Invariant states in statistical mechanics

Mathematically we consider aC*-algebra , acted upon by the groupT of space-translations, which has an asymptotic abelian property. We analyse invariant states over . Physically this programme can be considered as a kinematical study of equilibrium states in statistical mechanics. Each invariant state can be uniquely decomposed into elementary invariant states (E-states). These elementary states have, amongst other characteristics, the physical property that space-averages of local observables are constants in the corresponding representations. In anE-state the discrete spectrum S _D of space-translations is additive which gives rise to the classificationE _I,E _II, andE _III corresponding to the three possibilities that S _D contains one point, a lattice of points, or a set with accumulation points. AnE _II-state can be uniquely decomposed into states (L-states) having a symmetry with respect to a closed subgroupT _L of (S _D and T _L are reciprocal lattices).L-states have properties with respect toT _L analogous to the properties ofE _I-states with respect toT. The decomposition intoL-states is the inverse process of homogenizing a lattice state by smearing it over a lattice distance. The mathematical methods which we employ have more general applications.     

Stochastic differential equations in quantum statistical mechanics. Observables and multiple wiener integrals

The physical and mathematical framework for quantum mechanical stochastic differential equations is discussed as the quantization ofc-number equations that typically describe Brownian motion in polynomial potentials.     

Rapidity gap correlations in short range order models

We show that short range order models relate the multiplicity distribution produced in a rapidity interval R of the central region, to the distribution of such intervals which all contain a fixed multiplicity N. This is an asymptotic result which furthermore implies that the asymptotic behavior of the Mueller moments be related to certain rapidity gap correlation moments. The behavior of these gap correlations in specific models depends in a direct way on the assumptions made about clustering and about the range of the interaction.     

On the equilibrium states in quantum statistical mechanics

Representations of theC*-algebra of observables corresponding to thermal equilibrium of a system at given temperatureT and chemical potential are studied. Both for finite and for infinite systems it is shown that the representation is reducible and that there exists a conjugation in the representation space, which maps the von Neumann algebra spanned by the representative of onto its commutant. This means that there is an equivalent anti-linear representation of in the commutant. The relation of these properties with the Kubo-Martin-Schwinger boundary condition is discussed.     

On locally normal states in quantum statistical mechanics

A sufficient condition is given in order that a von Neumann algebra with cyclic vector is quasi-standard. With the help of this result it is proved that a locally normal state with a cyclic and separating vector in the representation space gives rise to a quasi-standard von Neumann algebra. Furthermore it is proved that the representation space determined by a locally normal state in the G.N.S. construction is separable.     

Mean entropy of states in classical statistical mechanics

The equilibrium states for an infinite system of classical mechanics may be represented by states over AbelianC* algebras. We consider here continuous and lattice systems and define a mean entropy for their states. The properties of this mean entropy are investigated: linearity, upper semi-continuity, integral representations. In the lattice case, it is found that our mean entropy coincides with theKolmogorov-Sinai invariant of ergodic theory.     

Classical pure states: Information and symmetry in statistical mechanics

The aim of this paper is to find classical counterparts of pure quantum states. It is shown that these are singular probability distributions concentrated on the so-called maximal null manifolds in a phase space. They are equivalent to densities studied by Van Vleck and Schiller and to WKB solutions (cf. Van Vleck, 1928; Schiller, 1962). Properties of such distributions and their relativistic generalisations have been studied in previous papers (Sawianowski, 1971; Slawianowski, 1972). However, it has not been shown there that such distributions arise actually in the limith0. When working with the standard apparatus of differential geometry we mostly use the language of Kobayashi & Nomizu (1963).     

Electronic states in disordered systems with statistical correlations: Self-consistent born approximation

The electronic states in a weak, spatially correlated disordered potential are investigated using a translationally invariant formalism within a tight binding model. The effect of the disorder is mapped intok-space. The influence of the statistical correlation on the density of states and their localization properties is studied in the one-dimensional limit. It is shown that clustering supports tail states while the middle of the band is strongly affected by rapidly alternating configurations.     

Dobrushin uniqueness techniques and the decay of correlations in continuum statistical mechanics

Uniqueness of Gibbs states and decay properties of averaged, two point correlation functions are proved for many-body potentials in continuum statistical mechanical models via Dobrushin uniqueness techniques.     

