Entropy,the central limit theorem and the algebra of the canonical commutation relation

The central limit theorem of Cushen and Hudson is reformulated on the algebra of the CCR. Namely, for a gauge invariant state , the weighted convolutions _n of the central limit tend to the quasi-free reduction _Q of pointwise. It is proved that if the initial relative entropy S(, _Q ) is finite, then S( _n , _Q ) goes to 0 and so _n – _Q 0. No restriction on the dimension of the test function space is made.     

Perturbations of flows on Banach spaces and operator algebras

For automorphism groups of operator algebras we show how properties of the difference _t – ' _t are reflected in relations between the generators , . Indeed for a von Neumann algebraM with separable predual we show that if _t – '_t 0.28 for smallt, then = 0(+)°^-1 where is an inner automorphism ofM and is a bounded derivation ofM. If the difference _t – ' _t =O(t) ast ; 0, then = + and if _t – ' _t 0.28 for allt then =. We prove analogous results for unitary groups on a Hilbert space andC ₀,C ₀ ^* groups on a Banach space.This paper subsumes an earlier work of the same title which appeared as a report from Z.I.F. der Universität BielefeldWith partial support of the U.S. National Science Foundation     

Microstructure of fiber-like SiC/Si3N4 composite particulate

The microstructure of fiber-like SiC/Si₃N₄ composite particulate was investigated using high-resolution transmission electron microscopy techniques. The SiC/Si₃N₄ composite particulate consisted of a-SiC core and a -Si₃N₄ outer shell. Two kinds of composite particulate were distinguished when the observed orientation of the SiC core was <110>. In one type of the SiC/Si₃N₄ composite particulate, a crystal relationship of (111)-SiC | (102) -Si₃N₄ and (111)-SiC (114) -Si₃N₄ was identified; in the other type of the SiC/Si₃N₄ composite particulate, a crystal relationship of (111)-SiC (001) -Si₃N₄, and (111)-SiC (101) -Si₃N₄ was observed.     

Computer simulation of driven diffusive systems with exchanges

The field-driven Kawasaki model with a fractionp admixture of Glauber dynamics is studied by computer simulation:p=0 corresponds to the order-parameter-onserving driven diffusive system, whilep=1 is the equilibrium Ising model. Forp=0.1 our best estimates of critical exponents based on a system of size 4096×128 are0.22, ^RS0.45, andv v 1. These exponents differ from both the values predicted by a field-theoretic method forp=0 and those of the equilibrium Ising model. Anisotropic finite-size scaling analyses are carried out, both for subsystems of the large system and for fully periodic systems. The results of the latter, however, are inconsistent, probably due to the complexity of the size effects. This leaves open the possibility that we are in a crossover regime fromp=0 top0 and that our critical exponents are effective ones. Forp=0 our results are consistent with the predictionsv >v .     

Determination of internal scale of artificial ionospheric turbulence in direction of geomagnetic field

A 150-MHz satellite beacon is used to determine the internal scale in the direction of the geomagnetic field I₀ for the spectrum of artificial ionospheric turbulence created by the Yastreb heating facility located near Nizhny Novgorod in continuous operation at a frequency of 5.75 MHz (ordinary polarization) with effective power P·G100·150 kW. It is found that I₀ 3–4 km for transverse inhomogeneity scales I 1–2 km and I 0.7–0.9 km for I 0.5 km.Nizhny Novgorod Scientific-Research Radio-Physics Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 4, pp. 521–525, April, 1994.     

First-order phase transitions in finite-size strips with interfaces

Finite-size rounding of the magnetization discontinuity at the magnetic phase transition atH=0 (T<T _c ) in 2d Ising-type strips of sizeL ×L , with ± boundary conditions alongL inducing an interface of lengthL , is studied by phenomenological considerations and transfer matrix techniques. Scaling expressions are derived forL =O(L ) and also in the infinite strip limitL . Most of the results can be extended to the 3d case.     

