Nguồn ngoài

Advanced Statistical Mechanics

Statistical Mechanics provides the connection between microscopic motion of individual atoms of matter and macroscopically observable properties such as temperature, pressure, entropy, free energy, heat capacity, chemical potential, viscosity, spectra, reaction rates, etc.

Physical and Theoretical Chemistry Textbook Maps Chemistry

Tác giả: Mark Tuckerman
Nhà xuất bản: New York University
Nguồn: LibreTexts
Giấy phép: CC BY-NC-SA
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

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Mục lục· 105 mục

01: Classical mechanics
1.01: The Lagrangian Formulation of Classical Mechanics
1.02: The Hamiltonian formulation of classical mechanics
1.03: The Microscopic Laws of Motion
1.04: Phase Space
1.05: Classical microscopic states or microstates and ensembles
1.06: Phase space distribution functions and Liouville's theorem
02: Foundations of classical statistical mechanics
2.01: The Ensemble Concept (Heuristic Definition)
2.02: Liouville's Theorem for non-Hamiltonian systems
2.03: The Liouville Operator and the Poisson Bracket
2.04: Equilibrium ensembles
03: The Microcanonical Ensemble
3.01: Basic Thermodynamics
3.02: The Partition Function
3.03: The Classical Virial Theorem (Microcanonical Derivation)
04: The canonical ensemble
4.01: Classical Virial Theorem (canonical ensemble derivation)
4.02: Legendre Transforms
4.03: Relation between Canonical and Microcanonical Ensembles
4.04: Preservation of Phase Space Volume and Liouville's Theorem
4.05: Energy Fluctuations in the Canonical Ensemble
05: The Isothermal-Isobaric Ensemble
5.01: Basic Thermodynamics
5.02: Pressure and Work Virial Theorems
5.03: The partition function and relation to thermodynamics
5.04: Temperature and pressure estimators
06: The Grand Canonical Ensemble
6.01: Thermodynamics
6.02: Partition Functions
6.03: Ideal Gas
6.04: Particle Number Fluctuations
07: Distribution Functions and Liquid Structure
7.01: General Formulation of Distribution Functions
7.02: General Distribution Functions and Correlation Functions
7.03: Structure and distribution functions in classical liquids and gases
7.04: General Correlation Functions
7.05: Thermodynamic quantities in terms of g(r)
7.06: The Pair Correlation Function
7.07: Derivation of the Van der Waals equation
08: Rare-event sampling and free energy calculations
8.02: Free-energy Perturbation Theory
8.03: Adiabatic Switching and Thermodynamic Integration
8.04: Reaction Coordinates
8.05: Jarzynski's Equality and Nonequilibrium Methods
8.06: The blue moon'' Ensemble Approach
09: Review of the basic postulates of quantum mechanics
9.01: Measurement
9.02: Physical Observables
9.03: The Fundamental Postulates of Quantum Mechanics
9.04: The Heisenberg Picture
9.05: The Heisenberg Uncertainty Principle
9.06: The Physical State of a Quantum System
9.07: Time Evolution of the State Vector
10: Fundamentals of quantum statistical mechanics
10.01: Principles of quantum statistical mechanics
10.02: The Density Matrix and Density Operator
10.03: Time evolution of the density operator
10.04: A simple example - the quantum harmonic oscillator
10.05: The quantum equilibrium ensembles
10.5.01: The microcanonical ensemble
10.5.02: The canonical ensemble
10.5.03: Isothermal-isobaric and grand canonical ensembles
11: Introduction to path integrals in quantum mechanics and quantum statistical mechanics
11.01: Discretized and Continuous Path Integrals
11.1.01: Derivation of the Discretized Path Integral
11.1.02: Doing the Path Integral - the Free Particle
11.1.03: Dominant Paths in the Propagator and Density Matrix
11.1.04: The Continuous Limit
11.02: Calculation of observables from path integrals
11.2.01: Expectation values of observables
11.2.02: Path integrals for N-particle systems
11.2.03: Path integral molecular dynamics (optional reading)
11.2.04: Thermodynamics from path integrals
11.03: Expansion about the classical path and stationary phase
11.3.01: The harmonic Oscillator - Expansion about the Classical Path
11.3.02: The Stationary Phase Approximation
12: Time-dependent Processes - Classical case
12.01: Perturbative solution of the Liouville equation
12.02: Kubo Transform Expression for the Time Correlation Function
12.03: Generalized Equations of Motion
12.04: General Properties of Time Correlation Functions
12.05: Perturbative solution of the Liouville equation
12.06: The Onsager Fluctuation Regression Theorem
12.07: Relation to Spectra
12.08: Time Correlation Functions and Transport Coefficients
12.8.01: Shear Viscosity
12.8.02: The Diffusion Constant
13: Time-dependent Processes - Quantum Case
13.01: Calculation of spectra from perturbation theory
13.1.01: The Hamiltonian
13.1.02: The Transition Rate
13.1.03: Examples
13.02: Iterative solution for the interaction-picture state vector
13.03: The Interaction Picture
13.04: Fermi's Golden Rule
13.05: Quantum Linear Response Theory
14: The Langevin and Generalized Langevin equations
14.01: The harmonic bath Hamiltonian
14.02: The Random Force Term
14.03: The Dynamic Friction Kernel
14.04: Relation between the Dynamic Friction Kernel and the Random Force
14.05: Derivation of the GLE
14.06: Mori-Zwanzig Theory- A more general derivation of the GLE
14.07: Example- Vibrational dephasing and energy relaxation