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LongTime Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann’s 1929 Article on the Quantum Ergodic Theorem
, 2010
"... The renewed interest in the foundations of quantum statistical mechanics in recent years has led us to study John von Neumann’s 1929 article on the quantum ergodic theorem. We have found this almost forgotten article, which until now has been available only in German, to be a treasure chest, and to ..."
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The renewed interest in the foundations of quantum statistical mechanics in recent years has led us to study John von Neumann’s 1929 article on the quantum ergodic theorem. We have found this almost forgotten article, which until now has been available only in German, to be a treasure chest, and to be much misunderstood. In it, von Neumann studied the longtime behavior of macroscopic quantum systems. While one of the two theorems announced in his title, the one he calls the “quantum Htheorem, ” is actually a much weaker statement than Boltzmann’s classical Htheorem, the other theorem, which he calls the “quantum ergodic theorem, ” is a beautiful and very nontrivial result. It expresses a fact we call “normal typicality ” and can be summarized as follows: For a “typical ” finite family of commuting macroscopic observables, every initial wave function ψ0 from a microcanonical energy shell so evolves that for most times t in the long run, the joint probability distribution of these observables obtained from ψt is close to their microcanonical distribution. PACS: 05.30.d. Key words: quantum statistical mechanics; approach to thermal equilibrium; macroscopic observable; microcanonical energy shell; typical longtime behavior.
Counting in Lattices: Combinatorial Problems from Statistical Mechanics
, 1994
"... In this thesis we consider two classical combinatorial problems arising in statistical mechanics: counting matchings and selfavoiding walks in lattice graphs. The first problem arises in the study of the thermodynamical properties of monomers and dimers (diatomic molecules) in crystals. Fisher, Kas ..."
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In this thesis we consider two classical combinatorial problems arising in statistical mechanics: counting matchings and selfavoiding walks in lattice graphs. The first problem arises in the study of the thermodynamical properties of monomers and dimers (diatomic molecules) in crystals. Fisher, Kasteleyn and Temperley discovered an elegant technique to exactly count the number of perfect matchings in two dimensional lattices, but it is not applicable for matchings of arbitrary size, or in higher dimensional lattices. We present the first efficient approximation algorithm for computing the number of matchings of any size in any periodic lattice in arbitrary dimension. The algorithm is based on Monte Carlo simulation of a suitable Markov chain and has rigorously derived performance guarantees that do not rely on any assumptions. In addition, we show that these results generalize to counting matchings in any graph which is the Cayley graph of a finite group. The second problem is countin...
Transverse energy flows in vectorial fields of paraxial light beams
, 2007
"... A general study of transverse energy flows (TEF) as physically meaningful and informative characteristics of paraxial light beams' spatial structure is presented. The total TEF can be decomposed into the spin and orbital contributions giving rise to the spin and orbital angular momentums, corre ..."
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A general study of transverse energy flows (TEF) as physically meaningful and informative characteristics of paraxial light beams' spatial structure is presented. The total TEF can be decomposed into the spin and orbital contributions giving rise to the spin and orbital angular momentums, correspondingly. Definitions and properties of these constituents are discussed in relation with the optical field representation through linear and circular orthogonal polarization bases. An analysis of TEFs near singular points has been carried out. General discussion of the evolution of the optical field singularities is presented. Possible mechanical action of light beams associated with the TEF is studied on the example of an absorptive medium described by the Drude–Lorentz model.
Symmetry breaking in monoatomic 2lattices
"... In this paper we describe all the possibilities for symmetry breaking transformations in monoatomic 2lattices (crystal structures with two identical points in their unit translational cell). This is done by establishing the symmetry hierarchies (partial ordering) for the arithmetic classes of symme ..."
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In this paper we describe all the possibilities for symmetry breaking transformations in monoatomic 2lattices (crystal structures with two identical points in their unit translational cell). This is done by establishing the symmetry hierarchies (partial ordering) for the arithmetic classes of symmetry groups of these crystals (Fig. 1). We also study the ‘EricksenPitteri neighbourhoods ’ for them, thus making a local analysis of their configuration space. We give details about two physically relevant cases, analysing the neighbourhoods and the possible symmetrybreaking mechanisms for the diamond and the hexagonal closepacked structures (Figs. 2 and 3). 1
The Arithmetic Symmetry of Multilattices: Another View on the 29 Types of Monoatomic 2Lattices
"... This paper studies the ensuing arithmetic classification in the simplest threedimensional case, that is, monoatomic 2lattices (triply periodic structures with two indistinguishable points in their unit cell). We show that there exist 29 distinct arithmetic types of monoatomic 2lattices. As all mo ..."
