On the dynamics of a quantum system which is classically chaotic

We investigate the dynamics of one anisotropic spin in an external time-dependent magnetic field. The classical dynamics of the system is nonintegrable (and very similar to the standard map). We present results on this model for a quantum spin (i.e. for finite values of the spin lengthS). In particular we discuss the semiclassical regime,S1, using the concept of Wigner functions to define a suitable probability distribution. In regular regions of phase space the time evolution of the probability distribution shows an algebraic decay of correlations as in quantum mechanics. In chaotic regions of phase space it is characterised by a positive Lyapunov exponent which depends onS. In these regions semiclassical trajectories coincide with classical ones fort <₀ where ₀InS.     

Statistical Dynamics of Clustering in the Genome Structure

Clustering and long-range correlations in the nucleotide sequences of different categories of organisms are studied. As a result of clustering, the size distribution of coding and non-coding DNA regions is estimated analytically using the Generalised Central Limit Theorem.The alternation of coding regions (which follow a short range size distribution) with non-coding regions (which follow a long range size distribution in higher organisms) leads to DNA structures which have a striking resemblance to random Cantor Fractals. For lower organisms (such as viruses, procaryotes etc.) long-range correlations are sporadically observed and the DNA structures do not present fractality.Statistical models are proposed based on biologically motivated dynamical mechanisms (such as aggregation of oligonucleotides, influx and DNA length reduction), which can account for the above statistical features.     

Diffusion in heterogeneous biphase structures

The present paper deals with the determination of temperature dependence of the effective diffusion coefficient in heterogeneous biphase structures using diffusion coefficients measured in both phases and the short-range order parameter. A new interpretation of this short-range order parameter is given as the relative volume of the ordered structure in the sample,V _(ord)/V.For the AuCu₃ alloy, the lacking values of the Au diffusion coefficients at temperaturesT<760 K in the partially ordered structure of this alloy were calculated on the basis of long-range order parameter values and diffusion characteristics which are valid for the perfectly ordered or disordered structures, respectively. For solid solutions of theAB andAB ₃ type the relation between the long and short-range parameters is given; numerical calculations of short-range order parameters were carried out for -brass and for the Cu₃Au alloy with the use of long-range order parameters and heats of formation.An explanation of the diffusion anomaly in ferromagnetic materials close to the Curie temperature is given and the temperature dependence of the relative volume of the paramagnetic phase in -iron is calculated.ikova 22, Brno, Czechoslovakia.The author wishes to express his thanks to Professor L. M. Slifkin for providing a xerox-copy of a part of Mr. Alexander's thesis [15] which facilitated the evaluation of diffusion characteristics in Cu₃Au alloy, and to Mr. M. Szob for recalculating some equations.     

How are rescaled range analyses affected by different memory and distributional properties? A Monte Carlo study

In this paper, we present the results of Monte Carlo simulations for two popular techniques of long-range correlation detection — classical and modified rescaled range analyses. A focus is put on an effect of different distributional properties on an ability of the methods to efficiently distinguish between short-term memory and long-term memory. To do so, we analyze the behavior of the estimators for independent, short-range dependent, and long-range dependent processes with innovations from eight different distributions. We find that apart from a combination of very high levels of kurtosis and skewness, both estimators are quite robust to distributional properties. Importantly, we show that R/S$R/S$ is biased upwards (yet not strongly) for short-range dependent processes, while M-R/S$M\text{-}R/S$ is strongly biased downwards for long-range dependent processes regardless of the distribution of innovations.     

Nonextensive statistical approach to non-coding human DNA

We use q-exponential distributions, which maximize the nonextensive entropy S_q (defined as ), to study the size distributions of non-coding DNA (including introns and intergenic regions) in all human chromosomes. We show that the value of the exponent q describing the non-coding size distributions is similar for all chromosomes and varies between 2≤q≤2.3 with the exception of chromosomes X and Y.     

Cross-Over Between First-Order and Critical Wetting at the Liquid-Vapour Interface of n-Alkane/Methanol Mixtures: Tricritical Wetting and Critical Prewetting

A simple mean-field theory is presented which describes the basic observations of recent experiments revealing rich wetting behaviour of n-alkane/methanol mixtures at the liquid-vapour interface. The theory, qualitative and in part heuristic, is based on a microscopic lattice-gas model from which a Cahn–Landau approach is distilled. Besides the physics associated with the short-range components of the intermolecular interactions, effects of the long-range tails of the net van der Waals forces between interfaces are also taken into account. Further, gravitational thinning of the wetting phase is incorporated. The calculation of the spreading coefficient S is extended to the experimentally relevant situation in which the bulk adsorbate is slightly away from two-phase coexistence due to gravity. Analysis of this novel approximation to S for systems with short-range forces leads to the conclusion that the surface specific heat exponents _s =1,1/2, and 0, for first-order wetting, tricritical wetting and critical wetting, respectively, are robust with respect to (weak) gravitational thinning, consistently with experiment. For three different systems the adsorption is calculated as a function of temperature and compared with the experimentally measured ellipticity. Including weak long-range forces which favour wetting in the theory does not visibly alter the critical wetting transition for the nonane/methanol mixture, in contrast with the generic expectation of first-order wetting for such systems, but in good agreement with experiment. For decane/methanol weak long-range forces bring the transition very close to the prewetting critical point, leading to an adsorption behaviour closely reminiscent of short-range tricritical wetting, observed experimentally for alkane chain length between 9.6 and 10. Finally, for undecane/methanol the transition is clearly of first order. First-order wetting is also seen in the experiment.     

