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book-icon-openmaktabaBook Title: Modern Condensed Matter Physics
author-icon-openmaktabaBook Author: STEVEN M. GIRVIN, KUN YANG
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 Modern Condensed Matter Physics

Book Description

“Modern Condensed Matter Physics” by Steven M. Girvin and Kun Yang is a comprehensive and in-depth exploration of the fundamental principles, theories, and experimental methods in the field of condensed matter physics. The book is organized into multiple chapters, each covering a specific aspect of condensed matter physics, and it offers readers a thorough understanding of the subject. Below is the detailed book description to capture its main topics and key areas of focus:

Chapter 1: Overview of Condensed Matter Physics
The book starts by providing an essential overview of condensed matter physics. It defines the field, its goals, and its significance in understanding and manipulating the physical properties of matter in various forms.

Chapter 2: Classification of Condensed Matter Systems
This chapter delves into the classification and phases of condensed matter systems, considering atomic spatial structures and electronic properties. Readers gain insights into the different states of matter, such as solids, liquids, and gases, and how they relate to the underlying atomic and electronic structures.

Chapter 3: Spatial Structure
The book explores the spatial structure of condensed matter systems. It discusses how experimental techniques, such as X-ray scattering and neutron scattering, can be used to probe the atomic arrangements in solids, as well as the significance of spatial correlations and the distinction between the liquid and crystal states.

Chapter 4: Lattices and Symmetries
Readers are introduced to the concept of lattices and symmetries in crystalline materials. This chapter covers topics like Bravais lattices, reciprocal lattices, and their relation to X-ray scattering. It also touches on the effects of lattice fluctuations.

Chapter 5: Dynamics of Lattice Vibrations
This chapter focuses on the dynamics of lattice vibrations in crystalline materials. It explores topics such as elasticity, sound modes, and the quantum theory of harmonic crystals. The Debye-Waller factor and the Mössbauer effect are also discussed.

Chapter 6: Electronic Structure of Crystals
Here, the book delves into the electronic structure of crystalline materials. It covers fundamental models like the Drude theory, independent electron model, and Bloch’s theorem. The tight-binding method is introduced as a tool to describe electronic band structures, and various phenomena, including band gaps, Van Hove singularities, and spin-orbit coupling, are explained.

Chapter 7: Semiclassical Transport Theory
This chapter transitions to the study of semiclassical transport theory in materials. Readers explore the behavior of Bloch electrons in different bands, the Boltzmann equation, and thermoelectric effects in semiconductors.

Chapter 8: Semiconductors
A detailed examination of semiconductors follows. The book covers various aspects of semiconductor physics, including impurity levels, optical processes, and the operation of p-n junctions. Applications like light-emitting diodes, solar cells, and field-effect transistors are explained.

Chapter 9: Non-local Transport in Mesoscopic Systems
This chapter focuses on non-local transport in mesoscopic systems. The Landauer formula, conductance quantization, and universal conductance fluctuations are discussed, along with the concept of noise in mesoscopic systems and Anderson localization.

Chapter 10: Quantum Monte Carlo Methods
The book then shifts its attention to quantum Monte Carlo methods. It covers the path integral representation of quantum mechanics, the Hubbard model, and the second-quantized Hamiltonians, along with various quantum effects and interactions.

Chapter 11: Quantum Phase Transitions
Readers are introduced to quantum phase transitions and the associated theoretical and experimental aspects. Topics like quantum critical points and scaling theory of localization are explored in detail.

Chapter 12: Advanced Topics
This chapter offers an advanced overview of topics such as cold atoms, superconductors, novel orders, superfluidity, quantum antiferromagnets, the Hubbard model, and more.

Chapter 13: Conclusion
The book concludes by summarizing its content and providing readers with a comprehensive understanding of modern condensed matter physics.

“Modern Condensed Matter Physics” provides a thorough and accessible foundation for students, researchers, and physicists interested in the complexities of condensed matter systems. It covers a wide range of topics, from the basic principles of crystallography and electronic band structures to advanced topics like quantum phase transitions and quantum Monte Carlo methods. With its detailed explanations and comprehensive coverage, this book is an invaluable resource for anyone seeking to explore the fascinating world of condensed matter physics.

