Diffusion and hopping conductivity in disordered one-dimensional lattice systems

We investigate one-dimensional lattice systems with (symmetric) nearest neighbor transfer ratesW _{n, n+1} which are independently distributed according to a probability density(w). For two general classes of(w), we rigorously determine the asymptotic behavior of the relevant single site Green function ₀() near=0, and obtain exact results for the long time decay of the initial probability amplitude and for the low energy density of states. A scaling hypothesis, accurately confirmed by computer simulations, is used to relate the low frequency hopping conductivity() uniquely to ₀(–i), and we conjecture that the resulting asymptotic behavior for() is also exact. The critical exponents associated with the various asymptotic laws depend on(w) and show a crossover from universal to non-universal behavior. Comparison is made with the results of several approximate treatments.     

Anisotropy of the low temperature resistivity of hexagonal single crystalline spin glass systems

The impurity contribution to the resistivity in zero field (T) of dilute hexagonal single crystals of ZnMn, CdMn and MgMn has been studied in the mK range on samples cut parallel () and perpendicular () to thec-axis, using a SQUID technique for the measurements. Typical spin glass behavior is found in (T) as well as (T) for all alloys, with Kondo like logarithmic increases at higher temperatures and maxima atT _m at lower temperatures, indicating the influence of impurity interactions. The differences in the corresponding isotropic resistivity _poly(T) between the three systems can qualitatively be understood within the framework of a theoretical model by Larsen, describing (T) as a function of universal quantitiesT/T _K and _RKKY/T _K , where _RKKY is the RKKY-interaction strength andT _K the Kondo temperature. With respect to the two lattice directions studied, the behavior of (T and (T is anisotropic in the Kondo regime as well as in the range where ordering becomes important. While the anisotropy in the Kondo slope can be understood by an anisotropic unitarity limit, the understanding of the anisotropy in region where impurity interactions are important remains problematic.Dedicated to Prof. Dr. S. Methfessel on the occasion of his 60th birthday     

Analytic relativistic model for a superdense star

A new analytic relativistic model has been obtained for superdense stars by solving the Einstein field equations for the spherically symmetric and static case. The model stands all the tests of physical reality. The density,, remains positive under all conditions and decreases smoothly from the center to the surface of the structure. The pressure,P, the ratioP/ anddP/d decrease with decreasing density. For all the finite values of pressure, the configurations are stable under radial perturbation. FordP/d 1, the maximum mass of neutron star model is 4.17, and the surface and central red shifts are 0.63 and 1.60, respectively. For an infinite central pressure, the surface red shift is 1.61. The structures are bound and the binding coefficients increase with the increasing mass.     

Computer simulation of shock waves in the completely asymmetric simple exclusion process

We study the evolution of the completely asymmetric simple exclusion process in one dimension, with particles moving only to the right, for initial configurations corresponding to average density _– ( ₊) left (right) of the origin, _{– +}. The microscopic shock position is identified by introducing a second-class particle. Results indicate that the shock profile is stable, and that the distribution as seen from the shock positionN(t) tends, as time increases, to a limiting distribution, which is locally close to an equilibrium distribution far from the shock. Moreover , withV=1– _–– ₊, as predicted, and the dispersion ofN(t), ²(t), behaves linearly, for not too small values of ₊– _–, i.e., , whereS is equal, up to a scaling factor, to the valueS _WA predicted in the weakly asymmetric case. For ₊= _– we find agreement with the conjecture .Dedicated to the memory of Paola Calderoni.     

High-temperature resistivity of Ti1-X Al X alloys

We have measured the high-temperature resistivities of dilute Ti_1-x Al _x alloys withx0.135 up to 1100 K (2.6 _D , where _D is the Debye temperature). We observe that possesses a strong downward deviation from a linear temperature-dependence at high temperatures (several hundred degrees Kelvin). Eventually, saturates to a constant. This non-Bloch-Grüneisen-like behavior is compared with the predictions of current theories.     

Gelfand Pairs with Coherent States

The notion of solvable Gelfand pairs (K,N) (K is a compact Lie group acting on N, a solvable connected and simply connected Lie group) is due to Benson, Jenkins and Ratcliff. Thanks to the localization lemma, they came back to the case where K is a connected subgroup of U(n) acting on N = Hn, the 2n + 1-dimensional Heisenberg group. They gave a geometrical condition for such a pair: (K,Hn) is a Gelfand pair if and only if the intersection of each coadjoint orbit of G = K Hn with (Lie K) contains at most one integral K-orbit. Using coherent states, we define here a generating function of multiplicity m for each in K^. m is holomorphic on D(0,1), m (r) = n = 0 an rn, an and limr 1 m (r) = mtp (, W) (W is the generic representation of Hn naturally extended to K). (K,Hn) is thus a Gelfand pair if and only if limr 1 m 1. We prove here that if m is a non homogeneous function, then there is at least two K-orbits in the intersection of the generic coadjoint orbit associated to with (Lie K).     