Dynamic short-range order observed in the (Zn)[Fe2]O4 spinel by neutron diffraction, μSR,and Mössbauer experiments

Using neutron diffraction (ND), muon-spin rotation/relaxation (SR), and⁵⁷Fe-Mössbauer spectroscopy (MS) we have investigated magnetic properties of the normal spinel (Zn)[Fe₂]O₄. In compounds which are slowly cooled from 1200°C to room temperature inversion is below detection limits. AtT _N = 10.5 K the spinel exhibits long-range antiferromagnetic order (LRO). The transition as seen in thermal-scan spectra by MS is very sharp. However, ND andSR experiments show that already at temperatures of 10T _N a short-range antiferromagnetic ordering (SRO) develops which extends through 70% of the sample volume just aboveT _N . BelowT _N SRO and LRO coexist. At 4.2 K still 25% of the sample is short-range ordered. The regions over which the SRO extends have a size of 3 nm. Their fluctuation rates are in the GHz range. Modern ab initio cluster calculations successfully describe the magnetic hyperfine fields as well as the electric field gradient (EFG) tensor at the Fe sites. Covalency of the Fe-O and Zn-O bonds is important. The physical origin of the regions exhibiting SRO, however, remains unresolved at this point.     

Renormalization group treatment of the scaling properties of finite systems with subleading long-range interaction

The finite size behavior of the susceptibility, Binder cumulant and some even moments of the magnetization of a fully finite O(n) cubic system of size L are analyzed and the corresponding scaling functions are derived within a field-theoretic ɛ-expansion scheme under periodic boundary conditions. We suppose a van der Waals type long-range interaction falling apart with the distance r as r ^{- (d + σ)}, where 2 < σ < 4, which does not change the short-range critical exponents of the system. Despite that the system belongs to the short-range universality class it is shown that above the bulk critical temperature T _c the finite-size corrections decay in a power-in-L, and not in an exponential-in-L law, which is normally believed to be a characteristic feature for such systems. Received 8 August 2001     

Correlations in inhomogeneous Ising models

Using general methods developed in a previous treatment we study correlations in inhomogeneous Ising models on a square lattice. The nearest neighbour couplings can vary both in strength and sign such that the coupling distribution is translationally invariant in horizontal direction. We calculate correlations parallel to the layering in the horizontally layered model with periodv=2. If the model has a finite critical temperature,T _c>0, the order parameter in the frustrated case may become discontinuous forT0. Correlations atT=T _c decay algebraically with critical exponent =1/4 and exponentially forT>T _c. If the critical temperature vanishes,T _c=0, we always have exponential decay at finite temperatures, while atT=T _c=0 we encounter either long-range order or algebraic decay with critical index =1/2, i.e.T=0 is thus a critical point.Work performed within the research program of the Sonder forschungsbereich 125 Aachen-Jülich-Köln     

Force Relaxation in the q-Model for Granular Media

We study the relaxation of force distributions in the q-model, assuming a uniform q-distribution. We show that diffusion of correlations makes this relaxation very slow. On a d-dimensional lattice, the asymptotic state is approached as l ^(1–d)/2, where l is the number of layers from the top. Furthermore, we derive asymptotic modes of decay, along which an arbitrary short-range correlated initial distribution will decay towards the stationary state.     

On existence and behaviour of asymptotically flat solutions to the stationary Einstein equations

We show existence and uniqueness of asymptotically flat solutions to the stationary Einstein equations inS=³–B _r , whereB _r is a ball of radiousr>0, when a small enough continuous complex function û on S is given. Regularity and decay estimates imply that these solutions are analytic in the interior ofS and also at infinity, when suitably conformally rescaled.     

Fractional Moment Estimates for Random Unitary Operators

We consider unitary analogs of d-dimensional Anderson models on l²( $$\mathbb(z)$$^d) defined by the product U=D S where S is a deterministic unitary and D is a diagonal matrix of i.i.d. random phases. The operator S is an absolutely continuous band matrix which depends on parameters controlling the size of its off-diagonal elements. We adapt the method of Aizenman–Molchanov to get exponential estimates on fractional moments of the matrix elements of U(U –z)^–1, provided the distribution of phases is absolutely continuous and the parameters correspond to small off-diagonal elements of S. Such estimates imply almost sure localization for U.     