Universality test of short range nucleon-nucleon correlations in nuclei with strange and charmed probes

Understanding the EMC effect and its relation to the short-range nucleon-nucleon correlations(SRC)in nuclei is a major challenge for modem nuclear physics.One of the key aspects of the connection between these phenomena is the universality.The universality states that the SRC is responsible for the EMC effect and that the modification of the partonic structure of the SRC is the same in different nuclei.The flavor dependence of the universal-ity is one of the unanswered questions.The investigations conducted to date have demonstrated the existence and universality of the SRC for light u and d quarks.Recently,it was suggested that the universality for heavy flavors can be studied through their deep subthreshold production in yA and eA collisions.In this paper,we discuss an alternative possibility to access the strange and gluon high-A"structure of the SRC and to establish universality for heavy flavors using nuclear semi-inclusive deep inelastic scattering(nSIDIS),which probes different quark flavor combinations depending on the final state hadron.The specific reaction can be"tagged"by observation of a strange or charmed particle registered in coincidence with the scattering lepton.The universality of the SRC can be tested in the kinematic region,i.e.,X>1,where the contribution to the cross section from SRC becomes dominant.Exploring the strangeness,charmonium,and open charm will shed light on the role of quarks and gluons in nuclei,thereby developing an understanding of how nuclei emerge within QCD.     

On the anomalous Kondo effect in disordered magnetic binary alloys with statistical short range order and its utilization for structural studies beyond pair correlations

Substitutional binary alloys with statistical short range order are investigated for the existence of the anomalous Kondo effect. For these alloys the concentrations of the anomalous Kondo scatterers are calculated and the existing experimental data are then analysed. Also, a theoretical model shows that the anomalous Kondo effect can yield a wider variation of the temperature-dependence or resistivity than the normal effect.     

Periodic,incommensurate and chaotic states in a continuum statistical mechanics model

We study the thermodynamic behavior of a continuum system with competing periodicities. We show that in addition to commensurate and incommensurate phases, there exist configurations which are chaotic in nature and exhibit no long-range order. These phases are metastable and characterized by an order parameter with a continuous spectrum. By transforming the problem of determining the ground states of the system into a classical mechanics problem, we construct a two-dimensional area-preserving map which can be used to study the qualitative nature of the orbits. Our results might be of relevance to adsorbed monolayers on periodic substrates.     

Effects of short range correlations on nuclear mass and momentum distributions

Effects of short range correlations on the form factor and the momentum distribution of nuclear systems are investigated. The present analysis, performed in the framework of the Jastrow approach, indicates that an independent-particle wave function (Slater determinant) cannot reproduce simultaneously the form factor and the momentum distribution of a correlated system. It is found that the momentum distribution is strongly affected by correlations beyond ≈2 fm^?1     

New slow and short range magnetic correlations in superconducting La2-xSrxCuO4

Inelastic neutron scattering measurements have been performed on high quality single crystals of in order to study the spin dynamics of this compound. In addition to the well-established incommensurate magnetic response, we show the existence of a new set of low energy excitations present in the whole superconducting region of the phase diagram. This new feature of the dynamical cross section is characterized, below about 10 K, by very short range ( lattice spacing) antiferromagnetic correlations and by a low energy scale of meV. At higher temperatures these fluctuations become nearly Q-independent. Different possible origins of these new spin correlations are discussed. Received: 3 September 1997 / Revised: 21 November 1997 / Accepted: 26 January 1998     

Formation of correlations and energy-conservation at short times

The formation of correlations due to collisions in an interacting nucleonic system is investigated. Results from one-time kinetic equations are compared with the Kadanoff and Baym two-time equation with collisions included in Born approximation. A reasonable agreement is found for a proposed approximation of the memory effects by a finite duration of collisions. This form of collision integral is in agreement with intuitive estimates from Fermi's golden rule. The formation of correlations and the build up time is calculated analytically for the high temperature and the low temperature limit. Different approximate expressions are compared with the numerical results. We present analytically the time dependent interaction energy and the formation time for Gau?- and Yukawa type of potentials. Received: 25 November 1998 / Revised version: 11 January 1999     

The influence of overlapping potentials and short range correlations on high-energy scattering

High-energy nucleon scattering from light nuclei is investigated using several different scattering formalisms. Off-energy-shell effects due to overlapping target particle potentials and short range correlations are included in some of the calculations. The results indicate that the uncertainties in the computed cross section due to choice of scattering formalism, and due to neglect or inclusion of off-energy-shell effects, or two-body correlations are all of comparable size.     

An alternative approach to calculate the density of states in nonextensive statistical mechanics

A relation between the generalized partition function (Tsallis) and density of states is established by using the method of integral transform which enables reducing some integral equations into the algebraic equations. Inverse Mellin transformation of this equation gives the density of states. Similar relation is also hold the for standard partition function (Boltzmann-Gibbs) and the density of states. Using these relations, we recover the density of states for the classical ideal gas within both statistics.