PUBLICATION PLANNED FOR: March 2020AVAILABILITY: Not yet published -
PaperbackISBN: 9781107656147
Quantum information theory is a branch of science at the frontier of physics, mathematics, and information science, and offers a variety of solutions that are impossible using classical theory. This book provides a detailed introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory. The second edition contains new sections and entirely new chapters: the hot topic of multipartite entanglement; in-depth discussion of the discrete structures in finite dimensional Hilbert space, including unitary operator bases, mutually unbiased bases, symmetric informationally complete generalized measurements, discrete Wigner function, and unitary designs; the Gleason and Kochen?Specker theorems; the proof of the Lieb conjecture; the measure concentration phenomenon; and the Hastings' non-additivity theorem. This richly-illustrated book will be useful to a broad audience of graduates and researchers interested in quantum information theory. Exercises follow each chapter, with hints and answers supplied.
'True story: A few years ago my daughter took a break from her usual question, 'Dad, what is your favourite colour?' and asked instead, 'What is your favourite shape?' I was floored! 'What a wonderful question; my favourite shape is Hilbert space!' 'What does it look like?' she asked. My answer: 'I don't know! But every day when I go to work, that's what I think about.' What I was speaking of, of course, is the geometry of quantum-state space. It is as much a mystery today as it was those years ago, and maybe more so as we learn to focus on its most key and mysterious features. This book, the worn first-edition of which I've had on my shelf for 11 years, is the indispensable companion for anyone's journey into that exotic terrain. Beyond all else, I am thrilled about the inclusion of two new chapters in the new edition, one of which I believe goes to the very heart of the meaning of quantum theory.' Christopher A. Fuchs, University of Massachusetts, Boston
'The quantum world is full of surprises as is the mathematical theory that describes it. Bengtsson and ?yczkowski prove to be expert guides to the deep mathematical structure that underpins quantum information science. Key concepts such as multipartite entanglement and quantum contextuality are discussed with extraordinary clarity. A particular feature of this new edition is the treatment of SIC generalised measurements and the curious bridge they make between quantum physics and number theory.' Gerard J. Milburn, University of Queensland
Praise for the first edition: 'Geometry of Quantum States can be considered an indispensable item on a bookshelf of everyone interest in quantum information theory and its mathematical background.' Mi?osz Michalski, editor of Open Systems and Information Dynamics
Praise for the first edition: 'Bengtsson's and Zyczkowski's book is an artful presentation of the geometry that lies behind quantum theory … the authors collect, and artfully explain, many important results scattered throughout the literature on mathematical physics. The careful explication of statistical distinguishability metrics (Fubini-Study and Bures) is the best I have read.' Gerard Milburn, University of Queensland
Preface
1. Convexity, colours, and statistics
2. Geometry of probability distributions
3. Much ado about spheres
4. Complex projective spaces
5. Outline of quantum mechanics
6. Coherent states and group actions
7. The stellar representation
8. The space of density matrices
9. Purification of mixed quantum states
10. Quantum operations
11. Duality: maps versus states
12. Discrete structures in Hilbert space
13. Density matrices and entropies
14. Distinguishability measures
15. Monotone metrics and measures
16. Quantum entanglement
17. Multipartite entanglement
Appendix 1. Basic notions of differential geometry
Appendix 2. Basic notions of group theory
Appendix 3. Geometry ? do it yourself
Appendix 4. Hints and answers to the exercises
Bibliography
Index.
Part of Cambridge Monographs on Mathematical Physics
PUBLICATION PLANNED FOR: November 2020 - available from November 2020
FORMAT: HardbackISBN: 9781108492683
Tau functions are a central tool in the modern theory of integrable systems. This volume provides a thorough introduction, starting from the basics and extending to recent research results. It covers a wide range of applications, including generating functions for solutions of integrable hierarchies, correlation functions in the spectral theory of random matrices and combinatorial generating functions for enumerative geometrical and topological invariants. A self-contained summary of more advanced topics needed to understand the material is provided, as are solutions and hints for the various exercises and problems that are included throughout the text to enrich the subject matter and engage the reader. Building on knowledge of standard topics in undergraduate mathematics and basic concepts and methods of classical and quantum mechanics, this monograph is ideal for graduate students and researchers who wish to become acquainted with the full range of applications of the theory of tau functions.