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This paper studies the ensuing arithmetic classification in the simplest threedimensional case, that is, monoatomic 2lattices (triply periodic structures with two indistinguishable points in their unit cell). We show that there exist 29 distinct arithmetic types of monoatomic 2lattices. As all monoatomic 2lattices are constituted by a single crystallographic orbit, these structures are also classified by the established criterion of Fischer and Koch (1975, 1996); the two classifications coincide. Among the 29 types we retrieve the 5 Strukturberichte that are themselves monoatomic 2lattices, which indicates how many more such structures there exist in theory (to compare, recall that the arithmetic types of 1lattices are the classical 14 Bravais types, among which 6 are listed as Strukturberichte) . 1. Introduction 1.1. Background
Theoretical Models of Superbursts on Accreting Neutron Stars
, 2005
"... We carry out a generalrelativistic global linear stability analysis of the amassed carbon fuel on the surface of an accreting neutron star to determine the conditions under which superbursts occur. We reproduce the general observational characteristics of superbursts, including burst fluences, recu ..."
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We carry out a generalrelativistic global linear stability analysis of the amassed carbon fuel on the surface of an accreting neutron star to determine the conditions under which superbursts occur. We reproduce the general observational characteristics of superbursts, including burst fluences, recurrence times, and the absence of superbursts on stars with accretion rates ˙ M < 0.1 ˙ MEdd, where ˙MEdd denotes the Eddington limit. By comparing our results with observations, we are able to set constraints on neutron star parameters such as the stellar radius and neutrino cooling mechanism in the core. Specifically, we find that accreting neutron stars with ordered crusts and highly efficient neutrino emission in their cores (due to direct URCA or pionic reactions, for example) produce extremely energetic (> 10 44 ergs) superbursts which are inconsistent with observations, in agreement with previous investigations. Also, because of pycnonuclear burning of carbon, they do not have superbursts in the range of accretion rates at which superbursts are actually observed unless the crust is very impure. Stars with
unknown title
, 1998
"... Orbital evolution of a binary neutron star and gravitational radiation ..."
Institute of Spectroscopy, Russian Academy of Sciences,
, 1995
"... We consider the generalization of Haldane’s statecounting procedure to describe all possible types of exclusion statistics which are linear in the deformation parameter g. The statistics are parametrized by elements of the symmetric group of the particles in question. For several specific cases we ..."
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We consider the generalization of Haldane’s statecounting procedure to describe all possible types of exclusion statistics which are linear in the deformation parameter g. The statistics are parametrized by elements of the symmetric group of the particles in question. For several specific cases we determine the form of the distribution functions which generalizes results obtained by Wu. Using them we analyze the lowtemperature behavior and thermodynamic properties of these systems and compare our results with previous studies of the thermodynamics of a gas of gons. Various possible physical applications of these constructions are discussed. hepth/9506111
on Hierarchic Theory of Matter and Field, developed by the author
, 2000
"... In accordance to our Hierarchic Model of Consciousness (HMC), each specific kind of neuron ensembles excitation corresponds to hierarchical system of threedimensional (3D) standing waves of following interrelated kinds: thermal de Broglie waves (waves B), produced by unharmonic translations and l ..."
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In accordance to our Hierarchic Model of Consciousness (HMC), each specific kind of neuron ensembles excitation corresponds to hierarchical system of threedimensional (3D) standing waves of following interrelated kinds: thermal de Broglie waves (waves B), produced by unharmonic translations and librations of molecules and providing the possibility of hightemperature molecular Bose condensation; electromagnetic (IR) waves; acoustic waves; vibrogravitational waves, excited by coherent translational and librational oscillations of molecules, accompanied by alternating accelerations. Corresponding hierarchic system of 24 excitations, describing virtually all the properties of any condensed matter, can be generated by quantum transitions of the coherent water clusters, localized in cytoplasm and in the microtubules of neurons bodies. Most important primary collective excitations in form of coherent clusters are resulted from hightemperature molecular Bosecondensation of water (see Appendix). We assume in our model the existence of feedback reaction between
INVESTIGATION OF ZEROSOUND DISPERSION EQUATION IN THE COMPLEX PLANE OF FREQUENCY
, 2005
"... The known solutions to the zerosound dispersion equation are considered as placed on the physical and unphysical sheets in the complex plane of frequency. I. ..."
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The known solutions to the zerosound dispersion equation are considered as placed on the physical and unphysical sheets in the complex plane of frequency. I.