Random Matrices and the Statistical Theory of Energy Levels

Random Matrices and the Statistical Theory of Energy Levels

Author: M. L. Mehta

Publisher: Academic Press

Published: 2014-05-12

Total Pages: 270

ISBN-13: 1483258564

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Random Matrices and the Statistical Theory of Energy Levels focuses on the processes, methodologies, calculations, and approaches involved in random matrices and the statistical theory of energy levels, including ensembles and density and correlation functions. The publication first elaborates on the joint probability density function for the matrix elements and eigenvalues, including the Gaussian unitary, symplectic, and orthogonal ensembles and time-reversal invariance. The text then examines the Gaussian ensembles, as well as the asymptotic formula for the level density and partition function. The manuscript elaborates on the Brownian motion model, circuit ensembles, correlation functions, thermodynamics, and spacing distribution of circular ensembles. Topics include continuum model for the spacing distribution, thermodynamic quantities, joint probability density function for the eigenvalues, stationary and nonstationary ensembles, and ensemble averages. The publication then examines the joint probability density functions for two nearby spacings and invariance hypothesis and matrix element correlations. The text is a valuable source of data for researchers interested in random matrices and the statistical theory of energy levels.


Collision Theory and Statistical Theory of Chemical Reactions

Collision Theory and Statistical Theory of Chemical Reactions

Author: S. G. Christov

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 336

ISBN-13: 3642931421

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Since the discovery of quantum mechanics,more than fifty years ago,the theory of chemical reactivity has taken the first steps of its development. The knowledge of the electronic structure and the properties of atoms and molecules is the basis for an un derstanding of their interactions in the elementary act of any chemical process. The increasing information in this field during the last decades has stimulated the elaboration of the methods for evaluating the potential energy of the reacting systems as well as the creation of new methods for calculation of reaction probabili ties (or cross sections) and rate constants. An exact solution to these fundamental problems of theoretical chemistry based on quan tum mechanics and statistical physics, however, is still impossible even for the simplest chemical reactions. Therefore,different ap proximations have to be used in order to simplify one or the other side of the problem. At present, the basic approach in the theory of chemical reactivity consists in separating the motions of electrons and nu clei by making use of the Born-Oppenheimer adiabatic approximation to obtain electronic energy as an effective potential for nuclear motion. If the potential energy surface is known, one can calculate, in principle, the reaction probability for any given initial state of the system. The reaction rate is then obtained as an average of the reaction probabilities over all possible initial states of the reacting ~artic1es. In the different stages of this calculational scheme additional approximations are usually introduced.


Nuclear Reactions II: Theory / Kernreaktionen II: Theorie

Nuclear Reactions II: Theory / Kernreaktionen II: Theorie

Author: S. Flügge

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 587

ISBN-13: 3642459234

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449 one finds that for y = Fo (e) C= :n; V3 [Po (2'Yj) 3 -kjF(i) + (2'Yj)! Fd (2'Yj) 3 -ijF (·m, } 1 (14.17) C2 = :n; [- (2'Yj)! Fd (2'Yj) 3 -ijF(i) + Fo (2'Yj) 3 -~;r(i)J, and if y is to be Go(e), C and Chave the same form with Go (2'Yj) replacing Po (2'Yj) 1 2 and G~(2'Yj) replacing Fd(2'Yj). The values of the functions at eo =2'Yj may be ob tained from (14.8). 1 J.K. TYSON has employed the modified Hankel functions of order one third 2 as solutions of (13.4) to obtain expressions for the Coulomb functions for L =0 which converge near e =2'Yj. His results appear as linear combinations of the real and imaginary parts of n ~(x) = (12)!e- ;/6 [A;{- x) - iB;( -x)J, (14.18) and its derivatives multiplying power series in x = (e - 2'Yj)j(2'Yj)1. For values 1 away from the turning point for L =0, TYSON has obtained forms for Po{e) and Go(e) which are similar to (13.1) to (13.3). The JWKB approximation is again the leading term, and some higher order corrections are given. Expressions similar to Eqs. (14.11) and (14.12) have been obtained by T.D. 3 NEWTON employing the integral representation of (4.4). His results give re presentations of FL(e), Gde) in the vicinity of e=2'Yj [whereas (14.11), (14.12) converge near e=eLJ when L.


Statistical Models for Nuclear Decay

Statistical Models for Nuclear Decay

Author: A.J Cole

Publisher: CRC Press

Published: 2000-01-01

Total Pages: 354

ISBN-13: 1420033476

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Statistical Models for Nuclear Decay: From Evaporation to Vaporization describes statistical models that are applied to the decay of atomic nuclei, emphasizing highly excited nuclei usually produced using heavy ion collisions. The first two chapters present essential introductions to statistical mechanics and nuclear physics, followed by a descript


Nuclear Reaction Data And Nuclear Reactors - Physics, Design And Safety: Proceedings Of The Workshop

Nuclear Reaction Data And Nuclear Reactors - Physics, Design And Safety: Proceedings Of The Workshop

Author: Pavol Oblozinsky

Publisher: World Scientific

Published: 1999-07-22

Total Pages: 550

ISBN-13: 9814543675

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This volume provides the up-to-date information behind nuclear reactor calculations, focusing on a key role of nuclear reaction data, down to the physics of nuclear interactions. It is divided into three parts. Part 1 deals with nuclear reaction models, including neutron resonances, fission, the optical model, statistical and preequilibrium models as well as nuclear level densities. Part 2 is devoted to nuclear data filling and processing; it includes lectures on nuclear data evaluation and formatting, data libraries and services, with emphasis on nuclear-data-processing codes. Part 3 presents applications in nuclear reactor calculations, emphasizing physics, design and safety.


Nuclear Reaction Mechanisms - Proceedings Of The Xxth International Symposium On Nuclear Physics

Nuclear Reaction Mechanisms - Proceedings Of The Xxth International Symposium On Nuclear Physics

Author: Dieter Seeliger

Publisher: World Scientific

Published: 1991-07-03

Total Pages: 312

ISBN-13: 9814556076

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The symposium covered the following topics: Physical foundation of preequilibrium reaction models; Randomness in nuclei and nuclear reactions; Statistical multistep compound and direct reactions; Exit channels in nuclear reactions: n, p, α, and γ-emission as well as fission; Multiple emission processes; Parameter systematics for nuclear model calculations; New approaches to angular distributions; Experiments for reaction mechanism studies; Applications for nuclear data evaluation.


Claude Bloch

Claude Bloch

Author: R Balian

Publisher: Elsevier

Published: 2012-12-02

Total Pages: 819

ISBN-13: 0444601147

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Claude Bloch: Scientific Works Oeuvre Scientifique covers the collection of scientific works of Claude Bloch. The book includes topics on field theories with non-localized interaction and notes on the symmetry properties of nuclear wave functions. It also covers theory of nuclear level density; the theory of imperfect fermi gases; the structure of nuclear matter; and the canonical form of an antisymmetric tensor and its application to the theory of superconductivity.