Vlatko Vedral

Introduction to Quantum Information Science

(Hardback)
ISBN-10: 0-19-921570-7
Estimated publication date: September 2006
196 pages, 30 line drawings, 246x171 mm
Series: Oxford Graduate Texts

Description

A modern introduction to quantum information with emphasis on quantum entanglement.
Discusses the physics behind introduced concepts at great length and favours this to mathematical formalism.
Covers a number of non-standard topics, such as Maxwell's demon, Landauer's erasure, the Bekenstein bound and Caratheodory's view of the Second Law of thermodynamics.
Includes an explanation of the basic rules of quantum mechanics as well as the more advanced topics of mixed states and completely positive maps.
Includes an introduction to classical information theory.

This book offers a concise and up-to-date introduction to the popular field of quantum information. It has originated in a series of invited lecture courses at various universities in different countries. This is reflected in its informal style of exposition and presentation of key results in the subject. In addition to treating quantum communication, entanglement and algorithms in great depth, this book also addresses a number of interesting miscellaneous topics, such as Maxwell's demon, Landauer's erasure, the Bekenstein bound and Caratheodory's treatment of the Second law of thermodyanmics. All mathematical derivations are based on clear physical pictures which make even the most involved results - such as the Holevo bound - look comprehensible and transparent. The book is ideal as a first introduction to the subject, but may also appeal to the specialist due to its unique presentation.

Readership: Graduates and professionals in physics, mathematics, computer science and engineering.

Contents

1. Classical Information
2. Quantum Mechanics
3. Quantum Information - The Basics
4. Quantum Communication with Entanglement
5. Quantum Information I
6. Quantum Information II
7. Quantum Entanglement - Introduction
8. Witnessing Quantum Entanglement
9. Quantum Entanglement Detection in Practice
10. Measures of Entanglement
11. Quantum Algorithms
12. Entanglement, Computation and Quantum Measurement
13. Quantum Error Correction
14. Outlook

Sylvie Benzoni-Gavage and Denis Serre

Multi-dimensional hyperbolic partial differential equations
First-order systems and applications

(Hardback)
ISBN-10: 0-19-921123-X
Estimated publication date: November 2006
512 pages, 234x156 mm
Series: Oxford Mathematical Monographs

Description

Authored by leading academics
Comprehensive, self-contained work
Adopts an original approach, presents new results, and fills gaps in proofs of important theorems
Extensive bibliography, including classical and recent papers in both PDE analysis and in applications (mainly to gas dynamics)

Authored by leading scholars, this comprehensive, self-contained text presents a view of the state of the art in multi-dimensional hyperbolic partial differential equations, with a particular emphasis on problems in which modern tools of analysis have proved useful. Ordered in sections of gradually increasing degrees of difficulty, the text first covers linear Cauchy problems and linear initial boundary value problems, before moving on to nonlinear problems, including shock waves. The book finishes with a discussion of the application of hyperbolic PDEs to gas dynamics, culminating with the shock wave analysis for real fluids.

With an extensive bibliography including classical and recent papers both in PDE analysis and in applications (mainly to gas dynamics), this text will be valuable to graduates and researchers in both hyperbolic PDEs and compressible fluid dynamics.

Readership: Graduates and researchers in Applied Mathematics

Contents

Preface
Introduction
Notations
The linear Cauchy problem

1. Linear Cauchy problem with constant coefficients
2. Linear Cauchy problem with variable coefficients
The linear initial boundary value problem

3. Friedrichs symmetric dissipative IBVPs
4. Initial boundary value problem in a half-space with constant coefficients
5. Construction of a symmetrizer under (UKL)
6. The characteristic IBVP
7. The homogeneous IBVP
8. A classification of linear IBVPs
9. Variable coefficients initial boundary value problems
Nonlinear problems

10. The Cauchy problem for quasilinear systems
11. The mixed problem for quasilinear systems
12. Persistence of multidimensional shocks
Applications to gas dynamics

13. The Euler equations for real fluids
14. Boundary conditions for Euler equations
15. Shock stability in gas dynamics
Appendix

A. Basic calculus results
B. Fourier and Laplace analysis
C. Pseudo/para-differential calculus
Bibliography
Index

Alastair Fletcher and Vladimir Markovic

Quasiconformal Maps and Teichmuller Theory

(Hardback)
ISBN-10: 0-19-856926-2
Estimated publication date: January 2007
352 pages, 18 black and white line drawings, 234x156 mm
Series: Oxford Graduate Texts in Mathematics number 11