Self-diffusion in simple models: Systems with long-range jumps

We review some exact results for the motion of a tagged particle in simple models. Then, we study the density dependence of the self-diffusion coefficientD _N() in lattice systems with simple symmetric exclusion in which the particles can jump, with equal rates, to a set ofN neighboring sites. We obtain positive upper and lower bounds onF _N()=N{(1–)–[D_N()/D_N(0)]}/[(1–)]x for [0, 1]. Computer simulations for the square, triangular, and one-dimensional lattices suggest thatF _N becomes effectively independent ofN forN20.     

Radius,perimeter, and density profile for percolation clusters and lattice animals

Monte Carlo simulation and series expansion shows the radius of gyration of large clusters withs sites each to vary ass with0.56 in two and0.47 in three dimensions at the percolation threshold, and with(d=2)0.65 and(d=3)0.53 for random lattice animals (zero concentration). Clusters up tos=100 were used. The perimeter of random animals approaches 2.8s for larges on the simple cubic lattice. Monte Carlo simulation of the Eden process (growing animals) up tos=5,000 indicates a systematic variation of about ±0.05 for the effective exponent=(s) and thus suggests that the true asymptotic exponents may be compatible with the predictions of hyper-scaling.     

A Lipatov bound for Φ 4 4 Euclidean field theory

We bound the large order behavior of these pieces of the renormalized perturbation expansion for ₄ ⁴ which do not contain renormalons [1]. The bound we obtain has the form of the leading asymptotic behavior computed by the Lipatov method, with the exact value of the Lipatov constant. Therefore, this paper is a step towards the rigorous study of the large order behavior of ₄ ⁴ and towards a proof of existence of the first renormalon singularity which should prevent the theory from being Borel summable. Using the results of this paper and the techniques of [15], one can for instance improve [17] the estimate [18] on the finiteness of the radius of convergence of the Borel transform of renormalized ₄ ⁴ and obtain that this radius is at least the exact value conjectured in [1].Supported in part by the National Science Foundation under Grant PHY 85-13554     

Gravitomagnetic and Gravitoelectric Waves in General Relativity

Lower-order terms in expansions of the equations of General Relativity in powers of v/c (post-Newtonian approximations) have long been a source of analogies with em theory. A classic textbook example is the steadily spinning sphere generating a constant dipole gravitomagnetic field, with its associated vector potential B^* ₀ = × (analog of the magnetic field B of a spinning charged sphere). In the nonsteady case there are associated gravitoelectric fields E* = – _t – * also, where * is the gravitational Coulomb potential. The case of a rigid sphere spun up from rest by an external (nongravitational) torque at t = 0 is enlightening, as it demonstrates the generation of B* and E* wave fields propagating outward with the velocity of light c: for large t, B* B^* ₀. In a coordinate system for which the metric tensor is nearly equal to the Minkowski tensor, the three-vector potential obeys an equation isomorphic to the electrodynamic equation, that is, ² = –*j* with j* = –v, where is the mass density, v the three-velocity, and * = 16Gc^–2 = 3.7 × 10^–26 mksu, G being the gravitational constant. Significantly, one can construct a gauge invariant four-vector potential F* = (ic^–14*, ), obeying field equations isomorphic to Maxwell's in the Lorentz gauge F _, = 0. The traveling transient dipole field exerts torques on matter in its path, setting up shear strains that may be measurable for very large momentum transfers, for example, between massive astronomical bodies. A rough calculation suggests that such strains are in principle observable.     

Growth of correlation in the Hopfield model

Introducing a finite correlation ₀ between any two learned patterns (others remaining uncorrelated), we observe in a numerical simulation that the Hopfield model stores these two patterns with correlation _f such that _f0 for any loading capacity. The patterns are memorized perfectly (with _f= ₀) up to -0.05 for finite correlations ₀ not exceeding a value _c(), where _c() decreases continuously to zero at -0.05.     

Analysis of the dc-resistivity of YBa2Cu3Ox: Deduction of the intragrain resistivity

The resistivity (100 K) scatters very much for YBa₂Cu₃O_x prepared as single crystals, epitaxial films or bulk samples which consist of grains of 1 to 10 m diameter. An analysis of (T) for granular bulk samples is presented indicating the existence of a low intrinsic resistivity ⁱ (T)= _0L ⁱ + ⁱ T with _0L ⁱ 0 and ⁱ 0.5µcm/K. The large grain boundary resistivity _b between the grains (>1 m) yield a macroscopic percolative conduction path lengtheningL/L ₀>1 with a reduced effective cross sectionC<C ₀ and thus, (T)= _b +(LC ₀/L ₀ C)· ⁱ (T). Evidence is presented for weak links inside single crystals and grains.     

