282 pages, 6 x 9, 2004, ISBN 0-309-08051-2
Description
For the better part of a century, attempts to explain what was
really going on in the quantum world seemed doomed to failure.
But recent technological advances have made the question both
practical and urgent. A brilliantly imaginative group of
physicists at Oxford University have risen to the challenge. This
is their story.
At long last, there is a sensible way to think about quantum
mechanics. The new view abolishes the need to believe in
randomness, long-range spooky forces, or conscious observers with
mysterious powers to collapse cats into a state of life or death.
But the new understanding comes at a price: we must accept that
we live in a multiverse wherein countless versions of reality
unfold side-by-side. The philosophical and personal consequences
of this are awe-inspiring.
The new interpretation has allowed imaginative physicists to
conceive of wonderful new technologies: measuring devices that
effectively share information between worlds and computers that
can borrow the power of other worlds to perform calculations.
Step by step, the problems initially associated with the original
many-worlds formulation have been addressed and answered so that
a clear but startling new picture has emerged.
Just as Copenhagen was the centre of quantum discussion a
lifetime ago, so Oxford has been the epicenter of the modern
debate, with such figures as Roger Penrose and Anton Zeilinger
fighting for single-world views, and David Deutsch, Lev Vaidman
and a host of others for many-worlds.
An independent physicist living in Oxford, Bruce has had a
ringside seat to the debate. In his capable hands, we understand
why the initially fantastic sounding many-worlds view is not only
a useful way to look at things, but logically compelling.
Parallel worlds are as real as the distant galaxies detected by
the Hubble Space Telescope, even though the evidence for their
existence may consist only of a few photons.
Review
"To the average reader trying to understand current theories
of the subatomic quantum world, terms like nonlocality,
decoherence and quantum collapse must sound like fantastical
notions tossed about at an ivory-tower tea party. British
physicist Bruce attempts to put into plain English what
physicists, especially those based in Oxford, think is happening
in this invisible world that binds the universe together. ...
Bruce illustrates these mind-altering concepts via accessible
stories and illustrations."
-- Publishers Weekly, October 18
"Schrodinger's Rabbits made me feel less bad for never
having understood quantum physics. Excellent for broadening the
mind of the non-expert; valuable psychotherapy for the confused
physicist."
-- Joao Magueijo, author of Faster Than the Speed of Light
"A lucid and vivid exposition of a murky subject which
famously confuses even professional physicists."
-- A. Zee, author of Einstein's Universe and Fearful Symmetry
"Bruce's witty, fast-paced account of current controversies
in quantum physics will keep you on the edge of your seat. An
eloquent introduction to one of the deepest mysteries in modern
science."
-- Paul Halpern, author of The Great Beyond: Higher Dimensions,
Parallel Universes and the Extraordinary Search for a Theory of
Everything
"Mr. Bruce is our expert tour guide on a wild, thought-provoking
ride through the Twilight Zone world of quantum theory, where
objects can be two places at the same time, disappear and
reappear somewhere else, and exist simultaneously in many
parallel universes."
-- Michio Kaku, author of Hyperspace, Parallel Worlds, and
Einstein's Cosmos
(Pure and Applied Mathematics, Volume 142)
ISBN: 0-12-088409-7 Book/Hardback
Measurements: 9 15/16 X 5 in Pages: 708
Presentation of many new results in one place for the first time.
First time coverage of skew-orthogonal and bi-orthogonal
polynomials and their use in the evaluation of some multiple
integrals.
Fredholm determinants and Painleve equations.
The three Gaussian ensembles (unitary, orthogonal, and symplectic);
their n-point correlations, spacing probabilities.
Fredholm determinants and inverse scattering theory.
Probability densities of random determinants.
Description
This book gives a coherent and detailed description of analytical
methods devised to study random matrices. Given the distribution
of matrix elements satisfying certain symmetry conditions, the
problem is to find the distribution of quantities depending on a
few of its eigenvalues. The passage from matrix elements to all
the eigenvalues is simpler than that from all the eigenvalues to
a few of them. To achieve this purpose one introduces two kinds
of skew-orthogonal polynomials and the method of integration over
alternate variables. In the limit of large matrices one is led to
the theory of integral equations and non-linear differential
equations. All this is relevent to describe nuclear excitations,
ultra-sonic resonances of structural materials, spectra of
chaotic systems, zeros of Riemann and other zeta functions and in
general, the characteristic energies of any sufficiently
complicated system. The same mathematiical tools can be hopefully
applied in the study of stationary random processes.
Since the publication of the second editiion of Random Matrices
in 1991, an old result has been better appreciated and many new
ones have emerged. This revised and enlarged edition reflects
these developements. For example, the theory of skew-orthogoanl
and bi-orthogonal polynomials, parallel to that of the widely
known and used orthogonal polynomials, is explained here for the
first time. As the new material added one may list the intimate
relations among the three classic ensembles (orthogonal, unitary
and symplectic), power series expansions of the spacing
functions, use fo non-linear differential equations to deduce
power series and asymptotic expansions surpassing the previously
used inverse scattering method, statistical properties of
Gaussian real matrices without symmetry, correlations for
Hermitian matrices coupled in a chain, probability density of the
determinants of matrices taken from various matrix ensembles, and
the relatiion between random permutations to the so called
unitary ensembles, circular or Gaussian.