Anisotropic properties of volume holograms in Bi12SiO20 monocrystals

A theoretical and experimental study is made on light diffraction from holographic diffraction gratings, recorded in cubic photorefractive crystals Bi₁₂SiO₂₀ with (110) cut, for two orientation of the grating wave vector,K [001] andK [110], when an external electric field is applied.     

Finite-size effects at critical points with anisotropic correlations: Phenomenological scaling theory and Monte Carlo simulations

Various thermal equilibrium and nonequilibrium phase transitions exist where the correlation lengths in different lattice directions diverge with different exponentsv ,v : uniaxial Lifshitz points, the Kawasaki spin exchange model driven by an electric field, etc. An extension of finite-size scaling concepts to such anisotropic situations is proposed, including a discussion of (generalized) rectangular geometries, with linear dimensionL in the special direction and linear dimensionsL in all other directions. The related shape effects forL L but isotropic critical points are also discussed. Particular attention is paid to the case where the generalized hyperscaling relationv +(d–1)v =+2 does not hold. As a test of these ideas, a Monte Carlo simulation study for shape effects at isotropic critical point in the two-dimensional Ising model is presented, considering subsystems of a 1024x1024 square lattice at criticality.Visiting Supercomputer Senior Scientist at Rutgers University.     

Coherent states of theq-canonical commutation relations

For theq-deformed canonical commutation relationsa(f)a (g)=(1-q)f,g 1+qa (g)a(f) forf, g in some Hilbert space we consider representations generated from a vector satisfyinga(f)=<f, >, where . We show that such a representation exists if and only if 1. Moreover, for <1 these representations are unitarily equivalent to the Fock representation (obtained for =0). On the other hand representations obtained for different unit vectors are disjoint. We show that the universal C^*-algebra for the relations has a largest proper, closed, two-sided ideal. The quotient by this ideal is a naturalq-analogue of the Cuntz algebra (obtained forq=0). We discuss the conjecture that, ford<, this analogue should, in fact, be equal to the Cuntz algebra itself. In the limiting casesq=±1 we determine all irreducible representations of the relations, and characterize those which can be obtained via coherent states.Supported in part by the NSF(USA), and NATO Available by anonymous FTPfrom nostrom.physik.Uni-Osnabrueck.DE     

Dual-oriented thin crystals of molybdenum grown under Ar+ ion bombardment

Ar⁺ sputtering of an Cu(111) surface while simultaneously supplying Mo atoms is known to induce an oriented growth of Mo thin crystals, or seed-layers, on evolving conical Cu protrusions. The seed-layers thus formed are shown to be dual-oriented, or bicrystalline, consisting of columnar crystallites grown homo-epitaxially. The orientation relationship between the two types of crystallites was (100)_I (111)_II with [001]_I [110]_II, and this bicrystallinity probably resulted from a non-uniform charge-up of the layers' growth front. As concluded from high-resolution electron microscopy, the Mo(100) stacking is elastically converted into the Mo(111) stacking and vice versa, under the influence of tensile stress. The homo-epitaxy that the seed-layers exhibited is believed to reflect the mutual convertibility of the Mo(100) and (111) stackings.     

Diffusion in a one-dimensional gas of hard point particles

We simulate the classical diffusion of a particle of massM in an infinite one-dimensional system of hard point particles of massm in equilibrium. Each computer run corresponds to about 10⁸ collisions of the diffusive particle. We find that (t) 1/t fort large enough, and a crossover from an M m regime where=2 to=3 forM=m. The diffusion constant has a sharp maximum atM=m. We study moments x(t)² and x(t)⁴, and examine the behavior ofq ² (t)=x(t)⁴/3x(t)²². We find thatq(t)1 (consistent with a normal distribution) in theM limit (for all timest) and in the t limit for allM. On sabbatical leave from IVIC-Instituto Venezolano de Investigaciones Cientificas.     

