| Description |
1 online resource |
| Series |
Lecture notes in physics ; 965 |
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Lecture notes in physics ; 965.
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| Contents |
Intro -- Preface -- Acknowledgements -- Contents -- 1 Introduction -- References -- 2 Theory of Adiabatic Evolution -- 2.1 Introduction -- 2.2 Adiabatic Time-Evolution -- 2.2.1 Adiabatic Theorem -- 2.2.2 Adiabatic Approximation -- 2.2.3 The Marzlin-Sanders Paradox -- 2.2.4 The Importance of the Energy Gap: Local Adiabatic Quantum Search -- 2.3 Gauge Structure of Time-Dependent Adiabatic Systems -- 2.3.1 The Wilczek-Zee Holonomy -- 2.3.2 Adiabatic Evolution of a Tripod -- 2.3.3 Closing the Energy Gap: Abelian Magnetic Monopole in Adiabatic Evolution -- 2.4 Born-Oppenheimer Theory |
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2.4.1 Synthetic Gauge Structure of Born-OppenheimerTheory -- 2.4.2 Adiabatic Versus Diabatic Representations -- 2.4.3 Born-Oppenheimer Approximation -- 2.4.4 Synthetic Gauge Structure of an Atom in an Inhomogeneous Magnetic Field -- References -- 3 Conical Intersections in Molecular Physics -- 3.1 Introduction -- 3.2 Where Electronic Adiabatic Potential Surfaces Cross: Intersection Points -- 3.2.1 The Existence of Intersections -- 3.2.2 Topological Tests for Intersections -- 3.2.3 The Molecular Aharonov-Bohm Effect on the Nuclear Motion -- 3.3 The Jahn-Teller Effect |
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4.1.6.2 Chern and Winding Numbers -- 4.2 Spin-Orbit Couplings -- 4.2.1 Rashba and Dresselhaus Spin-Orbit Couplings -- 4.2.2 Intrinsic Spin Hall Effect -- 4.3 Superconductors -- 4.4 Graphene -- 4.4.1 Tight-Binding Band Spectrum -- 4.4.2 Relativity at Almost ̀Zero' -- 4.4.3 The Haldane Model -- 4.5 Weyl Semimetals -- References -- 5 Conical Intersections in Cold Atom Physics -- 5.1 Introduction -- 5.2 Light-Matter Interactions and Optical Forces -- 5.3 Adiabatic Dynamics and Synthetic Gauge Potentials -- 5.3.1 The Adiabatic Principle and Dressed States |
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5.3.2 A Pedagogical Example: The Two-Level System -- 5.4 Spin-Orbit Coupling and Non-Abelian Phenomena -- 5.4.1 Spectrum -- 5.4.2 A Quasi-Relativistic Example: The AtomicZitterbewegung -- 5.4.2.1 The Dirac Limit -- 5.4.2.2 Zitterbewegung -- 5.4.2.3 Dark State Dynamics -- 5.4.2.4 Exact Solutions in the Schrödinger Limit -- 5.5 Cold Atoms and the Bose-Einstein Condensate -- 5.5.1 The Description of a Condensate -- 5.5.2 Conical Intersections and the Gross-Pitaevskii Equation -- References -- 6 Conical Intersections in Other Physical Systems -- 6.1 Cavity Quantum Electrodynamics |
| Summary |
This concise book introduces and discusses the basic theory of conical intersections with applications in atomic, molecular and condensed matter physics. Conical intersections are linked to the energy of quantum systems. They can occur in any physical system characterized by both slow and fast degrees of freedom - such as e.g. the fast electrons and slow nuclei of a vibrating and rotating molecule - and are important when studying the evolution of quantum systems controlled by classical parameters. Furthermore, they play a relevant role for understanding the topological properties of condensed matter systems. Conical intersections are associated with many interesting features, such as a breakdown of the Born-Oppenheimer approximation and the appearance of nontrivial artificial gauge structures, similar to the Aharonov-Bohm effect. Some applications presented in this book include - Molecular Systems: some molecules in nonlinear nuclear configurations undergo Jahn-Teller distortions under which the molecule lower their symmetry if the electronic states belong to a degenerate irreducible representation of the molecular point group. - Solid State Physics: different types of Berry phases associated with conical intersections can be used to detect topologically nontrivial states of matter, such as topological insulators, Weyl semi-metals, as well as Majorana fermions in superconductors. - Cold Atoms: the motion of cold atoms in slowly varying inhomogeneous laser fields is governed by artificial gauge fields that arise when averaging over the fast internal degrees of freedom of the atoms. These gauge fields can be Abelian or non-Abelian, which opens up the possibility to create analogs to various relativistic effects at low speed |
| Bibliography |
Includes bibliographical references and index |
| Subject |
Gauge fields (Physics)
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Gauge fields (Physics)
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| Form |
Electronic book
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| Author |
Sjöqvist, Erik
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Öhberg, Patrik
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| ISBN |
9783030348823 |
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3030348822 |
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