Contents
This book gives a coherent and detailed description of analytical
methods devised to study random matrices. Given the distribution
of matrix elements satisfying certain symmetry conditions, the
problem is to find the distribution of quantities depending on a
few of its eigenvalues. The passage from matrix elements to all
the eigenvalues is simpler than that from all the eigenvalues to
a few of them. To achieve this purpose one introduces two kinds
of skew-orthogonal polynomials and the method of integration over
alternate variables. In the limit of large matrices one is led to
the theory of integral equations and non-linear differential
equations. All this is relevent to describe nuclear excitations,
ultra-sonic resonances of structural materials, spectra of
chaotic systems, zeros of Riemann and other zeta functions and in
general, the characteristic energies of any sufficiently
complicated system. The same mathematiical tools can be hopefully
applied in the study of stationary random processes.
Since the publication of the second editiion of Random Matrices
in 1991, an old result has been better appreciated and many new
ones have emerged. This revised and enlarged edition reflects
these developements. For example, the theory of skew-orthogoanl
and bi-orthogonal polynomials, parallel to that of the widely
known and used orthogonal polynomials, is explained here for the
first time. As the new material added one may list the intimate
relations among the three classic ensembles (orthogonal, unitary
and symplectic), power series expansions of the spacing
functions, use fo non-linear differential equations to deduce
power series and asymptotic expansions surpassing the previously
used inverse scattering method, statistical properties of
Gaussian real matrices without symmetry, correlations for
Hermitian matrices coupled in a chain, probability density of the
determinants of matrices taken from various matrix ensembles, and
the relatiion between random permutations to the so called
unitary ensembles, circular or Gaussian.
2004, XII, 202 p., Softcover
ISBN: 3-7643-4292-7
About this book
This book examines results on transfinite graphs and networks
achieved through research over the past several years. Two
initial chapters present preliminary theory, summarizing all
essential ideas needed. Subsequent chapters are devoted entirely
to novel results and cover: Connectedness ideas and their
relationship to hypergraphs ? Distance ideas and their extension
to transfinite graphs with more complications, such as the
replacement of natural-number distances by ordinal-number
distances ? Nontransitivity of path-based connectedness
alleviated by replacing paths with walks, leading to a more
powerful theory for transfinite graphs and networks ? The use of
nonstandard analysis in novel ways that leads to several entirely
new results concerning hyperreal operating points; this use of
hyperreals encompasses for the first time transfinite networks
and transmission lines containing inductances and capacitances,
in addition to resistances. The book will appeal to diverse
readers, including graduate students, electrical engineers,
mathematicians, and physicists. Moreover, the growing and
presently substantial number of mathematicians working in
nonstandard analysis may well be attracted by the novel
application of the analysis employed in the work.
Table of contents
Preface * Some Preliminaries * Transfinite Graphs *
Connectedness, Trees, and Hypergraphs * Ordinal Distances in
Transfinite Graphs * Walk-Based Transfinite Graphs and Networks *
Hyperreal Currents and Voltages in Transfinite Networks *
Hyperreal Transients in Transfinite RLC Networks * Nonstandard
Graphs and Networks * Appendix A: Some Elements of Nonstandard
Analysis * Appendix B: The Fibonacci Numbers * Appendix C: A
Laplace Transform for an Artificial RC Cable * References * Index
2004, Approx. 468 p., Softcover
ISBN: 3-7643-7153-6
October 2004
About this textbook
This book is the first of a three volume introduction to analysis.
It is distinguished by its modern and clear presentation,
concentrating always on the essential concepts. In contrast to
most other textbooks, there is no artificial separation between
the theories of one variable and that of many variables. Emphasis
is placed on the early development of a solid foundation in
topology. As well, the basics of complex analysis are covered.
"This textbook provides an outstanding introduction to
analysis. It is distinguished by its high level of presentation
and its focus on the essential." Zeitschrift fur Analysis
und ihre Anwendung 18 (1999), No. 4 (G. Berger, review of the
first German edition) "One advantage of this presentation is
that the power of the abstract concepts are convincingly
demonstrated using concrete applications." W. Grolz, review
of the first German edition
Table of contents
Preface.- Basics.- Convergence.- Continuous Functions.- Calculus
in One Variable.- Sequences of Functions.- Bibliography.- Index
Series : Progress in Nonlinear Differential Equations and
Their Applications , Vol. 57
2004, VIII, 144 p. 16 illus., Softcover
ISBN: 0-8176-3781-8
About this book
This work is devoted to the motion of surfaces for which the
normal velocity at every point is given by the mean curvature at
that point; this geometric heat flow process is called mean
curvature flow. Mean curvature flow and related geometric
evolution equations are important tools in mathematics and
mathematical physics. A major example is Hamilton's Ricci flow
program, which has the aim of settling Thurston's geometrization
conjecture, with recent major progress due to Perelman. Another
important application of a curvature flow process is the
resolution of the famous Penrose conjecture in general relativity
by Huisken and Ilmanen. Under mean curvature flow, surfaces
usually develop singularities in finite time. This work presents
techniques for the study of singularities of mean curvature flow
and is largely based on the work of K. Brakke, although more
recent developments are incorporated.
Table of contents
Preface.- Introduction.- Special Solutions and Global Behaviour.-
Local Estimates via the Maximum Principle.- Integral Estimates
and Monotonicity Formulas.- Regularity Theory at the First
Singular Time.- A Geometry of Hypersurfaces.- Derivation of the
Evolution Equations.- Background on Geometric Measure Theory.-
Local Results for Minimal Hypersurfaces.- Remarks on Brakke's
Clearing Out Lemma.- Local Monotonicity in Closed Form.-
Bibliography.- Index.