Books in Nonlinear statistical and applied physics

Integrable Systems in Quantum Field Theory and Statistical Mechanics

1st Edition
May 19, 2014
M. Jimbo + 2 more
English
eBook
9 7 8 1 4 8 3 2 9 5 2 5 1

Advanced Studies in Pure Mathematics, Volume 19: Integrable Systems in Quantum Field Theory and Statistical Mechanics provides information pertinent to the advances in the study of pure mathematics. This book covers a variety of topics, including statistical mechanics, eigenvalue spectrum, conformal field theory, quantum groups and integrable models, integrable field theory, and conformal invariant models. Organized into 17 chapters, this volume begins with an overview of the eigenvalues of the three-state superintegrable chiral Potts model of the associated spin chain by use of a functional equation. This text then illustrates the importance of the star-triangle equation with a few results for the two-dimensional Ising model. Other chapters consider the conformal field theories on manifolds with a boundary, and the constraints placed by modular invariance on their partition functions. This book discusses as well the topological invariants for knots and links. The final chapter deals with equations of motion for two-dimensional quantum field theory. This book is a valuable resource for mathematicians.

Random Matrices

2nd Edition
May 19, 2014
Madan Lal Mehta
English
eBook
9 7 8 1 4 8 3 2 9 5 9 5 4

Since the publication of Random Matrices (Academic Press, 1967) so many new results have emerged both in theory and in applications, that this edition is almost completely revised to reflect the developments. For example, the theory of matrices with quaternion elements was developed to compute certain multiple integrals, and the inverse scattering theory was used to derive asymptotic results. The discovery of Selberg's 1944 paper on a multiple integral also gave rise to hundreds of recent publications. This book presents a coherent and detailed analytical treatment of random matrices, leading in particular to the calculation of n-point correlations, of spacing probabilities, and of a number of statistical quantities. The results are used in describing the statistical properties of nuclear excitations, the energies of chaotic systems, the ultrasonic frequencies of structural materials, the zeros of the Riemann zeta function, and in general the characteristic energies of any sufficiently complicated system. Of special interest to physicists and mathematicians, the book is self-contained and the reader need know mathematics only at the undergraduate level.

Elastic Wave Field Extrapolation

1st Edition
Volume 2
April 14, 2014
C.P.A. Wapenaar
A. J. Berkhout
English
eBook
9 7 8 1 4 8 3 2 9 1 0 0 0

Extrapolation of seismic waves from the earth's surface to any level in the subsurface plays an essential role in many advanced seismic processing schemes, such as migration, inverse scattering and redatuming. At present these schemes are based on the acoustic wave equation. This means not only that S-waves (shear waves) are ignored, but also that P-waves (compressional waves) are not handled correctly. In the seismic industry there is an important trend towards multi-component data acquisition. For processing of multi-component seismic data, ignoring S-waves can no longer be justified. Wave field extrapolation should therefore be based on the full elastic wave equation.In this book the authors review acoustic one-way extrapolation of P-waves and introduce elastic one-way extrapolation of P- and S-waves. They demonstrate that elastic extrapolation of multi-component data, decomposed into P- and S-waves, is essentially equivalent to acoustic extrapolation of P-waves. This has the important practical consequence that elastic processing of multi-component seismic data need not be significantly more complicated than acoustic processing of single-component seismic data. This is demonstrated in the final chapters, which deal with the application of wave field extrapolation in the redatuming process of single- and multi-component seismic data.Geophysicists, and anyone who is interested in a review of acoustic and elastic wave theory, will find this book useful. It is also a suitable textbook for graduate students and those following courses in elastic wave field extrapolation as each subject is introduced in a relatively simple manner using the scalar acoustic wave equation. In the chapters on elastic wave field extrapolation the formulation, whenever possible, is analogous to that used in the chapters on acoustic wave field extrapolation. The text is illustrated throughout and a bibliography and keyword index are provided.

Applications of Quantum and Classical Connections in Modeling Atomic, Molecular and Electrodynamic Systems

1st Edition
November 22, 2013
Alexandru Popa
English
Paperback
9 7 8 0 1 2 4 1 7 3 1 8 7
eBook
9 7 8 0 1 2 4 1 8 6 6 5 1

Applications of Quantum and Classical Connections in Modeling Atomic, Molecular and Electrodynamical Systems is a reference on the new field of relativistic optics, examining topics related to relativistic interactions between very intense laser beams and particles. Based on 30 years of research, this unique book connects the properties of quantum equations to corresponding classical equations used to calculate the energetic values and the symmetry properties of atomic, molecular and electrodynamical systems. In addition, it examines applications for these methods, and for the calculation of properties of high harmonics in interactions between very intense electromagnetic fields and electrons. This resource is the only one of its kind, a valuable tool for scientists and graduate students interested in the foundations of quantum mechanics, as well as applied scientists interested in accurate atomic and molecular models.

