Models Of Quantum Statistical Mechanics Research Articles

Distinct critical behaviors from the same state in quantum spin and population dynamics perspectives.

There is a deep connection between the ground states of transverse-field spin systems and the late-time distributions of evolving viral populations-within simple models, both are obtained from the principal eigenvector of the same matrix. However, that vector is the wave-function amplitude in the quantum spin model, whereas it is the probability itself in the population model. We show that this seemingly minor difference has significant consequences: Phase transitions that are discontinuous in the spin system become continuous when viewed through the population perspective, and transitions that are continuous become governed by new critical exponents. We introduce a more general class of models that encompasses both cases and that can be solved exactly in a mean-field limit. Numerical results are also presented for a number of one-dimensional chains with power-law interactions. We see that well-worn spin models of quantum statistical mechanics can contain unexpected new physics and insights when treated as population-dynamical models and beyond, motivating further studies.

The Principle of the Largest Terms and Large Deviations for a Class of Nonlinear Functionals

We give an approach to large deviations for asymptotic problems without evident probabilistic representation behind. An example provided by the mean field models of quantum statistical mechanics are considered.

FORM FACTORS IN THE FINITE VOLUME

We study exactly solvable models of quantum statistical mechanics. Our main example is the Quantum nonlinear Schrödinger equation. This model can be solved by algebraic Bethe Ansatz. We are interested in the expression for a form factor of the local field in the finite volume [Formula: see text]. We found a determinant representation for this form factor. We think that this is the universal feature: finite volume form factor of any exactly solvable model can be represented a determinant.

Stochastically positive structures on Weyl algebras. The case of quasi-free states

We consider quasi-free stochastically positive ground and thermal states on Weyl algebras in the imaginary time formulation. In particular, we obtain a new derivation of a general form of thermal quasi-free state and give conditions when such a state is stochastically positive, i.e., when it defines a periodic stochastic process with respect to imaginary time, a so-called thermal process. Then we show that the thermal process completely determines modular structure canonically associated with the quasi-free thermal state on Weyl algebra. We discuss a variety of examples connected with free quantum field theories on globally hyperbolic stationary space–times and models of quantum statistical mechanics.

Van der Waals force between dielectric plates derived from the quantum statistical mechanical path integral method

The Van der Waals force (or Casimir force) between two semi-infinite dielectric slabs – conventionally derived via field theoretical methods – is derived in a novel way using the quantum statistical mechanical model introduced earlier by Høye–Stell and others. Both the static case, and the time-dependent case, are considered. The present paper generalizes earlier work of the present authors [I. Brevik, J.S. Høye, Physica A 153 (1988) 420], dealing with the Van der Waals force between monatomics.

Normal ordering in the theory of correlation functions of exactly solvable models

We study models of quantum statistical mechanics which can be solved by the algebraic Bethe ansatz. The general method of calculation of correlation functions is based on the method of determinant representations. The auxiliary Fock space and auxiliary Bose fields are introduced in order to remove the two body scattering and represent correlation functions as a mean value of a determinant of a Fredholm integral operator; the representation has a simple form for large space and time separations. In this paper we explain how to calculate the mean value in the auxiliary Fock space of asymptotic expression of the Fredholm determinant. It is necessary for the evaluation of the asymptotic form of the physical correlation functions.

Time and temperature dependent correlation functions of 1D models of quantum statistical mechanics

We consider exactly solvable, gapless models of statistical mechanics. We found the universal formula which describes the asymptotics of correlation functions at any temperature and an arbitrary coupling constant.

The kinetic deuterium isotope effect of proton‐transfer reactions in solution. Comparison of the marcus and the quantum‐statistical mechanical models

AbstractThe free energy dependence of the kinetic deuterium isotope effect of proton‐transfer reactions in solution is usually analysed in terms of the Marcus model. By means of modern computer techniques, the more general quantumstatistical mechanical model is also amenable to routine application. The differnces in the basic assumptions of the two approaches concerning the kinetic isotope effect are discussed. Reaction series for which both the Brønsted relation and the free‐energy dependence of the kinetic isotope effect are available are analysed by means of the two models using one set of parameters for both free‐energy relations.

Van der Waals force derived from a quantum statistical mechanical path integral method

The main purpose of this paper is to apply the quantum statistical mechanical model for polarizable fluids, used by Høye-Stell and others, to the calculation of the van der Waals force (dispersion force) between monatomics. The results are in agreement with those obtained by quantum perturbation theory. The quantum statistical method implies considerable formal simplifications. The introductory sections of the paper show, for illustrative purposes, how the dispersion forces in limiting cases also can be obtained from macroscopic quantum electromagnetic theory when two dilute dielectric media with plane-parallel surfaces are separated by a vacuum (Casimir effect).

The Kinetic Deuterium Isotope Effect of Proton Transfer Reactions in Solution

The theoretical models for the treatment of the kinetic isotope effect of proton-transfer reactions (tunneling, Marcus and quantum-statistical mechanical model) are described. Scope and limits of these models are discussed with respect to intermolecular interaction, free energy relations, temperature, solvent and pressure dependence, and ultrafast protontransfer.

LINEAR BOSON MODELS OF TIME EVOLUTION IN QUANTUM STATISTICAL MECHANICS

This paper contains a construction of time evolution for linear boson models of quantum statistical mechanics. The main result is a theorem on convergence to a quasifree moment functional in the course of linear time evolution. A connection between linear evolution of the moment functional and evolution of the corresponding state of an infinite quantum system is discussed. Bibliography: 30 titles.

Effect of alkylation of ammonia on the optical band shape of solvated electrons

At 200 K the width at half height, W1/2, of the e−solv optical absorption band in n-propyl amine is 2.1-fold greater than that in ammonia. Three quarters of the broadening occurs on the high energy side of the band. The energy Er at half height on the low energy side of the band is nearly the same in the amine as in ammonia, while Eb, the energy at half height on the high energy side, is 42% greater in the amine. The temperature coefficient dEAmax/dT is 1.8-fold greater in the amine than in ammonia. The larger width is consistent with there being a less uniform distribution of localization sites in the system, and the larger temperature coefficient implies that the sites are more easily disturbed by thermal agitation. A quantum statistical mechanical model, such as the one begun by Simons, is needed to extend the theoretical treatment of e−solv spectra. The correlation between optical absorption energies of e−solv and the structure of the solvent, as partially reflected in the Kirkwood correlation factor, is re-emphasized.