Book Contents

  • Overview of Condensed Matter Physics
  • Definition of Condensed Matter and Goals of Condensed Matter Physics
  • Classification (or Phases) of Condensed Matter Systems
  • Atomic Spatial Structures
  • Electronic Structures or Properties
  • Symmetries
  • Beyond Symmetries [bend]
  • Theoretical Descriptions of Condensed Matter Phases
  • Experimental Probes of Condensed Matter Systems
  • Spatial Structure
  • Probing the Structure
  • Semiclassical Theory of X-Ray Scattering
  • Quantum Theory of Electron–Photon Interaction and X-Ray Scattering [bend]
  • X-Ray Scattering from a Condensed Matter System
  • Relationship of S([vector(q)]) and Spatial Correlations
  • Liquid State versus Crystal State
  • Lattices and Symmetries
  • The Crystal as a Broken-Symmetry State
  • Bravais Lattices and Lattices with Bases
  • Bravais Lattices
  • Lattices with Bases
  • Lattice Symmetries in Addition to Translation
  • Reciprocal Lattices
  • X-Ray Scattering from Crystals
  • Effects of Lattice Fluctuations on X-Ray Scattering
  • Notes and Further Reading
  • Neutron Scattering
  • Introduction to Neutron Scattering
  • Inelastic Neutron Scattering
  • Dynamical Structure Factor and f-Sum Rule
  • Classical Harmonic Oscillator
  • Quantum Harmonic Oscillator
  • Single-Mode Approximation and Superfluid [sup(4)]He
  • Dynamics of Lattice Vibrations
  • Elasticity and Sound Modes in Continuous Media
  • Adiabatic Approximation and Harmonic Expansion of Atomic Potential
  • Classical Dynamics of Lattice Vibrations
  • Quantum Theory of Harmonic Crystals
  • Heat Capacity
  • Canonical Quantization of Lattice Vibrations
  • Quantum Dynamical Structure Factor
  • Debye–Waller Factor and Stability of Crystalline Order
  • Mössbauer Effect
  • Electronic Structure of Crystals
  • Drude Theory of Electron Conduction in Metals
  • Independent Electron Model
  • Bloch’s Theorem
  • Band Gaps and Bragg Reflection
  • Van Hove Singularities
  • Velocity of Bloch Electrons
  • Tight-Binding Method
  • Bonds vs. Bands
  • Wannier Functions
  • Continuum Limit of Tight-Binding Hamiltonians
  • Limitations of the Tight-Binding Model
  • s–d Hybridization in Transition Metals [bend]
  • Graphene Band Structure
  • Polyacetylene and the Su–Schrieffer–Heeger Model
  • Dirac electrons in 1D and the Peierls instability
  • Ground-State Degeneracy and Solitons
  • Zero Modes Bound to Solitons
  • Quantum Numbers of Soliton States and Spin–Charge Separation
  • Thermodynamic Properties of Bloch Electrons
  • Specific Heat
  • Magnetic Susceptibility
  • Spin–Orbit Coupling and Band Structure
  • Photonic Crystals
  • Optical Lattices
  • Oscillator Model of Atomic Polarizability
  • Quantum Effects in Optical Lattices
  • Semiclassical Transport Theory
  • Review of Semiclassical Wave Packets
  • Semiclassical Wave-Packet Dynamics in Bloch Bands
  • Derivation of Bloch Electron Equations of Motion [bend]
  • Zener Tunneling (or Interband Transitions)
  • Holes
  • Uniform Magnetic Fields
  • Quantum Oscillations
  • Semiclassical [vecter(E)] X [vecter(B)] Drift
  • The Boltzmann Equation
  • Boltzmann Transport
  • Einstein Relation
  • Thermal Transport and Thermoelectric Effects
  • Semiconductors
  • Homogeneous Bulk Semiconductors
  • Impurity Levels
  • Optical Processes in Semiconductors
  • Angle-Resolved Photoemission Spectroscopy
  • The p–n Junction
  • Light-Emitting Diodes and Solar Cells
  • Other Devices
  • Metal–Oxide–Semiconductor Field-Effect Transistors (MOSFETs)
  • Heterostructures
  • Quantum Point Contact, Wire and Dot
  • Notes and Further Reading
  • Non-local Transport in Mesoscopic Systems
  • Introduction to Transport of Electron Waves
  • Landauer Formula and Conductance Quantization
  • Multi-terminal Devices
  • Universal Conductance Fluctuations
  • Transmission Eigenvalues
  • UCF Fingerprints
  • Noise in Mesoscopic Systems
  • Quantum Shot Noise
  • Dephasing
  • Anderson Localization
  • Absence of Diffusion in Certain Random Lattices
  • Classical Diffusion
  • Semiclassical Diffusion
  • Review of Scattering from a Single Impurity
  • Scattering from Many Impurities
  • Multiple Scattering and Classical Diffusion
  • Quantum Corrections to Diffusion
  • Real-Space Picture
  • Enhanced Backscattering
  • Weak Localization in 2D
  • Magnetic Fields and
  • Quantum Coherence
    • Quantum Hall Effects
    • Quantum Hall Resistance [bend]
    • Two-Dimensional Electron Gas
