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Table of Contents
Intro; Supervisor's Foreword; Abstract; Preface; References; Publications; Acknowledgements; Contents; Symbols; Part I General Introduction; 1 Perspectives and Outline; 1.1 Frontiers of Quantum Interference; 1.2 Quantum Measurements; 1.2.1 Complex Quantum Systems and Statistics; 1.2.2 Measurements and Interpretations; 1.3 Outline; References; 2 Essentials of Quantum Theory; 2.1 Quantum Mechanics as a Probabilistic Theory*; 2.2 Quantisation*; 2.2.1 Old and New Quantum Theory*; 2.2.2 Quantum Algebra and Quantum Probability*; 2.3 Observables and States; 2.3.1 Observables; 2.3.2 States.
2.3.3 The Probabilistic Interpretation2.4 Dynamics of Quantum Systems; 2.4.1 The Heisenberg Picture; 2.4.2 The Schrödinger Picture; 2.5 Quantum Interference; 2.5.1 From Waves to Wave Functions; 2.5.2 Projections and Quantum Probability; 2.6 Scattering Systems; 2.7 Concluding Remarks; References; 3 Complex Quantum Systems and Random Matrix Theory; 3.1 Complex Systems; 3.1.1 Heuristics; 3.1.2 Complexity and Information Theory*; 3.1.3 Complexity of Quantum Dynamical Systems; 3.2 Complex Networks; 3.3 Aspects of Random Matrix Theory; 3.3.1 From Atoms and Orbits to Random Matrix Theory*
3.3.2 The Gaussian Ensembles of Random Matrix Theory3.3.3 Statistical Properties of GOE Eigenvalues; 3.3.4 Statistical Properties of GOE Eigenvectors; 3.4 Concluding Remarks; References; Part II Single-Particle Quantum Transport; 4 Efficient Transport in Closed Systems; 4.1 Introduction; 4.2 Measuring Transfer Efficiency; 4.3 Influence of Network Structures; 4.3.1 Regular Networks; 4.3.2 Random Networks; 4.4 Design Principles; 4.4.1 Centrosymmetry; 4.4.2 The Dominant Doublet; 4.5 Statistical Control; 4.5.1 Statistics of the Dominant Doublet; 4.5.2 Statistics of the Transfer Time.
4.5.3 Scaling Properties4.5.4 Numerics; 4.6 Summary and Outlook; References; 5 Scattering Approach to Efficient Transport; 5.1 Introduction; 5.2 Transfer Probability and Dwell Time; 5.3 The Two Level System; 5.3.1 The Model; 5.3.2 The Symmetric Case; 5.4 Designing the System; 5.5 Statistical Treatment; 5.5.1 The Indirect Treatment; 5.5.2 The Direct Treatment; 5.5.3 Numerical Results; 5.6 Summary and Outlook; References; 6 Quantum Effects in Biological Systems; 6.1 From Schrödinger to "Quantum Biology''; 6.2 Photosynthesis: Disorder Versus Noise; 6.3 Design Principles in Photosynthesis.
6.4 OutlookReferences; Part III Many-Particle Quantum Transport; 7 Describing Many-Particle Quantum Systems; 7.1 Introduction; 7.2 Postulates for Bosons and Fermions; 7.2.1 The Two-Particle System; 7.2.2 The N-Particle System; 7.2.3 Permanents and (Slater) Determinants; 7.3 Fock Space; 7.3.1 Constructing Fock Space; 7.3.2 Structuring Fock Space; 7.3.3 Exponential Vectors; 7.4 Commutation Relations; 7.5 Second Quantisation; 7.6 Many-Particle Quantum States; 7.6.1 Number States; 7.6.2 Bosonic Coherent States*; 7.6.3 Bosonic Squeezed States*; 7.6.4 Representing Bosonic States*
2.3.3 The Probabilistic Interpretation2.4 Dynamics of Quantum Systems; 2.4.1 The Heisenberg Picture; 2.4.2 The Schrödinger Picture; 2.5 Quantum Interference; 2.5.1 From Waves to Wave Functions; 2.5.2 Projections and Quantum Probability; 2.6 Scattering Systems; 2.7 Concluding Remarks; References; 3 Complex Quantum Systems and Random Matrix Theory; 3.1 Complex Systems; 3.1.1 Heuristics; 3.1.2 Complexity and Information Theory*; 3.1.3 Complexity of Quantum Dynamical Systems; 3.2 Complex Networks; 3.3 Aspects of Random Matrix Theory; 3.3.1 From Atoms and Orbits to Random Matrix Theory*
3.3.2 The Gaussian Ensembles of Random Matrix Theory3.3.3 Statistical Properties of GOE Eigenvalues; 3.3.4 Statistical Properties of GOE Eigenvectors; 3.4 Concluding Remarks; References; Part II Single-Particle Quantum Transport; 4 Efficient Transport in Closed Systems; 4.1 Introduction; 4.2 Measuring Transfer Efficiency; 4.3 Influence of Network Structures; 4.3.1 Regular Networks; 4.3.2 Random Networks; 4.4 Design Principles; 4.4.1 Centrosymmetry; 4.4.2 The Dominant Doublet; 4.5 Statistical Control; 4.5.1 Statistics of the Dominant Doublet; 4.5.2 Statistics of the Transfer Time.
4.5.3 Scaling Properties4.5.4 Numerics; 4.6 Summary and Outlook; References; 5 Scattering Approach to Efficient Transport; 5.1 Introduction; 5.2 Transfer Probability and Dwell Time; 5.3 The Two Level System; 5.3.1 The Model; 5.3.2 The Symmetric Case; 5.4 Designing the System; 5.5 Statistical Treatment; 5.5.1 The Indirect Treatment; 5.5.2 The Direct Treatment; 5.5.3 Numerical Results; 5.6 Summary and Outlook; References; 6 Quantum Effects in Biological Systems; 6.1 From Schrödinger to "Quantum Biology''; 6.2 Photosynthesis: Disorder Versus Noise; 6.3 Design Principles in Photosynthesis.
6.4 OutlookReferences; Part III Many-Particle Quantum Transport; 7 Describing Many-Particle Quantum Systems; 7.1 Introduction; 7.2 Postulates for Bosons and Fermions; 7.2.1 The Two-Particle System; 7.2.2 The N-Particle System; 7.2.3 Permanents and (Slater) Determinants; 7.3 Fock Space; 7.3.1 Constructing Fock Space; 7.3.2 Structuring Fock Space; 7.3.3 Exponential Vectors; 7.4 Commutation Relations; 7.5 Second Quantisation; 7.6 Many-Particle Quantum States; 7.6.1 Number States; 7.6.2 Bosonic Coherent States*; 7.6.3 Bosonic Squeezed States*; 7.6.4 Representing Bosonic States*