Description

An up-to-date coverage of this topical yet classical area
Vladimir Markovic is an outstanding mathematician with an excellent research reputation
Examples and exercises are given throughout to clarify the text

Based on a series of graduate lectures given by Vladimir Markovic at the University of Warwick in spring 2003, this book is accessible to those with a grounding in complex analysis looking for an introduction to the theory of quasiconformal maps and Teichmuller theory. Assuming some familiarity with Riemann surfaces and hyperbolic geometry, topics covered include the Grotzch argument, analytical properties of quasiconformal maps, the Beltrami differential equation, holomorphic motions and Teichmuller spaces. Where proofs are omitted, references to where they may be found are always given, and the text is clearly illustrated throughout with diagrams, examples, and exercises for the reader.

Readership: Graduates and researchers in Pure Mathematics

Contents

Preface
1. The Grotzch argument
2. Geometric definition of quasiconformal maps
3. Analytic properties of quasiconformal maps
4. Quasi-isometries and quasisymmetric maps
5. The Beltrami differential equation
6. Holomorphic motions and applications
7. Teichmuller spaces
8. Extremal quasiconformal mappings
9. Unique extremality
10. Isomorphisms of Teichmuller space
11. Local rigidity of Teichmuller spaces
References
Index

Edited by Geoffrey Grimmett and Colin McDiarmid

Combinatorics, Complexity, and Chance
A Tribute to Dominic Welsh

(Hardback)
ISBN-10: 0-19-857127-5
Estimated publication date: January 2007
320 pages, b/w photo, 37 b/w line drawings, 234x156 mm
Series: Oxford Lecture Series in Mathematics and Its Applications number 34

Description

A fitting tribute to the influential Oxford academic, Professor Dominic Welsh, on his retirement
Contains original articles from notable academics in the field
Provides clear accounts of important areas in combinatorics and discrete probability

Professor Dominic Welsh has made significant contributions to the fields of combinatorics and discrete probability, including matroids, complexity, and percolation, and has taught, influenced and inspired generations of students and researchers in mathematics. This volume summarises and reviews the consistent themes from his work through a series of articles written by renowned experts. These articles contain original research work, set in a broader context by the inclusion of review material. As a reference text in its own right, this book will be valuable to academic researchers, research students, and others seeking an introduction to the relevant contemporary aspects of these fields.

Readership: Graduates and researchers in probability and combinatorics

Contents

Preface
1. Orbit counting and the Tutte polynomial , Peter Cameron
2. Eulerian and bipartite orientable matroids , Laura Chavez Lomeli and L.A. Goddyn
3. Tutte-Whitney polynomials: some history and generalisations , Graham Farr
4. A survey on the use of Markov chains to randomly sample colorings , Alan Frieze and Eric Vigoda
5. Towards a matroid-minor structure theory , Jim Geelen, Bert Gerards, Geoff Whittle
6. Random planar graphs with a fixed number of edges , Stefanie Gerke, Colin McDiarmid, Angelika Steger, Andreas Weissl
7. Fourier analysis on finite Abelian groups: some graphical applications , Andrew Goodall
8. Flows and ferromagnets , Geoffrey Grimmett
9. Approximating the Tutte polynomial , Mark Jerrum
10. Non-separating circuits and cocircuits in matroids , Braulio Maia Junior, Manoel Lemos, T.R.B. Melo
11. Expanding the Tutte polynomial of a matroid over the independent sets , Koko Kalambay Kayibi
12. Connection matrices , Laszlo Lovasz
13. Complexity of graph polynomials , Steven Noble
14. Random planar graphs and the number of planar graphs , Marc Noy
15. The contributions of Dominic Welsh to matroid theory , James Oxley
16. On the unknotting problem , J.L. Ramirez Alfonsin
17. Advances on the Erdos-Faber-Lovasz conjecture , David Romero, Abdon Sanchez-Arroyo
18. Stochastic set-backs , David Stirzaker

Loebl, Martin

Discrete Mathematics in Statistical Physics
Introductory Lectures

Advanced Lectures in Mathematics

2006. Approx. 240 pp. Softc.
ISBN: 3-528-03219-7

The book first describes connections between some basic problems and technics of combinatorics and statistical physics. The discrete mathematics and physics terminology are related to each other. Using the established connections, some exciting activities in one field are shown from a perspective of the other field. The purpose of the book is to emphasize these interactions as a strong and successful tool. In fact, this attitude has been a strong trend in both research communities recently.
It also naturally leads to many open problems, some of which seem to be basic. Hopefully, this book will help making these exciting problems attractive to further students and researchers.