    • Magnetic Fields
    • Composite Fermions
    • Reentrance at ν = 5/2
    • Two-Species Hall Effect
    • Metal–Insulator Transition in 2D
    • Percolation Threshold and the Correlation Length [bend]
    • Disordered 2D Electron Gas
    • Band Gaps and Unconventional Quantum Hall Effects
    • Quantum Phase Transitions
    • Critical Theory
    • Scaling Theory of Localization
    • Scale-Invariant Quantity and Fractal Dimension
    • Spatial Scale Invariance
    • Dimension
    • Dynamic Scaling
    • Power-Law Dependence of Conduction at the Transition
    • Conductance Distribution in 1D
    • Non-Integer Exponents
    • Conductance Universality
    • Localization in 1D
    • Correlation Functions
    • Correlation Length
    • Geometric and Quantum Phases
    • Phase of the Harmonic Oscillator
    • WKB Tunneling Probability
    • Exponential Damping of Wave Functions
    • Time-Reversal Symmetry
    • Time-Reversal Symmetry of the Dirac Equation
    • Two-Species Quantum Hall Effect [bend]
    • Superconductivity and Quantum Hall Transitions
    • Experimental Tests of the Scaling Theory
    • AC Measurement of [vecter(g)]
    • Quantum Localization of Sound [bend]
    • Two-Parameter Scaling
    • Soft Modes
    • Quantum Percolation [bend]
    • Scaling Theory of Localization: Exact Results
    • Notes and Further Reading
    • Quantum Monte Carlo Methods
    • Path Integral Representation of Quantum Mechanics
    • Hubbard Model and the Half-Filled Band
    • Two-Component Fermion System [bend]
    • Density Matrix
    • The Path Integral for Bosons
    • Green Function of the Hubbard Model
    • Pauli Paramagnetism of Free Electrons [bend]
    • Model of Spin Dynamics
    • Electron Density
    • Propagator of Fermion System
    • Excitons [bend]
    • Diagrammatic Series
    • Second-Quantized Hamiltonians and Operator Diagrams [bend]
    • Operators and Second Quantization
    • Time Evolution Operator in Interaction Picture
    • Interactions
    • Luttinger–Ward Functional
    • Pairing Field: Antiferromagnetism and Superconductivity
    • Hartree–Fock Approximation
    • Phases in Systems with Competing Orders
    • Overview of the Book
    • Acknowledgments [bend]
    • Chapter 1: Cold Atoms [bend]
    • Chapter 2: Superconductors [bend]
    • Chapter 3: Novel Orders [bend]
    • Chapter 4: Superfluidity and Supersolids [bend]
    • Chapter 5: Quantum Antiferromagnets [bend]
    • Chapter 6: Hubbard Model [bend]
    • Chapter 7: Boson Hubbard Model [bend]
    • Chapter 8: Path Integral QMC for Fermions [bend]
    • Chapter 9: Path Integral QMC for Bosons [bend]
    • Chapter 10: Determinant QMC and Other Methods [bend]
    • Chapter 11: Spin and Fermion Ladders and Applications [bend]
    • Chapter 12: Fermion-Hard-Core Boson and Other Hamiltonians [bend]
    • Chapter 13: Quantum Phase Transitions: Experiments [bend]
    • Chapter 14: Quantum Phase Transitions: Theory [bend]
    • Chapter 15: Fermion Superfluids [bend]
    • Chapter 16: Quantum Antiferromagnetism: Theoretical Approaches [bend]
    • Chapter 17: Fermion-Hard-Core Boson: Experiments [bend]
    • Chapter 18: Fermion-Hard-Core Boson: Theory [bend]
    • Chapter 19: Lattice Bose Gas [bend]
    • Chapter 20: Phase-Separated States [bend]
    • Chapter 21: Polyacetylene and the Su–Schrieffer–Heeger Model [bend]
    • Chapter 22: Quantum Oscillations in Metals [bend]
    • Chapter 23: Graphene Band Structure [bend]
    • Chapter 24: Luttinger Liquid Theory [bend]
    • Chapter 25: Quantum Critical Points [bend]
    • Chapter 26: Quantum Monte Carlo Methods: Review and Discussion [bend]
    • Chapter 27: Path Integral QMC and Realistic Applications [bend]
    • Chapter 28: Randomness, Geometry, and Quantum Hall Effect [bend]
    • Chapter 29: Quantum Localization of Sound Waves [bend]
    • Chapter 30: Localization of Electrons in Disordered Media [bend]
    • Chapter 31: Kondo Effect [bend]
    • Chapter 32: Scaling Theory of Localization [bend]
    • Chapter 33: Quantum Hall Systems [bend]
    • Chapter 34: Localization: Exact Results and the Landauer Formula [bend]
    • Chapter 35: Prologue to Modern Day: The General Theory of Conductance [bend]
    • Chapter 36: Spectral and Transport Properties [bend]
    • Chapter 37: Optical and Thermal Conductivity [bend]
    • Chapter 38: Quantum Oscillations in Metals [bend]
    • Chapter 39: Thermoelectric Effects
    • Tables
    • Index

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