworth. As in theS=1 system K₂NiF₄, the gap energy in Sr₂CuO₂Cl₂ scales linearly with the order parameter up to the Néel temperature. We also reanalyze static structure factor data for K₂NiF₄ using the exact low temperature result for the correlation length of Hasenfratz and Niedermayer and including the Ising anisotropy explicitly. Excellent agreement between experiment and theory is obtained for the correlation length, albeit with the spin-stiffness _s reduced by 20% from the spin-wave value. As in Sr₂CuO₂Cl₂ we find thatS(0) ² for the reduced temperature range 0.22<T/2 _s <0.47.     

Observation of sub-Poisson field in a gas laser with feedback

Conclusions The author's earlier work [6, 7] has demonstrated the feasibility in principle of controlling the statistics of laser emission using photoreceiver—pump feedback, and the photodetector photocurrent in the FB circuit was made lower than the SN level, i.e., sub-Poisson fields with values _in+ [6] and ₊ [7] was observed. The experimental results can be adequately described by using the balance equations.Presented at the International Workshop on Squeezed and Correlated States, Moscow, December 3–7, 1990.     

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.     

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.