Memory functions, projection operators, and the defect technique : some tools of the trade for the condensed matter physicist / V.M. (Nitant) Kenkre.Material type: TextSeries: Lecture notes in physics ; 982.Publisher: Cham : Springer, Description: 1 online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783030686673; 3030686671Subject(s): Condensed matter | Condensed matterGenre/Form: Electronic books. Additional physical formats: Print version:: No titleDDC classification: 530.4/1 LOC classification: QC173.454Online resources: Click here to access online
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Includes bibliographical references and index.
This book provides a graduate-level introduction to three powerful and closely related techniques in condensed matter physics: memory functions, projection operators, and the defect technique. Memory functions appear in the formalism of the generalized master equations that express the time evolution of probabilities via equations non-local in time, projection operators allow the extraction of parts of quantities, such as the diagonal parts of density matrices in statistical mechanics, and the defect technique allows solution of transport equations in which the translational invariance is broken in small regions, such as when crystals are doped with impurities. These three methods combined form an immensely useful toolkit for investigations in such disparate areas of physics as excitation in molecular crystals, sensitized luminescence, charge transport, non-equilibrium statistical physics, vibrational relaxation, granular materials, NMR, and even theoretical ecology. This book explains the three techniques and their interrelated nature, along with plenty of illustrative examples. Graduate students beginning to embark on a research project in condensed matter physics will find this book to be a most fruitful source of theoretical training. .
Chapter 1. The Memory Function Formalism: What and Why -- Chapter 2. Zwanzig Projection Operators: How They Yield Memories -- Chapter 3. Building Coarse-Graining into Projections and Generalizing Energy Transfer Theory -- Chapter 4. Relations of Memories to Other Entities and GME Solutions for the Linear Chain -- Chapter 5. Direct Determination of Frenkel Exciton Coherence from Ronchi Ruling and Transient Grating Experiments -- Chapter 6. Application to Charges Moving in Crystals: Resolution of the Mobility Puzzle in Naphthalene and Related Results -- Chapter 7. Projections and Memories for Microscopic Treatment of Vibrational Relaxation -- Chapter 8. Projection Operators for Various Contexts -- Chapter 9. Spatial Memories and Granular Compaction -- Chapter 10. Memories and Projections in Nonlinear Equations of Motion -- Chapter 11. The Montroll Defect Technique and its Application to Molecular Crystals -- Chapter 12. The Defect Technique in the Continuum -- Chapter 13. Memory Functions from Static Disorder: Effective Medium Theory -- Chapter 14. Effective Medium Theory Application to Molecular Movement in Cell Membranes -- Chapter 15. A Mathematical Approach to Non-Physical Defects -- Chapter 16. Concluding Remarks.
Online resource; title from PDF title page (SpringerLink, viewed April 21, 2021).