Memory Functions, Projection Operators, and the Defect Technique

<p>Dedication page</p><p>Acknowledgments</p><p>Foreword</p><p>Authors' Preface</p><p>1 The Memory Function Formalism:&nbsp;What and Why</p> 1.1 Introduction to Memory Functions<p></p><p> 1.2 An Example of How Memory Functions Arise: the&nbsp;Railway-Track Model</p><p> 1.3 An Overview of Areas in which&nbsp;the Memory Formalism Helps</p><p>2 Zwanzig’s Projection Operators: How They Yield Memories</p><p> 2.1 The Derivation of the Master Equation: a Central&nbsp;Problem in Quantum Statistical Mechanics</p><p> 2.2 Memories from Projection Operators that Diagonalize&nbsp;the Density Matrix</p><p> 2.3 Two Simple Examples of Projections and an Exercise</p> 2.3.1 Evolution of a Simple Complex Quantity<p></p><p> 2.3.2 Projection Operators for Quantum Control&nbsp;of Dynamic Localization</p><p> 2.3.3 Exercise for the Reader: the Open Trimer</p><p> 2.4 What is Missing from the Projection Derivation of&nbsp;the Master Equation</p><p>3 Building Coarse-Graining into the Projection Technique</p><p> 3.1 The Need to Coarse-Grain</p><p> 3.2 Constructing the Coarse-Graining Projection&nbsp;Operator</p><p> 3.3 Generalization of the Forster-Dexter Theory of&nbsp;Excitation Transfer</p><p> 3.4 Obtaining Realistic Memory Functions</p><p> 3.5 Implementing a General Plan</p><p> 3.5.1 Example in an Unrelated Area: Ferromagnetism</p><p>4 Features of Memory Functions and Relations to Other Entities</p> 4.1 Resolution of the Perrin-Forster-Davydov Puzzle<p></p><p> 4.2 Relations Among Theories of Excitation Transfer</p><p> 4.3 Long-range Transfer Rates as a Consequence of&nbsp;Strong Intersite Coupling</p><p> 4.4 Connection of Memories to Neutron Scattering and&nbsp;Velocity Auto-Correlation Functions, and Pausing&nbsp;Time Distributions</p><p>5 Applications to Experiments: Transient Gratings, Ronchi Rulings,&nbsp;and Depolarization</p><p> 5.1 Non-drastic Experiments: Fluorescence Depolarization&nbsp;as an Example</p><p> 5.2 Ronchi Rulings for Measuring Coherence of Triplet&nbsp;Excitons</p><p> 5.3 Fayer's Transient Gratings: an Ideal Experiment&nbsp;for Measuring Coherence of Singlet Excitons</p><p>6 Projection Operators for Various Contexts</p><p> 6.1 Projections for the Theory of Electrical Resistivity</p><p> 6.2 Projections that Integrate in Classical Systems</p><p> 6.2.1 The BBGKY Hierarchy</p><p> 6.2.2 Torrey-Bloch Equation for NMR Microscopy</p><p>6.3 Projections for Quantum Control of Dynamic&nbsp;Localization</p><p>6.4 Projections for the Railway-Track Model of Chapter&nbsp;2</p><p>7 Memories and Projections in Nonlinear Equations of Motion</p><p> 7.1 Extended Nonlinear Systems and the Physical&nbsp;Pendulum</p><p> 7.2 Nonlinear Waves in Reaction Di_usion systems</p><p> 7.3 Spatial Memories: Inuence Functions in the Fisher&nbsp;Equation</p><p>8 NMR Microsocopy and Granular Compaction</p><p> 8.1 Pulsed Gradient NMR Signals in Con_ned Geometries</p><p> 8.2 Analytic Solutions of a Generalized Torrey-Bloch&nbsp;Equation</p><p> 8.3 Non-local Analysis of Stress Distribution in Compacted&nbsp;Sand</p><p> 8.4 Spatial Memories and Correlations in the Theory&nbsp;of Granular Materials</p><p>9 Projections/Memories for Microscopic Treatment of Vibrational&nbsp;Relaxation</p><p> 9.1 The Importance of Vibrational Relaxation</p><p> 9.2 The Montroll-Shuler Equation and its Generalization&nbsp;to the Coherent Domain</p><p> 9.3 Reservoir E_ects in Vibrational Relaxation</p><p> 9.4 Approach to Equilibrium of a Simpler System: a&nbsp;Non-Degenerate Dimer</p><p>10 The Montroll Defect Technique</p><p> 10.1 Introduction: Experiments that Modify Substantially</p><p> 10.2 Overview of the Defect Technique and Simple Cases</p><p> 10.2.1 Trapping at a Single Site</p><p> 10.2.2 How Laplace Inversion may be avoided in&nbsp;Some Situations</p><p> 10.2.3 Trapping at More than 1 Site: Exercise for&nbsp;the Reader</p><p> 10.3 Coherence E_ects on Sensitized Luminescence</p><p> 10.4 End-Detectors in a Simpson Geometry</p> 10.5 High Defect Concentration: the&nbsp;_-function Approach<p></p><p> 10.6 Periodically Arranged Defects</p><p> 10.7 Remarks</p><p>11 The Defect Technique in the Continuum</p><p> 11.1 General Discussion</p><p> 11.2 Higher Dimensional Systems</p><p> 11.3 A Theory of Coalescence of Signaling Receptor&nbsp;Clusters in Immune Cells</p><p> 11.4 The Defect Technique with the Smoluchowski&nbsp;Equation</p> 11.5 Momentum-Space Theory of Capture<p></p><p>12 A Mathematical Approach to Non-Physical Defects</p><p> 12.1 Introduction</p><p> 12.2 Exciton Annihilation in Translationally Invariant&nbsp;Crystals</p><p> 12.3 Scattering Function from the Stochastic Liouville&nbsp;Equation with its Terms viewed as Defects</p><p> 12.4 Transmission of Infection in the Spread of Epidemics</p><p>13 Memory Functions from Static Disorder: E_ective Medium&nbsp;Approach</p><p> 13.1 Introduction</p><p> 13.2 Various Descriptions of Disorder</p><p> 13.3 E_ective Medium Approach: Philosophy and&nbsp;Prescription</p><p> 13.4 Examination of its Validity and Extension of its&nbsp;Applications</p><p>14 Concluding Remarks</p><p> 14.1 What We Have Learnt</p><p>Bibliography</p><p>Bibliography</p><p>Author index&nbsp;</p><p>Subject index&nbsp;</p>