Ideas of Quantum Chemistry

2nd Edition
November 12, 2013
Lucjan Piela
English
Hardback
9 7 8 0 4 4 4 5 9 4 3 6 5
eBook
9 7 8 0 4 4 4 5 9 4 5 7 0

Ideas of Quantum Chemistry shows how quantum mechanics is applied to chemistry to give it a theoretical foundation. From the Schroedinger equation to electronic and nuclear motion to intermolecular interactions, this book covers the primary quantum underpinnings of chemical systems. The structure of the book (a TREE-form) emphasizes the logical relationships among various topics, facts and methods. It shows the reader which parts of the text are needed for understanding specific aspects of the subject matter. Interspersed throughout the text are short biographies of key scientists and their contributions to the development of the field. Ideas of Quantum Chemistry has both textbook and reference work aspects. Like a textbook, the material is organized into digestible sections with each chapter following the same structure. It answers frequently asked questions and highlights the most important conclusions and the essential mathematical formulae in the text. In its reference aspects, it has a broader range than traditional quantum chemistry books and reviews virtually all of the pertinent literature. It is useful both for beginners as well as specialists in advanced topics of quantum chemistry. An appendix on the Internet supplements this book.

Mechanics and Electrodynamics

1st Edition
October 22, 2013
L D Landau + 1 more
English
eBook
9 7 8 1 4 8 3 2 8 5 2 9 0

Largely a condensed amalgamation of two previous books by the same authors - Mechanics and The Classical Theory of Fields - omitting the rather more advanced topics such as general relativity.

Problems in Quantum Mechanics

1st Edition
October 22, 2013
F. Constantinescu + 1 more
J.A. Spiers
English
eBook
9 7 8 1 4 8 3 2 9 2 9 4 6

International Series in Natural Philosophy, Volume 30: Problems in Quantum Mechanics focuses on the processes, principles, reactions, and methodologies involved in quantum mechanics. The publication first elaborates on the mathematical formalism of quantum mechanics, simple quantum systems, and mean values and uncertainty relations. Discussions focus on mean values of dynamical variables, uncertainty relations, eigenfunctions and the energy spectrum, motion in a central field, matrix representation of vectors and operators, Hubert spaces, and operators in Hilbert space. The text then takes a look at mean values and uncertainty relations, semi-classical approximation, and pictures and representations. The book takes a look at orbital angular momentum and spin, systems of identical particles, and perturbation theory. Topics include variational method, stationary state perturbation theory, isotopic spin, second quantization, properties of angular momentum operators, and angular momentum and rotations of coordinate axes. The manuscript also ponders on functions used in quantum mechanics, relativistic quantum mechanics, and radiation theory. The publication is a dependable reference for researchers interested in quantum mechanics.

The Analysis of Thermally Stimulated Processes

1st Edition
October 22, 2013
R. Chen + 1 more
Brian Pamplin
English
eBook
9 7 8 1 4 8 3 2 8 5 5 1 1

Thermally stimulated processes include a number of phenomena - either physical or chemical in nature - in which a certain property of a substance is measured during controlled heating from a 'low' temperature. Workers and graduate students in a wide spectrum of fields require an introduction to methods of extracting information from such measurements. This book gives an interdisciplinary approach to various methods which may be applied to analytical chemistry including radiation dosimetry and determination of archaeological and geological ages. In addition, recent advances are included, such as ionic thermocurrent of general order kinetics, polarization thermocurrents and some aspects of the superlinear dependence on the dose of thermoluminescence

Landau

1st Edition
October 22, 2013
A. Livanova + 1 more
English
eBook
9 7 8 1 4 8 3 2 8 5 5 4 2

A biography of Lev Landau, one of the greatest Soviet theoretical physicists, whose career was cut short by a catastrophic car accident in 1962 and who was still only sixty when he died six years later. He won the Nobel Prize 'for pioneering work on the theory of the condensed state of matter, particularly liquid helium'. But the book shows that Landau's characterisation of himself as 'one of the last of the universal men of theoretical physics' was fully justified. Clearly and concisely it describes his achievements in all areas of theoretical physics from hydrodynamics to the quantum theory of fields. Attention is also paid to his genius as a teacher and mentor of young scientists, and throughout the book the true humanity of the man is evident

The Classical Theory of Fields

4th Edition
Volume 2
October 22, 2013
L D Landau
English
eBook
9 7 8 1 4 8 3 2 9 3 2 8 8

Translated from the 6th Russian edition, this latest edition contains seven new sections with chapters on General Relativity, Gravitational Waves and Relativistic Cosmology, where Professor Lifshitz's interests lay. The text of the 3rd English edition has been thoroughly revised and additional problems inserted

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