Conical Intersections in Physics: An Introduction to Synthetic Gauge Theories (Lecture Notes in Physics (965))

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
		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
		3.3.1 Spontaneous Breaking of Molecular Symmetry: The Jahn–Teller Theorem
		3.3.2 The E ε JT Model
	3.4 Dynamical Manifestation of Conical Intersections
	References
4 Conical Intersections in Condensed Matter Physics
	4.1 Band Theory
		4.1.1 Bloch's Theorem
		4.1.2 Tight-Binding Model
		4.1.3 Bloch and Wannier Functions
		4.1.4 Single Particle Lattice Models and Bloch Hamiltonians
		4.1.5 Symmetries
			4.1.5.1 Time-Reversal Symmetry
			4.1.5.2 Particle-Hole Symmetry
			4.1.5.3 Chiral Symmetry
		4.1.6 Topological Invariant
			4.1.6.1 Geometric Phase Revisited
			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
		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
		6.1.1 The Jaynes–Cummings and Quantum Rabi Models
		6.1.2 The Intrinsic Anomalous Hall Effect in Cavity QED
	6.2 Trapped Ions
	6.3 Classical Optics
	6.4 Open Quantum Systems
		6.4.1 The Lindblad Master Equation
		6.4.2 Exceptional Points
	References
A Identical Particles
	A.1 Second Quantisation
	A.2 Peierls Substitution
		A.2.1 Hofstadter Butterfly
	References
Index