Hydrogenated and irradiatedA15 Nb3Sn layers — Preparation,Rutherford scattering analysis,resistivity and superconductivity

Niobium films on sapphire were reacted in tin-vapour to Nb₃Sn with resistance ratiosR(297 K)/R(18.3 K) up to 6 and resistively measured superconducting transition temperaturesT _c up to 17.93 K. The composition Nb_3+z Sn_1–z H _x of electrolytically hydrogenated samples was determined depth dependent by Rutherford backscattering of 30 MeV³²S and simultaneous detection of recoiled protons. Considerable concentration gradients in the thin layers (0.27 m) were detected. The increase of resistivity with hydrogen content and the change in the temperature dependence of is analyzed. A correlation betweenT _c and ₀= is found: An increase of T _c =0.2 K at ₀25cm andx0.03 is followed by a drastic decrease toT _c <1.1 K at ₀80cm andx1. TheT _c vs. ₀ andT _c vs. (T) characteristic correlations are different from universal irradiation or preparation induced correlations. The discrepancies can be interpreted by a stiffening of phonon modes and a band-shifting caused by the hydrogen.     

The hydrodynamic limit of a one-dimensional nearest neighbor gradient system

We study the hydrodynamic behavior of a one-dimensional nearest neighbor gradient system with respect to a positive convex potential . In the hydrodynamic limit the density distribution is shown to evolve according to the nonlinear diffusion equation ,(q)/t= (²/dq²){F([1/₁(q)]), with F= –.     

Metastable states in the van der Waals-Maxwell theory

A slight modification of the recent Penrose and Lebowitz treatment of thermodynamic metastable states is presented. For the case of periodic boundary conditions, this modification allows the condition of metastability to be extended to all the metastable states in the van der Waals-Maxwell theory of the liquid-vapor phase transition, that is, for all states satisfyingf ₀()+1/2 ²>f(, 0+) andf₀()+x>0 wheref(, 0+) is the (stable) Helmholtz free energy density of the generalized van der Waals-Maxwell theory andf ₀() is the Helmholtz free energy density of a reference system with no long-range interaction, is a mean field-type term arising from a long-range Kac interaction, is the overall mean particle density, andx is any positive number. For the case of rigid-wall boundary conditions, a more restrictive condition is placed onx.     

Reactive pulsed laser deposition and laser induced crystallization of SnO2 transparent conducting thin films

Transparent conducting SnO₂ thin films with a thickness between 1000–2000 Å were deposited on glass, quartz and silicon substrates using standard pulsed laser deposition techniques with two different targets (Sri and SnO₂) and with three different laser wavelengths (1.06, 0.532 and 0.266 ) from a Q-switched Nd: YAG laser. Tin dioxide films with optical transmission over most of the visible spectrum exceeding 80% were obtained using a Sn target and a background oxygen pressure of 20 Pa. The electrical resistivity () depended strongly on the substrate temperature during deposition, with the lowest values of of about 10^–2 -cm obtained when the substrate was maintained at 400°C during deposition. Using SnO₂ targets, predominantly amorphous phase SnO₂ films were deposited on Si substrates and then transformed into polycrystalline Sn₃O₄ by laser induced crystallization ( = 1.06 m). Whereas these later films were essentially non-conducting as deposited ( > 400 -cm), the electrical resistivity was permanently reduced after laser induced crystallization by a factor greater than 1000 to a value of approximately 4 × 10^–1 -cm.     

Relative change of the electron density at the Cu nucleus in Cu-Ag alloys

The decay constant of⁶⁴Cu in Cu–Ag solid solutions has been measured at various Cu concentrations. Deduced values of the relative changes of electron densities (0)/(0) at the Cu nucleus are given. The observed concentration dependence of (0)/(0) is discussed in terms of a volume effect and charge transfer from Cu to Ag.     

Self-Dual Solutions for SU(2) and SU(3) Gauge Fields on Euclidean Space

Self-dual solutions for SU(2) gauge fields on Euclidean space that satisfy Yang's ansatz are generalized by considering as a function of for a special case when is a complex analytic function and for SU(3) when _i, i = 1, 2, 3, are complex analytic functions.     

Scaling Cosmology

We show that with the help of a suitable coupling between dark energy and cold dark matter it is possible to reproduce any scaling solution _{X M} a , where _X and _M are the densities of dark energy and dark matter, respectively. We demonstrate how the case = 1 alleviates the coincidence problem. Future observations of supernovae at high redshift as well as quasar pairs which are planned to discriminate between different cosmological models will also provide direct constraints on the coupling between dark matter and dark energy.     

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.