The Geometric Phase in Quantum Systems: Foundations, Mathematical Concepts, and Applications in Molecular and Condensed Matter Physics

ISBN-13: 9783642055041 / Angielski / Miękka / 2010 / 427 str.

Arno Bohm; Ali Mostafazadeh; Hiroyasu Koizumi

Opis

Aimed at graduate physics and chemistry students, this is the first comprehensive monograph covering the concept of the geometric phase in quantum physics from its mathematical foundations to its physical applications and experimental manifestations. It contains all the premises of the adiabatic Berry phase as well as the exact Anandan-Aharonov phase. It discusses quantum systems in a classical time-independent environment (time dependent Hamiltonians) and quantum systems in a changing environment (gauge theory of molecular physics). The mathematical methods used are a combination of differential geometry and the theory of linear operators in Hilbert Space. As a result, the monograph demonstrates how non-trivial gauge theories naturally arise and how the consequences can be experimentally observed. Readers benefit by gaining a deep understanding of the long-ignored gauge theoretic effects of quantum mechanics and how to measure them.

Recenzje

From the reviews:

"[...] the present book is a modern presentation of the subject that takes the rich developments over recent decades, to which the authors contributed significantly, into account. [...] Overall it is a well written book that enjoys its uniqueness as a textbook in its field." (J.Pachos, Contemporary Physics 2004, vol. 45, page 273)

"The book is oriented to advanced undergraduate and graduate students in physics and chemistry but the clarity of exposition makes it accessible to much larger audience." (Zentralblatt MATH 2004, vol. 1039, page 54)

"The aim of this book is to systematically present the geometric phase, which can be regarded as one of the major discoveries of 20th century physics, in order to help readers to better understand the richness of the quantum world. ... this is a very interesting book, which deserves to be found in any physical library. This is the first book to be dedicated to the geometric phase ... ." (Daniela Dragoman, Optics & Photonics News, Vol. 16 (7-8), July/August, 2005)

"The book covers a very wide territory, showing in a convincing way the huge range of applicability of geometric phases. The mathematical treatment is clear and essentially correct ... and thus highlights the effectiveness of geometrical methods in quantum physics. Altogether, we have here a book that fills a conspicuous gap in the literature, and it does it rather well. Thus it can be recommended to physicists and chemists with a taste for new tools, and, of course, for physics departments libraries." (Jean-Pierre Antoine, Physicalia, Vol. 57 (3), 2005)

"I am pleased to introduce The Geometrical Phase in Quantum Systems ... which is the first book on this popular research subject in theoretical and experimental physics. ... Undoubtedly, the present book is a modern presentation of the subject that takes the rich developments over recent decades, to which the authors contributed significantly, into account. ... Overall it is a well written book that enjoys its uniqueness as a textbook in its field." (J. Pachos, Contemporary Physics, Vol. 45 (3), 2004)

"The exposition is uniform in depth and level and well balanced regarding exposition of mathematical and physical ideas and concepts. ... The book is oriented to advanced undergraduate and graduate students in physics and chemistry but the clarity of exposition makes it accessible to much larger audience. ... being the first comprehensive book on the subject it should be recognized as a quite valuable addition to the Springer Text and Monographs in Physics series in particular and mathematical physics literature in general." (Ivailo Mladenov, Zentralblatt MATH, Vol. 1039 (8), 2004)

Spis treści

1. Introduction.- 2. Quantal Phase Factors for Adiabatic Changes.- 3. Spinning Quantum System in an External Magnetic Field.- 4. Quantal Phases for General Cyclic Evolution.- 5. Fiber Bundles and Gauge Theories.- 6. Mathematical Structure of the Geometric Phase I: The Abelian Phase.- 7. Mathematical Structure of the Geometric Phase II: The Non-Abelian Phase.- 8. A Quantum Physical System in a Quantum Environment — The Gauge Theory of Molecular Physics.- 9. Crossing of Potential Energy Surfaces and the Molecular Aharonov-Bohm Effect.- 10. Experimental Detection of Geometric Phases I: Quantum Systems in Classical Environments.- 11. Experimental Detection of Geometric Phases II: Quantum Systems in Quantum Environments.- 12. Geometric Phase in Condensed Matter I: Bloch Bands.- 13. Geometric Phase in Condensed Matter II: The Quantum Hall Effect.- 14. Geometric Phase in Condensed Matter III: Many-Body Systems.- A. An Elementary Introduction to Manifolds and Lie Groups.- B. A Brief Review of Point Groups of Molecules with Application to Jahn-Teller Systems.- References.

O autorze

Intended for graduate physics and chemistry students, this is the first comprehensive monograph covering the concept of the geometric phase in quantum physics, from its mathematical foundations to its physical applications and experimental manifestations. It contains all the premises of the adiabatic Berry phase as well as the exact Anandan-Aharonov phase. It discusses quantum systems in a classical time-independent environment (time dependent Hamiltonians) and quantum systems in a changing environment (gauge theory of molecular physics). The mathematical methods used are a combination of differential geometry and the theory of linear operators in Hilbert Space. As a result, the monograph demonstrates how non-trivial gauge theories naturally arise and how the consequences can be experimentally observed. Readers benefit by gaining a deep understanding of the long-ignored gauge theoretic effects of quantum mechanics and how to measure them.