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Polarons and Bipolarons : an Introduction / Ashok Chatterjee.

By: Chatterjee, Ashok [author.]Contributor(s): Mukhopadhyay, SomaMaterial type: TextTextSeries: Chapman & Hall Pure and Applied MathematicsPublisher: Boca Raton, FL : CRC Press, 2017Edition: First editionDescription: 1 online resource (475 pages) : 170 black and white imagesContent type: text Media type: computer Carrier type: online resourceISBN: 9781315118635; 1315118637; 9781482244892; 1482244896; 9781351644921; 1351644920; 9781351635431; 1351635433Subject(s): SCIENCE -- Solid State Physics | TECHNOLOGY & ENGINEERING -- Material Science | Polarons | Quasiparticles (Physics) | SCIENCE / Quantum Theory | SCIENCE / Solid State Physics | TECHNOLOGY / Material ScienceDDC classification: 539.7/2112 LOC classification: QC176.8.P62Online resources: Taylor & Francis | OCLC metadata license agreement
Contents:
Cover; Half Title; Title Page; Copyright Page; Table of Contents; Preface; SECTION I: Basic Polaron Concepts; 1: Qualitative Picture; 1.1 Introduction; 1.2 What is a Polaron?; 1.3 Simple Classical Landau Picture; 1.4 A More Detailed Qualitative Analysis of Landau Picture: The Classical Picture; 1.5 Dynamical Regime: The Quantum Picture; 1.6 Polaron Motion in a Molecular Lattice: Mott-Austin Picture; SECTION II: Continuum Polarons; 2: The Fröhlich Hamiltonian; 2.1 Introduction; 2.2 Derivation of the Fröhlich Hamiltonian; 3: Exactly Soluble Polaron Models; 3.1 Introduction
3.2 A Localized Electron Interacting with Optical Phonons3.3 The Gross Model: An Electron Interacting with a Single Phonon Mode; 4: Weak and Intermediate Coupling Solutions of the Fröhlich Hamiltonian; 4.1 Introduction; 4.2 Rayleigh-Schödinger Perturbation Theory; 4.2.1 Unperturbed State and Translational Invariance of the System; 4.2.2 Perturbed Wave Function; 4.2.3 Perturbed Energy; 4.2.4 Polaron Effective Mass; 4.2.5 Average Number of Virtual Phonons; 4.2.6 Electron Life-Time; 4.2.7 Lattice Polarization Potential; 4.2.8 Validity of the RSPT Solutions
4.3 Brillouin-Wigner Perturbation Theory4.3.1 An Introduction to Brillouin-Wigner Perturbation Theory; 4.3.2 Application of Second-Order Brillouin-Wigner Perturbation Theory to the Polaron Problem; 4.4 The Variational Theory of Gurari; 4.4.1 The Wave Function; 4.4.2 Polaron Energy and Effective Mass; 4.4.3 Average Number of Virtual Phonons; 4.4.4 Polaron Polarization Potential; 4.5 Canonical Transformation Method of Lee, Low, and Pines; 4.5.1 Introduction; 4.5.2 Polaron Energy and Effective Mass; 4.5.3 Number of Virtual Phonons in the Polaron Cloud
4.5.4 Polarization Potential and Induced Polarization Charge Density4.5.5 Correspondence with Lee-Pines Approximation; 4.6 Improvements on the Lee, Low, and Pines Theory; 4.6.1 Introduction; 4.6.2 Lowest-Order Perturbative Correction to the Results from Lee, Low, and Pines; 4.6.3 Another Perturbative Extension of the Lee, Low, and Pines Theory: The Haga Method; 4.6.4 One-Phonon Tamm-Dancoff Variational Theory: The Haga Method; 4.6.5 One-Phonon TD Variational Theory Again: The Polaron Dispersion Analysis by Larsen; 4.7 Other Theories; 4.8 Lower Bounds to the Polaron Ground State Energy
4.8.1 The Method of Lieb and Yamazaki4.8.2 The Method of Larsen; 5: Strong-Coupling Solutions of the Fröhlich Hamiltonian; 5.1 Introduction; 5.2 The Landau-Pekar Method; 5.3 Fully Quantum Mechanical Approach to the Landau-Pekar Method; 5.4 Exact Landau-Pekar Numerical Solution; 5.5 Strong-Coupling Expansion (Adiabatic Solution); 6: Attempts at All-Coupling Solutions of the Fröhlich Hamiltonian; 6.1 Introduction; 6.2 The Method of Höhler; 6.3 The Lee-Low-Pines-Huybrechts Method; 6.3.1 Weak-Coupling Limit; 6.3.2 Strong-Coupling Limit; 6.4 The Lee-Low-Pines-Gross Method
Scope and content: "This book provides a comprehensive review of the subject of polaron and a thorough account of the sophisticated theories of the polaron. It explains the concept of the polaron physics in as simple a manner as possible and presents the theoretical techniques and mathematical derivations in great detail. Anybody who follows this book will develop a solid command over the subject both conceptually and technically and will be in a position to contribute to this field."--Provided by publisher.
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"This book provides a comprehensive review of the subject of polaron and a thorough account of the sophisticated theories of the polaron. It explains the concept of the polaron physics in as simple a manner as possible and presents the theoretical techniques and mathematical derivations in great detail. Anybody who follows this book will develop a solid command over the subject both conceptually and technically and will be in a position to contribute to this field."--Provided by publisher.