Preface
List of symbols
1. Examples
2. KP flows and the Sato-Segal-Wilson Grassmannian
3. The KP hierarchy and its standard reductions
4. Infinite dimensional Grassmannians
5. Fermionic representation of tau functions and Baker functions
6. Finite dimensional reductions of the infinite Grassmannian and their associated tau functions
7. Other related integrable hierarchies
8. Convolution symmetries
9. Isomonodromic deformations
10. Integrable integral operators and dual isomonodromic deformations
11. Random matrix models I. Partition functions and correlators
12. Random matrix models II. Level spacings
13. Generating functions for characters, intersection indices and Brezin-Hikami matrix models
14. Generating functions for weighted Hurwitz numbers: enumeration of branched coverings
Appendix A. Integer partitions
Appendix B. Determinantal and Pfaffian identities
Appendix C. Grassmann manifolds and flag manifolds
Appendix D. Symmetric functions
Appendix E. Finite dimensional fermions: Clifford and Grassmann algebras, spinors, isotropic Grassmannians
Appendix F. Riemann surfaces, holomorphic differentials and theta functions
Appendix G. Orthogonal polynomials
Appendix H. Solutions of selected exercises
References
Alphabetical Index.
Part of Cambridge Texts in Applied Mathematics
PUBLICATION PLANNED FOR: September 2020- available from September 2020
FORMAT: HardbackISBN: 9781107174658
Fluid dynamics plays a crucial role in many cellular processes, including the locomotion of cells such as bacteria and spermatozoa. These organisms possess flagella, slender organelles whose time periodic motion in a fluid environment gives rise to motility. Sitting at the intersection of applied mathematics, physics and biology, the fluid dynamics of cell motility is one of the most successful applications of mathematical tools to the understanding of the biological world. Based on courses taught over several years, it details the mathematical modelling necessary to understand cell motility in fluids, covering phenomena ranging from single-cell motion to instabilities in cell populations. Each chapter introduces mathematical models to rationalise experiments, uses physical intuition to interpret mathematical results, highlights the history of the field and discusses notable current research questions. All mathematical derivations are included for students new to the field, and end-of-chapter exercises help consolidate understanding and practise applying the concepts.
Part I. Fundamentals:
1. Biological background
2. The fluid dynamics of microscopic locomotion
3. The waving sheet model
4. The squirmer model
Part II. Cellular locomotion:
5. Flagella and the physics of viscous propulsion
6. Hydrodynamics of slender filaments
7. Waving of eukaryotic flagella
8. Rotation of bacterial flagellar filaments
9. Flows and stresses induced by cells
Part III. Interactions:
10. Swimming cells in flows
11. Self-propulsion and surfaces
12. Hydrodynamic synchronisation
13. Diffusion and noisy swimming
14. Hydrodynamics of collective locomotion
15. Locomotion and transport in complex fluids
References
Index.
Published November 4, 2019
Reference - 1000 Pages
ISBN 9780367398941 - CAT# K449407
A study of difference equations and inequalities. This second edition offers real-world examples and uses of difference equations in probability theory, queuing and statistical problems, stochastic time series, combinatorial analysis, number theory, geometry, electrical networks, quanta in radiation, genetics, economics, psychology, sociology, and other disciplines. It features 200 new problems, 400 additional references, and a new chapter on the qualitative properties of solutions of neutral difference equations.
Preliminaries; linear initial value problems; miscellaneous difference equations; difference inequalities; qualitative properties of solutions of difference systems; qualitative properties of solutions of higher order difference equations; qualitative properties of solutions of neutral difference equations; boundary value problems for linear systems; boundary value problems for nonlinear systems; miscellaneous properties of solutions of higher order linear difference equations; boundary value problems for higher order difference equations; Sturm-Liouville problems and related inequalities; difference inequalities in several independent variables.
March 12, 2020 Forthcoming
Textbook - 646 Pages
ISBN 9781138599499 - CAT# K387776
Series: Chapman & Hall/CRC Texts in Statistical Science
Statistical Analysis of Financial Data covers the use of statistical analysis and the methods of data science to model and analyze financial data. The first chapter is an overview of financial markets, describing the market operations and using exploratory data analysis to illustrate the nature of financial data. The software used to obtain the data for the examples in the first chapter and for all computations and to produce the graphs is R. However discussion of R is deferred to an appendix to the first chapter, where the basics of R, especially those most relevant in financial applications, are presented and illustrated. The appendix also describes how to use R to obtain current financial data from the internet.
Chapter 2 describes the methods of exploratory data analysis, especially graphical methods, and illustrates them on real financial data. Chapter 3 covers probability distributions useful in financial analysis, especially heavy-tailed distributions, and describes methods of computer simulation of financial data. Chapter 4 covers basic methods of statistical inference, especially the use of linear models in analysis, and Chapter 5 describes methods of time series with special emphasis on models and methods applicable to analysis of financial data.
* Covers statistical methods for analyzing models appropriate for financial data, especially models with outliers or heavy-tailed distributions.
* Describes both the basics of R and advanced techniques useful in financial data analysis.
* Driven by real, current financial data, not just stale data deposited on some static website.
* Includes a large number of exercises, many requiring the use of open-source software to acquire real financial data from the internet and to analyze it.