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Cover: 9783540000310 | The Geometric Phase in Quantum Systems | Arno Bohm (u. a.) | Buch
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The Geometric Phase in Quantum Systems
Foundations, Mathematical Concepts, and Applications in Molecular and Condensed Matter Physics
Buch von Arno Bohm (u. a.)
Sprache: Englisch

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Beschreibung
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.
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.
Zusammenfassung

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.

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2003
Fachbereich: Theoretische Physik
Genre: Physik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Theoretical and Mathematical Physics
Inhalt: xxi
427 S.
ISBN-13: 9783540000310
ISBN-10: 3540000313
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Bohm, Arno
Mostafazadeh, Ali
Zwanziger, Josef
Niu, Qian
Koizumi, Hiroyasu
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Theoretical and Mathematical Physics
Maße: 241 x 160 x 31 mm
Von/Mit: Arno Bohm (u. a.)
Erscheinungsdatum: 12.06.2003
Gewicht: 0,863 kg
Artikel-ID: 102566708
Zusammenfassung

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.

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2003
Fachbereich: Theoretische Physik
Genre: Physik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Theoretical and Mathematical Physics
Inhalt: xxi
427 S.
ISBN-13: 9783540000310
ISBN-10: 3540000313
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Bohm, Arno
Mostafazadeh, Ali
Zwanziger, Josef
Niu, Qian
Koizumi, Hiroyasu
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Theoretical and Mathematical Physics
Maße: 241 x 160 x 31 mm
Von/Mit: Arno Bohm (u. a.)
Erscheinungsdatum: 12.06.2003
Gewicht: 0,863 kg
Artikel-ID: 102566708
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