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

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Springer Science & Business Media, Nov 11, 2013 - Science - 427 pages
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.
 

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Contents

Introduction
1
Geometric Phase in Condensed Matter
3
Spinning Quantum System in an External Magnetic Field
31
Quantal Phases for General Cyclic Evolution
53
Fiber Bundles and Gauge Theories
65
Mathematical Structure of the Geometric Phase
107
Problems
126
5
141
Experimental Detection of Geometric Phases
225
Quantum Systems in Quantum Environments
255
Bloch Bands 277
276
Problems
299
A An Elementary Introduction to Manifolds and Lie Groups 361
360
B A Brief Review of Point Groups of Molecules
407
References 429
428
Index
437

Problems
191

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