This volume contains papers by invited speakers of the symposium "Zeta Functions, Topology and Quantum Physics" held at Kinki U- versity in Osaka, Japan, during the period of March 3-6, 2003. The aims of this symposium were to establish mutual understanding and to exchange ideas among researchers working in various fields which have relation to zeta functions and zeta values. We are very happy to add this volume to the series Developments in Mathematics from Springer. In this respect, Professor Krishnaswami Alladi helped us a lot by showing his keen and enthusiastic interest in publishing this volume and by contributing his paper with Alexander Berkovich. We gratefully acknowledge financial support from Kinki University. We would like to thank Professor Megumu Munakata, Vice-Rector of Kinki University, and Professor Nobuki Kawashima, Director of School of Interdisciplinary Studies of Science and Engineering, Kinki Univ- sity, for their interest and support. We also thank John Martindale of Springer for his excellent editorial work.

Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields. The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject. The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories. Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology. The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, general relativity, and bosonic string theory. Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics. The final two chapters are devoted to the most fascinating applications of geometry and topology in contemporary physics, namely the study of anomalies in gauge field theories and the analysis of Polakov's bosonic string theory from the geometrical point of view. Geometry, Topology and Physics, Second Edition is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics.

This 1998 book describes the physics of superconductivity and superfluidity, macroscopic quantum phenomena found in many conductors at low temperatures and in liquid helium 4 and helium 3. In the first part of the book the author presents the mean field theory of generalized pair condensation. This is followed by a description of the properties of ordinary superconductors using BCS theory. The book then proceeds with expositions of strong coupling theory and the Ginzberg-Landau theory. The remarkable properties of superfluid helium 3 are then described, as an example of a superfluid with internal degrees of freedom. The topics covered are dealt with in a coherent manner, with all necessary theoretical background given. Recent topics in the field, such as the copper-oxide high temperature superconductors and exotic superconductivity of heavy fermion systems are discussed in the final chapter. This book will be of interest to graduate students and researchers in condensed matter physics, especially those working in superconductivity and superfluidity.

This book is a collection of lecture notes from the Symposium on Quantum Computing, Thermodynamics, and Statistical Physics, held at Kinki University in March 2012. Quantum information theory has a deep connection with statistical physics and thermodynamics. This volume introduces some of the topics on interface among the mentioned fields. Subjects included in the lecture notes include quantum annealing method, nonequilibrium thermodynamics and spin glass theory, among others. These subjects were presented with much emphasis put in its relevance in quantum information theory. These lecture notes are prepared in a self-contained manner so that a reader with modest background may understand the subjects.

The open research center project "Interdisciplinary fundamental research toward realization of a quantum computer" has been supported by the Ministry of Education, Japan for five years. This is a collection of the research outcomes by the members engaged in the project. To make the presentation self-contained, it starts with an overview by Mikio Nakahara, which serves as a concise introduction to quantum information and quantum computing. Subsequent contributions include subjects from physics, chemistry, mathematics, and information science, reflecting upon the wide variety of scientists working under this project. These contributions introduce NMR quantum computing and related techniques, number theory and coding theory, quantum error correction, photosynthesis, non-classical correlations and entanglement, neutral atom quantum computer, among others. Each of contributions will serve as a short introduction to these cutting edge research fields.

This book is a collection of lecture notes and contributions in "Summer School on Diversities in Quantum Computation/Information" held on 1-5 August, 2010 at U-Community Hotel, Higashi-Osaka, Japan. Lecturers are world class authorities in respective areas in quantum information and quantum computing including physics, mathematics, chemistry and information science. They lectured on cutting-edge research frontiers where they are currently working, including quantum error correction, relativistic quantum information, quantum computing of link polynomials, quantum algorithms, etc. Each lecture note is written in a self-contained manner so that it may be used as a textbook for one semester graduate course or advanced undergraduate course. Contributions report current research subjects also in a self-contained manner. We believe that these articles are accessible to the readers form various disciplines.

This book is a collection of contributions to the Symposium on Interface between Quantum Information and Statistical Physics held at Kinki University in November 2011. Subjects of the symposium include quantum adiabatic computing, quantum simulator using bosons, classical statistical physics, among others. Contributions to this book are prepared in a self-contained manner so that a reader with a modest background may understand the subjects.

This book is a collection of lecture notes/contributions from a summer school on decoherence, entanglement & entropy and a workshop on MPS (matrix product states) & DMRG (density matrix renormalization group). Subjects of the summer school include introduction to MPS, black holes, qubits and octonions, weak measurement, entanglement measures and separability, generalized Bell inequalities, among others. Subjects of the workshop are dedicated to MPS and DMRG. Applications to strongly correlated systems and integrable systems are also mentioned. Contributions to this book are prepared in a self-contained manner so that a reader with a modest background in quantum information and quantum computing may understand the subjects.

This volume provides an overview on the decoherence suppression methods in quantum computing, open quantum systems, quantum error correction and fault-tolerant quantum computing. It also includes concepts in geometric quantum computing by composite pulses. Quantum wipe effect is explained as an approach for suppressing decoherence of the system. A short contribution on the implementation of holonomic quantum gates with NMR (Nuclear Magnetic Resonance) is presented.

he lecture notes contributed to this volume are prepared in a self-contained manner hence readers with limited knowledge on the topics could understand the discussions by following the sequence of chapters which begin with mathematical frameworks and progress to the most updated outcomes of the fields. The volume will be useful for a broad audience from graduate students to researchers interested in the field .

