Dedication page

Acknowledgments

Foreword

Authors' Preface

1 The Memory Function Formalism: What and Why

1.2 An Example of How Memory Functions Arise: the Railway-Track Model

1.3 An Overview of Areas in which the Memory Formalism Helps

2 Zwanzig's Projection Operators: How They Yield Memories

2.1 The Derivation of the Master Equation: a Central Problem in Quantum Statistical Mechanics

2.2 Memories from Projection Operators that Diagonalize the Density Matrix

2.3 Two Simple Examples of Projections and an Exercise

2.3.2 Projection Operators for Quantum Control of Dynamic Localization

2.3.3 Exercise for the Reader: the Open Trimer

2.4 What is Missing from the Projection Derivation of the Master Equation

3 Building Coarse-Graining into the Projection Technique

3.1 The Need to Coarse-Grain

3.2 Constructing the Coarse-Graining Projection Operator

3.3 Generalization of the F orster-Dexter Theory of Excitation Transfer

3.4 Obtaining Realistic Memory Functions

3.5 Implementing a General Plan

3.5.1 Example in an Unrelated Area: Ferromagnetism

4 Features of Memory Functions and Relations to Other Entities

4.2 Relations Among Theories of Excitation Transfer

4.3 Long-range Transfer Rates as a Consequence of Strong Intersite Coupling

4.4 Connection of Memories to Neutron Scattering and Velocity Auto-Correlation Functions, and Pausing Time Distributions

5 Applications to Experiments: Transient Gratings, Ronchi Rulings, and Depolarization

5.1 Non-drastic Experiments: Fluorescence Depolarization as an Example

5.2 Ronchi Rulings for Measuring Coherence of Triplet Excitons

5.3 Fayer's Transient Gratings: an Ideal Experiment for Measuring Coherence of Singlet Excitons

6 Projection Operators for Various Contexts

6.1 Projections for the Theory of Electrical Resistivity

6.2 Projections that Integrate in Classical Systems

6.2.1 The BBGKY Hierarchy

6.2.2 Torrey-Bloch Equation for NMR Microscopy

6.3 Projections for Quantum Control of Dynamic Localization

6.4 Projections for the Railway-Track Model of Chapter 2

7 Memories and Projections in Nonlinear Equations of Motion

7.1 Extended Nonlinear Systems and the Physical Pendulum

7.2 Nonlinear Waves in Reaction Di_usion systems

7.3 Spatial Memories: Inuence Functions in the Fisher Equation

8 NMR Microsocopy and Granular Compaction

8.1 Pulsed Gradient NMR Signals in Con_ned Geometries

8.2 Analytic Solutions of a Generalized Torrey-Bloch Equation

8.3 Non-local Analysis of Stress Distribution in Compacted Sand

8.4 Spatial Memories and Correlations in the Theory of Granular Materials

9 Projections/Memories for Microscopic Treatment of Vibrational Relaxation

9.1 The Importance of Vibrational Relaxation

9.2 The Montroll-Shuler Equation and its Generalization to the Coherent Domain

9.3 Reservoir E_ects in Vibrational Relaxation

9.4 Approach to Equilibrium of a Simpler System: a Non-Degenerate Dimer

10 The Montroll Defect Technique

10.1 Introduction: Experiments that Modify Substantially

10.2 Overview of the Defect Technique and Simple Cases

10.2.1 Trapping at a Single Site

10.2.2 How Laplace Inversion may be avoided in Some Situations

10.2.3 Trapping at More than 1 Site: Exercise for the Reader

10.3 Coherence E_ects on Sensitized Luminescence

10.4 End-Detectors in a Simpson Geometry