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Author: M. L. Mehta
Publisher: Academic Press
ISBN: 1483258564
Category : Mathematics
Languages : en
Pages : 270
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Book Description
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.
Author: Andreas Lambertus Spijkervet
Publisher:
ISBN:
Category :
Languages : en
Pages : 118
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Book Description
Author: M. L. Mehta
Publisher: Academic Press
ISBN: 1483258564
Category : Mathematics
Languages : en
Pages : 270
Get Book Here
Book Description
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.
Author: W. E. Burcham
Publisher: Springer Science & Business Media
ISBN: 3642458750
Category : Science
Languages : en
Pages : 559
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Book Description
Author: Lev D. Landau
Publisher: Springer
ISBN: 1489964576
Category : Technology & Engineering
Languages : en
Pages : 82
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Book Description
Author: S. Flügge
Publisher: Springer Science & Business Media
ISBN: 3642459234
Category : Science
Languages : en
Pages : 587
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Book Description
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.
Author: S. G. Christov
Publisher: Springer Science & Business Media
ISBN: 3642931421
Category : Science
Languages : en
Pages : 336
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Book Description
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.
Author: Pavol Oblozinsky
Publisher: World Scientific
ISBN: 9814543675
Category :
Languages : en
Pages : 550
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Book Description
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.
Author: R Balian
Publisher: Elsevier
ISBN: 0444601147
Category : Science
Languages : en
Pages : 819
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Book Description
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.
Author: Jutta Escher
Publisher: Springer Nature
ISBN: 3030580822
Category : Science
Languages : en
Pages : 312
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Book Description
The Compound-Nuclear Reaction and Related Topics (CNR*) international workshop series was initiated in 2007 with a meeting near Yosemite National Park. It has since been held in Bordeaux (2009), Prague (2011), Sao Paulo (2013), Tokyo (2015), and Berkeley, California (2018). The workshop series brings together experts in nuclear theory, experiment, data evaluations, and applications, and fosters interactions among these groups. Topics of interest include: nuclear reaction mechanisms, optical model, direct reactions and the compound nucleus, pre-equilibrium reactions, fusion and fission, cross section measurements (direct and indirect methods), Hauser-Feshbach theory (limits and extensions), compound-nuclear decays, particle and gamma emission, level densities, strength functions, nuclear structure for compound-nuclear reactions, nuclear energy, nuclear astrophysics, and other topics. This peer-reviewed proceedings volume presents papers and poster summaries from the 6th International Workshop on Compound-Nuclear Reactions and Related Topics CNR*18, held on September 24-28, 2018, at Lawrence Berkeley National Lab, Berkeley, CA.
Author: Dieter Seeliger
Publisher: World Scientific
ISBN: 9814556076
Category :
Languages : en
Pages : 312
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Book Description
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.