Evidence for an emission source of large space-time extent in Au+Au collisions at RHIC

The source imaging technique of Brown and Danielewicz has been used to extract two-pion emission source functions over a broad range of k _T and centralities in Au+Au collisions at $\sqrt s = 200$ GeV. The source functions reflect the combined contributions of a short-range Gaussian-like component and a long-range exponential-like component. A parametrization of the source function gives a RMS radius for the long-range source which is approximately three times that for the short-range source. The centrality dependence of the extracted source parameters for the short- and long-range sources indicate similar patterns.     

Lévy-flight spreading of epidemic processes leading to percolating clusters

We consider two stochastic processes, the Gribov process and the general epidemic process, that describe the spreading of an infectious disease. In contrast to the usually assumed case of short-range infections that lead, at the critical point, to directed and isotropic percolation respectively, we consider long-range infections with a probability distribution decaying in d dimensions with the distance as . By means of Wilson's momentum shell renormalization-group recursion relations, the critical exponents characterizing the growing fractal clusters are calculated to first order in an -expansion. It is shown that the long-range critical behavior changes continuously to its short-range counterpart for a decay exponent of the infection . Received: 17 July 1998 / Revised: 20 July 1998 / Accepted: 28 July 1998     

Localization for Random Unitary Operators

We consider unitary analogs of one-dimensional Anderson models on defined by the product U _ω=D _ω S where S is a deterministic unitary and D _ω is a diagonal matrix of i.i.d. random phases. The operator S is an absolutely continuous band matrix which depends on a parameter controlling the size of its off-diagonal elements. We prove that the spectrum of U _ω is pure point almost surely for all values of the parameter of S. We provide similar results for unitary operators defined on together with an application to orthogonal polynomials on the unit circle. We get almost sure localization for polynomials characterized by Verblunsky coefficients of constant modulus and correlated random phases Mathematics Subject Classification. 82B44, 42C05, 81Q05     

Three-body treatment of Coulomb effects in the problem of long-range effective interactions

The problem of Coulomb scattering of a charged particle by a two-particle bound system, consisting of a charged and a neutral particle, is investigated in the integral-equation approach of rigorous three-body theory. The bound state of the two particles is provided by a short-range interaction chosen in the simplest form using anS-wave separable potential. The integral equation defining the effective potential of the interaction of the charged particle with the two-particle bound system is formulated. It is shown that the multiple Coulomb scattering of the involved charged particles generates a sequence of long-range terms in the effective potential. It turns out that the long-range effects of Coulomb scattering are partly cancelled. As a result the polarization potential does not contain the longest-ranged terms which decrease at large distances as ^–2 and ^–3.     

Nonlinearity in cooperative systems-dynamical Bethe-Ising model

The dynamics of the short-range order as well as the long-range order in the nonlinear cooperative system is investigated specifically for a kinetic Ising model in the Bethe approximation. The phenomena of critical slowing down near the transition temperatureT _c and anomalous fluctuation belowT _c are directly related to the instability of the long-range order. The dynamics of the short-range order is essentially a fast mode and is noncritical. However, through the nonlinear coupling the short-range order is also influenced by the critical behavior of the long-range order.     

Spin-glass in the spinel-type CuCrTiS4

It is difficult to find a typical compound to understand the spin-glass (SG). Only a few model compounds for the SG have been investigated; Fe_0.50Mn_0.50TiO₃ as a short-range interacting three-dimensional (3D) Ising SG, Dy_0.103Y_0.897Ru₂Si₂ as a long-range 3D Ising SG, and AgMn as a long-range 3D Heisenberg SG. A spinel-type compound CuCrTiS₄ will be provided in this study as a realistic candidate for a short-range interacting 3D Heisenberg SG. This CuCrTiS₄ can cause a SG phase below T _g?=?7.91?K, which is obtained by a random non-magnetic 50% substitution of Ti for Cr on B-sites in the ferromagnetic mother spinel CuCr₂S₄. The localized magnetic moment of CuCrTiS₄ comes from Cr³⁺ with S?=?3/2, where a valence state of Cu⁺Cr³⁺Ti⁴⁺S₄ ^2? is built up. Experimental data will be focused only on the static properties of dc magnetization M(T) under various magnetic fields, without any dynamical magnetic feature. The spin-glass phase transition T _g is well defined at low field, nevertheless hardly in higher fields than approximately 40 Oe. An appearance of the field dependence of M(T) of CuCrTiS₄ is similar to that of Fe_0.50Mn_0.50TiO₃ with the short-range Ising SG, and also these of AgMn and CuMn with the long-range interacting Heisenberg SGs. This general nature in M(T) seems to originate from the common mechanism under magnetic fields for all the spin-glasses.