Expectations and entropy inequalities for finite quantum systems

We prove that the relative entropy is decreasing under a trace-preserving expectation inB(K ¹), and we show the connection between this theorem and the strong subadditivity of the entropy. It is also proved that a linear, positive, trace-preserving map ofB(K) into itself such that 1 decreases the value of any convex trace function.     

Directed compact lattice animals: Exact results

The partially directed compact lattice animal model on the square lattice is solved exactly for the cluster number and average cluster radius along the directed axis in terms of the appropriate generating functions. For the critical exponents we find=0 and =1. Caliper size distribution along the directed axis is also calculated analytically. It is used to confirm =1 and to study some finite-size scaling properties for this model. For the perpendicular cluster radius distribution, a combination of analytic arguments and computer results leads to a conjecture on the exact form of the appropriate generating function and to the result =1/2. Some calculations are reported for the triangular lattice and for hypercubic lattices ind>2.     

Surviving extrema for the action on the twisted SU(∞) one point lattice

We give a simplified construction of twist eating configurations, based on a theorem due to Frobenius. These configurations are defined through the equation:U U U ⁺ U ⁺ =exp(2in /N) withU SU(N), =1 tod andn an antisymmetric matrix with integer entries. In the (Twisted)-Eguchi-Kawai model they yield extrema some of which survive forN. Comparison is made with the Monte Carlo data of the internal energy in the small coupling region.     

Interacting spinor and scalar fields: Exact self-consistent solutions in Bianci I space

Exact self-consistent solutions of the equations that describe a system of interacting spinor and massless scalar fields with the interaction Lagrangian L_int=_,^,(S), where (S) is an arbitrary function of the invariant S=, are obtained in Bianci I space. The possibility of excluding the initial singularity is studied for the case of a power-law function (S), and isotropic expansion of the space as t is established.Russian University of International Amity. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 53–58, July, 1995.     

Analyticity in Hubbard Models

The Hubbard model describes a lattice system of quantum particles with local (on-site) interactions. Its free energy is analytic when t is small, or t ²/U is small; here, is the inverse temperature, U the on-site repulsion, and t the hopping coefficient. For more general models with Hamiltonian H=V+T where V involves local terms only, the free energy is analytic when T is small, irrespective of V. There exists a unique Gibbs state showing exponential decay of spatial correlations. These properties are rigorously established in this paper.     

Produits tensoriels continus d'espaces et d'algèbres de Banach

The notion of tensor product of a family (A _i ) _i I of Banach algebras is generalized to the case whenI is a topological space; in this case A _i is generated by some elements x _i , the family (x _i ) being subjected to certain conditions: for instance the functioni x _i must be continuous. This notion is applied to Quantum Field Theory in the following sense: certain algebras of observables can be considered as continuous tensor products of simpler ones, namely of algebras of observables with one degree of freedom.     

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     

Non-smoothness of event horizons of Robinson-Trautman black holes

It is shown that generic small data Robinson-Trautman space-times cannot beC ¹²³ extended beyond the r=2m Schwarzschild-like event horizon. This implies that an observer living in such a space-time can determine by local measurements whether or not he has crossed the event-horizon of the black-hole.     

From bunches of membranes to bundles of strings

Bunches of membranes and bundles of strings exhibit unbinding transitions from a bound state at low temperatures to an unbound state at high temperatures.N freely suspended manifolds unbind continuously at the unique unbinding temperatureT _u ^f which is independent ofN. The amplitudes of the critical singularities have a strongN-dependence, however, which implies that the critical region for the continuous transition becomes very small and the transition becomes very abrupt in the limit of largeN. IfN membranes or strings are bound to a rigid surface, they undergo a sequence of either two or ofN successive transitions. In general, the rigid surface affects the contact probabilities of the fluctuating manifolds. For effectively repulsive interactions, the contact exponent ₂ which governs the probability for local pair contacts satisfies the scaling relation ₂=d + whered and denote the dimensionality and the roughness exponent of these manifolds.Dedicated to Herbert Wagner on the occasion of his 60th birthday