This book provides an overview on physical realizations of quantum computing by means of molecular systems. It will be useful for graduate students and researchers interested in quantum computing from different areas of physics, physical chemistry, informatics and computer science. Each chapter is written in a self-contained manner and hence can be accessible for researchers and graduate students with even less background in the topics.

Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields. The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject. The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories. Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology. The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, general relativity, and bosonic string theory. Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics. The final two chapters are devoted to the most fascinating applications of geometry and topology in contemporary physics, namely the study of anomalies in gauge field theories and the analysis of Polakov's bosonic string theory from the geometrical point of view. Geometry, Topology and Physics, Second Edition is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics.

Der vorliegende Klassiker bietet Studierenden und Forschenden in den Gebieten der Theoretischen und Mathematischen Physik eine ideale Einfuhrung in die Differentialgeometrie und Topologie. Beides sind wichtige Werkzeuge in den Gebieten der Astrophysik, der Teilchen- und Festkoerperphysik. Das Buch fuhrt durch: - Pfadintegralmethode und Eichtheorie - Mathematische Grundlagen von Abbildungen, Vektorraumen und Topologie - Fortgeschrittene Konzepte der Geometrie und Topologie und deren Anwendungen im Bereich der Flussigkristalle, bei suprafluidem Helium, in der ART und der bosonischen Stringtheorie - Eine Zusammenfuhrung von Geometrie und Topologie: Faserbundel, charakteristische Klassen und Indextheoreme - Anwendungen von Geometrie und Topologie in der modernen Physik: Eichfeldtheorien und der Analyse der Polakov'schen bosonischen Stringtheorie aus einer geometrischen Perspektive

This volume contains papers by invited speakers of the symposium "Zeta Functions, Topology and Quantum Physics" held at Kinki U- versity in Osaka, Japan, during the period of March 3-6, 2003. The aims of this symposium were to establish mutual understanding and to exchange ideas among researchers working in various fields which have relation to zeta functions and zeta values. We are very happy to add this volume to the series Developments in Mathematics from Springer. In this respect, Professor Krishnaswami Alladi helped us a lot by showing his keen and enthusiastic interest in publishing this volume and by contributing his paper with Alexander Berkovich. We gratefully acknowledge financial support from Kinki University. We would like to thank Professor Megumu Munakata, Vice-Rector of Kinki University, and Professor Nobuki Kawashima, Director of School of Interdisciplinary Studies of Science and Engineering, Kinki Univ- sity, for their interest and support. We also thank John Martindale of Springer for his excellent editorial work.

Covering both theory and progressive experiments, Quantum Computing: From Linear Algebra to Physical Realizations explains how and why superposition and entanglement provide the enormous computational power in quantum computing. This self-contained, classroom-tested book is divided into two sections, with the first devoted to the theoretical aspects of quantum computing and the second focused on several candidates of a working quantum computer, evaluating them according to the DiVincenzo criteria. Topics in Part I Linear algebra Principles of quantum mechanics Qubit and the first application of quantum information processing-quantum key distribution Quantum gates Simple yet elucidating examples of quantum algorithms Quantum circuits that implement integral transforms Practical quantum algorithms, including Grover's database search algorithm and Shor's factorization algorithm The disturbing issue of decoherence Important examples of quantum error-correcting codes (QECC) Topics in Part II DiVincenzo criteria, which are the standards a physical system must satisfy to be a candidate as a working quantum computer Liquid state NMR, one of the well-understood physical systems Ionic and atomic qubits Several types of Josephson junction qubits The quantum dots realization of qubits Looking at the ways in which quantum computing can become reality, this book delves into enough theoretical background and experimental research to support a thorough understanding of this promising field.

This 1998 book describes the physics of superconductivity and superfluidity, macroscopic quantum phenomena found in many conductors at low temperatures and in liquid helium 4 and helium 3. In the first part of the book the author presents the mean field theory of generalized pair condensation. This is followed by a description of the properties of ordinary superconductors using BCS theory. The book then proceeds with expositions of strong coupling theory and the Ginzberg-Landau theory. The remarkable properties of superfluid helium 3 are then described, as an example of a superfluid with internal degrees of freedom. The topics covered are dealt with in a coherent manner, with all necessary theoretical background given. Recent topics in the field, such as the copper-oxide high temperature superconductors and exotic superconductivity of heavy fermion systems are discussed in the final chapter. This book will be of interest to graduate students and researchers in condensed matter physics, especially those working in superconductivity and superfluidity.

Der vorliegende Klassiker bietet Studierenden und Forschenden in den Gebieten der Theoretischen und Mathematischen Physik eine ideale Einfuhrung in die Differentialgeometrie und Topologie. Beides sind wichtige Werkzeuge in den Gebieten der Astrophysik, der Teilchen- und Festkoerperphysik. Das Buch fuhrt durch: - Pfadintegralmethode und Eichtheorie - Mathematische Grundlagen von Abbildungen, Vektorraumen und Topologie - Fortgeschrittene Konzepte der Geometrie und Topologie und deren Anwendungen im Bereich der Flussigkristalle, bei suprafluidem Helium, in der ART und der bosonischen Stringtheorie - Eine Zusammenfuhrung von Geometrie und Topologie: Faserbundel, charakteristische Klassen und Indextheoreme - Anwendungen von Geometrie und Topologie in der modernen Physik: Eichfeldtheorien und der Analyse der Polakov'schen bosonischen Stringtheorie aus einer geometrischen Perspektive