Cover; Half Title; Title Page; Copyright Page; Table of Contents; Preface; SECTION I: Basic Polaron Concepts; 1: Qualitative Picture; 1.1 Introduction; 1.2 What is a Polaron?; 1.3 Simple Classical Landau Picture; 1.4 A More Detailed Qualitative Analysis of Landau Picture: The Classical Picture; 1.5 Dynamical Regime: The Quantum Picture; 1.6 Polaron Motion in a Molecular Lattice: Mott-Austin Picture; SECTION II: Continuum Polarons; 2: The Fröhlich Hamiltonian; 2.1 Introduction; 2.2 Derivation of the Fröhlich Hamiltonian; 3: Exactly Soluble Polaron Models; 3.1 Introduction

3.2 A Localized Electron Interacting with Optical Phonons3.3 The Gross Model: An Electron Interacting with a Single Phonon Mode; 4: Weak and Intermediate Coupling Solutions of the Fröhlich Hamiltonian; 4.1 Introduction; 4.2 Rayleigh-Schödinger Perturbation Theory; 4.2.1 Unperturbed State and Translational Invariance of the System; 4.2.2 Perturbed Wave Function; 4.2.3 Perturbed Energy; 4.2.4 Polaron Effective Mass; 4.2.5 Average Number of Virtual Phonons; 4.2.6 Electron Life-Time; 4.2.7 Lattice Polarization Potential; 4.2.8 Validity of the RSPT Solutions

4.3 Brillouin-Wigner Perturbation Theory4.3.1 An Introduction to Brillouin-Wigner Perturbation Theory; 4.3.2 Application of Second-Order Brillouin-Wigner Perturbation Theory to the Polaron Problem; 4.4 The Variational Theory of Gurari; 4.4.1 The Wave Function; 4.4.2 Polaron Energy and Effective Mass; 4.4.3 Average Number of Virtual Phonons; 4.4.4 Polaron Polarization Potential; 4.5 Canonical Transformation Method of Lee, Low, and Pines; 4.5.1 Introduction; 4.5.2 Polaron Energy and Effective Mass; 4.5.3 Number of Virtual Phonons in the Polaron Cloud

4.5.4 Polarization Potential and Induced Polarization Charge Density4.5.5 Correspondence with Lee-Pines Approximation; 4.6 Improvements on the Lee, Low, and Pines Theory; 4.6.1 Introduction; 4.6.2 Lowest-Order Perturbative Correction to the Results from Lee, Low, and Pines; 4.6.3 Another Perturbative Extension of the Lee, Low, and Pines Theory: The Haga Method; 4.6.4 One-Phonon Tamm-Dancoff Variational Theory: The Haga Method; 4.6.5 One-Phonon TD Variational Theory Again: The Polaron Dispersion Analysis by Larsen; 4.7 Other Theories; 4.8 Lower Bounds to the Polaron Ground State Energy

4.8.1 The Method of Lieb and Yamazaki4.8.2 The Method of Larsen; 5: Strong-Coupling Solutions of the Fröhlich Hamiltonian; 5.1 Introduction; 5.2 The Landau-Pekar Method; 5.3 Fully Quantum Mechanical Approach to the Landau-Pekar Method; 5.4 Exact Landau-Pekar Numerical Solution; 5.5 Strong-Coupling Expansion (Adiabatic Solution); 6: Attempts at All-Coupling Solutions of the Fröhlich Hamiltonian; 6.1 Introduction; 6.2 The Method of Höhler; 6.3 The Lee-Low-Pines-Huybrechts Method; 6.3.1 Weak-Coupling Limit; 6.3.2 Strong-Coupling Limit; 6.4 The Lee-Low-Pines-Gross Method

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