Semiclassical Dynamics and Relaxation

Hardcover | December 4, 2007

byD.S.F. Crothers

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Condensed-matter physics plays an ever increasing role in photonics, electronic and atomic collisions research. Dispersion (Dynamics and Relaxation) includes scattering/collisions in the gaseous phase. It also includes thermal agitation, tunneling and relaxation in the liquid and solid phases. Classical mechanics, classical statistical mechanics, classical relativity and quantum mechanics are all implicated. 'Semiclassical' essentially means that there is a large or asymptotic real parameter. 'Semiclassical' can also mean 'classical with first-order quantal correction', based on an exponentiated Liouville series commencing with a simple pole in the -plane, being Planck's reduced constant and coming with all the attendant connection problems associated with the singularity at the turning or transition point and with the Stokes phenomenon. Equally,' semiclassical' can mean 'electrons described quantally and the heavy particles classically'. This latter gives rise to the so-called impact parameter method based on a pre-assigned classical trajectory.With evermore sophisticated experiments, it has become equally more important to test theory over a wider range of parameters. For instance, at low impact energies in heavy-particle collisions, the inverse velocity is a large parameter; in single-domain ferromagnetism, thermal agitation (including Brownian motion and continuous-time random walks) is faced with a barrier of height 'sigma', a possibly large parameter. Methods of solution include phase-integral analysis, integral transforms and change-of-dependent variable. We shall consider the Schrödinger time-independent and time-dependent equations, the Dirac equation, the Fokker Planck equation, the Langevin equation and the equations of Einstein's classical general relativity equations.There is an increasing tendency among physicists to decry applied mathematics and theoretical physics in favour of computational blackboxes. One may say applied mathematics concerns hard sums and products (and their inverses) but unless one can simplify and sum infinite series of products of infinite series, can one believe the results of a computer program? The era of the polymath has passed; this book proposal aims to show the relevance to, and impact of theory on, laboratory scientists.

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Condensed-matter physics plays an ever increasing role in photonics, electronic and atomic collisions research. Dispersion (Dynamics and Relaxation) includes scattering/collisions in the gaseous phase. It also includes thermal agitation, tunneling and relaxation in the liquid and solid phases. Classical mechanics, classical statistical...

From the Jacket

This text concerns 'semiclassical' within various meanings. These include the familiar JWKB approximation and its phase-integral generalizations in Chapter 2 to two and four transition points with or without one or two poles: by corollary, crossing and non-crossing nonadiabatic collision theory. Above and below threshold Wannier ioniza...

The author is an expert in quantum dynamics and the processes of atomic collisions over 42 years and he has developed the mathematics of the semiclassical theory over 18 years and has applied this to condensed-matter physics.  He is currently a Professor of Theoretical Physics in the Department of Applied Mathematics and Theoretical Ph...

other books by D.S.F. Crothers

Semiclassical Dynamics and Relaxation
Semiclassical Dynamics and Relaxation

Paperback|Nov 19 2010

$256.71 online$284.95list price(save 9%)
Format:HardcoverDimensions:353 pages, 9.25 × 6.14 × 0 inPublished:December 4, 2007Publisher:Springer New YorkLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:038774312X

ISBN - 13:9780387743127

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Table of Contents

Mathematics for the Semiclassicist.- Semiclassical Phase Integral.- Semiclassical Methods for Hyperspherical Coordinate Systems.- Ion-Atom Collisions.- Diffusion in Liquids and Solids.- Continued Fraction Solutions of Eq. (5.301).- Mittag-Leffler Fuctions.- Nonlinear Response to Alternating Fields.- References.- Index.

Editorial Reviews

From the reviews:"This book is based on some lectures given by the author to postgraduate Ph.D. students at the Centre for Atomic, Molecular and Optical Physics, School of Mathematics and Physics, of Queen's University Belfast, and reflects the author's research interests. . At the end of the book, the reader will find a very rich list of references. The book is very instructive, both to physicists and mathematicians, in that it gives many important instances of the use of the fundamental technique of semiclassical approximation."­­­ (Alberto Parmeggiani, Mathematical Reviews, Issue 2011 d)