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.     

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     

On the equivalence of boundary conditions

We show that ifb andb are two boundary conditions (b.c.) for general spin systems on ^d such that the difference in the energies of a spin configuration in ^d is uniformly bounded, |H _,b ()–H _,b()|C < , then any infinite-volume Gibbs states and obtained with these b.c. have the same measure-zero sets. This implies that the decompositions of and into extremal Gibbs states are equivalent (mutually absolutely continuous). In particular, if is extremal,=. Application of this observation yields in an easy way (among other things) (a) the uniqueness of the Gibbs states for one-dimensional systems with forces that are not too long-range; (b) the fact that various b.c. that are natural candidates for producing non-translation-invariant Gibbs states cannot lead to such an extremal Gibbs state in two dimensions.Supported in part by NSF Grant PHY 78–15920 and by the Swiss National Foundation For Scientific Research.     

Recursion method for the density of states and spectral dimension of central-force elastic percolation network

We use the recursion method to calculate the vibrational density of states () of site diluted central-force elastic percolation network on the triangular lattice. We find that () is proportional to at long wavelengths. At shorter wavelengths, i.e. in the fracton regime, () is proportional to , where is the spectral dimension of the elastic percolation network. A log-log plot of () vs gives a straight line in the fracton regime with a negative slope. From this we estimate {ie333-3} to be 0.625.     

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.     

Plane Symmetric Cosmological Macro Models in Self-creation Theory of Gravitation

We have constructed a class of plane symmetric macro models in Barber's second self-creation theory, when the source of the gravitational field is a macro matter field representing perfect fluid and satisfying the gamma-law equation of state p=(-1), where =4/3 and 3/2. The solutions of the field equations are derived and their physical aspects are studied.     

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.     

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.     

Cosmological Relativity: Determining the Universe by the Cosmological Redshift as Infinite and Curved

Using cosmological relativity theory, we derive the formula for the cosmological redshift written explicitly in terms of 1 – , where = /_c is the ratio of the average mass density to the critical closure density. Based on the present day data of observed redshifts, we conclude that < 1, which means the universe is infinite and curved, and expands forever.     

What determinates the chemical changes of the internal conversion coefficients for inner atomic shells?

Calculations of internal conversion coefficients (ICC) of the E1–E4 and M1–M4 transitions for nuclei in ions show that the relative changes _i / _i of the ICC _i for deep inner subshells can differ significantly from the relative changes _i/_i of the electron densities _i at the nucleus. For the K conversion _i/ _i are many times greater than _i/_i. Especially large deviations of _i/ _i are characteristic of transitions of high multipolarity; however, for the M1 transitions they can also be significant. Illustrations of various dependencies of _i/ _iare presented for the conversion in the regionZ-50.     

Determination of the electron density at the Cu nucleus in Cu-Au alloys

The half-life of⁶⁴Cu in Cu–Au solid solutions has been measured as a function of the Cu concentration. Relative changes of electron densities (0)/(0) at the Cu nucleus are deduced. The observed nonlinear concentration dependence of (0)/(0) is discussed in terms of volume and charge transfer effects.     

Entropy,information theory,and the approach to equilibrium of coupled harmonic oscillator systems

Finite segments of infinite chains of classical coupled harmonic oscillators are treated as models of thermodynamic systems in contact with a heat bath, i.e., canonical ensembles. The Liouville function for the infinite chain is reduced by integrating over the outside variables to a function _N of the variables of theN-particle segment that is the thermodynamic system. The reduced Liouville function _N which is calculated from the dynamics of the infinite chain and the statistical knowledge of the coordinates and momenta att = 0, is a time-dependent probability density in the 2N-dimensional phase space of the system. A Gibbs entropy defined in terms of _N measures the evolution of knowledge of the system (more accurately, the growth of missing pertinent information) in the sense of information theory. As ¦t ¦ , energy is equipartitioned, the entropy evolves to the value expected from equilibrium statistical mechanics, and _N evolves to an equilibrium distribution function. The simple chain exhibits diffusion in coordinate space, i.e., Brownian motion, and the diffusivity is shown to depend only on the initial distribution of momenta (not of coordinates) in the heat bath. The harmonically bound chain, in the limit of weak coupling, serves as an excellent model for the approach to equilibrium of a canonical ensemble of weakly interacting particles.     

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.     

Analysis of the order parameter for uniform nearest particle system

The uniform nearest particle system (UNPS) is studied, which is a continuoustime Markov process with state space . The rigorous upper bound ^(mf) = ( – 1)/ for the order parameter ₂, is given by the correlation identity and the FKG inequality. Then an improvement of this bound ^(mf) is shown in a similar fashion; C( – 1)/|log( – 1) for >1. Recently, Mountford proved that the critical value _c=1. Combining his result and our improved bound implies that if the critical exponent exists, it is strictly greater than the mean-field value 1 in the weak sense.     

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.     

Non-classical conductivity in a bulk semiconductor up to 35 K

We observed non-classical contributions to the conductivity in three-dimensional samples at temperatures up to 35 K. The experiments were carried out inn-type Hg_0.8Cd_0.2Te samples having dimensions as large as 8 ×28×25 m³. The two resistivity contributions, i.e. the normal metallic behaviour ₀ and a part provided by electron interference, are separated using a method disturbing the additional contribution by heating the electrons in electrical fields. The observed temperature and electric field dependence are compared with existing theories.     

The GHS inequality for a large external field

We consider general even ferromagnetic systems with pair interactions in a nonnegative external magnetic fieldh. Classes of single-site measures are found such that the GHS inequality is valid for allh h, whereh 0 is a number depending on but independent of the size of the system. These measures include both absolutely continuous and discrete measures. For =a ₀+{(1–a)/2} · ( ₁ + _–1), somea [0, 1),h is determined exactly.Alfred P. Sloan Research Fellow. Research supported in part by National Science Foundation grant No. MCS 80-02149.Alfred P. Sloan Research Fellow. Research supported in part by National Science Foundation grant No. MCS 77-20683 and by the U.S.-Israel Binational Science Foundation.     

Letter: Particle-like Behaviour of Some Bianchi Cosmologies: A Fundamental Unity in Nature?

We show that the equations of evolution of someBianchi cosmologies with equation of state p = (0 1) are formallysimilar to the equations of motion of a classical particle under the actionof suitably chosen potential functions. This appears topoint to a fundamental unity in Nature.     

Bifurcation phenomena near homoclinic systems: A two-parameter analysis

The bifurcations of periodic orbits in a class of autonomous three-variable, nonlinear-differential-equation systems possessing a homoclinic orbit associated with a saddle focus with eigenvalues ( ±i,), where ¦/¦ < 1 (Sil'nikov's condition), are studied in a two-parameter space. The perturbed homoclinic systems undergo a countable set of tangent bifurcations followed by period-doubling bifurcations leading to periodic orbits which may be attractors if ¦/¦ < 1/2. The accumulation rate of the critical parameter values at the homoclinic system is exp(-2¦/¦). A global mechanism for the onset of homoclinicity in strongly contractive flows is analyzed. Cusp bifurcations with bistability and hysteresis phenomena exist locally near the onset of homoclinicity. A countable set of these cusp bifurcations with scaling properties related to the eigenvalues±i of the stationary state are shown to occur in infinitely contractive flows. In the two-parameter space, the periodic orbit attractor domain exhibits a spiral structure globally, around the set of homoclinic systems, in which all the different periodic orbits are continuously connected.     

Electromagnetic effects in unified field theory

In unified field theory we derive expressions for the electric current densities j and. We show that j and depend on the intensitiesE andH;E andH possess a common limit 1/; and Coulomb's law is not compatible with the unified theory.