Ementa proposta:
1. Statistical Physics and Thermodynamics
1.1 Micro-states and macro-states
1.2 Statistical and thermal equilibrium
1.3 The thermodynamic limit, extensive and intensive variables
1.4 Work and Heat
1.5 Relations between thermodynamic variables
1.6 Non-interacting microscopic constituents: the ideal gas
1.7 The simplest ideal gas
1.8 Mixing entropy and the Gibbs paradox
1.9 Indistinguishability of identical particles
1.10 Thermodynamic transformations
2. Classical Statistical Ensembles
2.1 Classical mechanics
2.2 Time averaging
2.3 Statistical ensembles
2.4 The density function
2.5 The Liouville theorem
2.6 Equilibrium ensembles and distribution functions
2.7 The uniform ensemble
2.8 The micro-canonical ensemble
2.9 The canonical ensemble
2.10 Deriving the canonical from the micro-canonical ensemble
2.11 The Gibbs and the grand-canonical ensembles
3. Applications of Classical Statistical Ensembles
3.1 Application I: The Maxwell distribution
3.2 Application II: Magnetism in classical statistical mechanics
3.3 Application III: Diatomic ideal gasses (classical)
3.4 Quantum vibrational modes
3.5 Quantum rotational modes
4. Quantum Statistical Ensembles
4.1 Quantum Mechanics
4.2 Mixed quantum states
4.3 Subsystems of a quantum system in a pure state
4.4 The density matrix
4.5 Ensemble averages and time-evolution
4.6 The density matrix for a subsystem of a pure state
4.7 Statistical entropy of a density matrix
4.8 The uniform and micro-canonical ensembles
4.9 Construction of the density matrix in the canonical ensemble
4.10 Generalized equilibrium ensembles
5. Applications of the canonical ensemble
5.1 The statistics of paramagnetism
5.2 Non-relativistic Boltzmann ideal gas
5.3 Van der Waals equation of state
5.4 The Mayer cluster expansion
6. Systems of indistinguishable quantum particles
6.1 FD and BE quantum permutation symmetries
6.2 BE and FD statistics for N identical free particles
6.3 Boltzmann statistics rederived
6.4 Fermi-Dirac statistics
6.5 Bose-Einstein statistics
6.6 Comparing the behavior of the occupation numbers
7. Ideal Fermi-Dirac Gases
7.1 The simplest ideal Fermi-Dirac gas
7.2 Entropy, specific heat, and equation of state
7.3 Corrections to the Boltzmann gas
7.4 Zero temperature behavior
7.5 Low temperature behavior: The Sommerfeld expansion
7.6 Pauli paramagnetism of ideal gasses
7.7 Landau diamagnetism
7.8 White dwarfs
8. Bose-Einstein statistics
8.1 Black body radiation
8.2 Cosmic micro-wave background radiation
8.3 Thermodynamic variables for Bose-Einstein ideal gases
8.4 Bose-Einstein condensation
8.5 Behavior of the specific heat
9. Phase coexistence: thermodynamics
9.1 Conditions for phase equilibrium
9.2 Latent heat
9.3 Clausius-Clapeyron equation
9.4 Example of the Van der Waals gas-liquid transition
9.5 The Maxwell construction
10. Phase transitions: statistical mechanics
10.1 Classification of phase transitions
10.2 The Ising Model
10.3 Exact solution of the 1-dimensional Ising Model
10.4 Ordered versus disordered phases
10.5 Mean-field theory solution of the Ising model
11. Functional integral methods
11.1 Path integral representation for the partition function
11.2 The classical = high temperature limit
11.3 Integrating out momenta
Bibliografia:
- R.K. Pathria, Statistical Mechanics, Elsevier Publishing, (2011)
- Statistical Physics, Part 1, L.D. Landau and E.M. Lifschitz, Pergamon Press, Third edition (1982)
- Statistical Mechanics, A set of Lectures, R.P. Feynman, Benjamin Cummings Publishing (1982)
- Eric D'Hoker, Lecture Notes (2012)
- David Tong, Lecture Notes (2012)
Sugestões de seminários:
- Grupo de Renormalização: Renormalization Group and Critical Phenomena. I. Renormalization Group and the Kadanoff Scaling Picture - Kenneth G. Wilson
- Modelos na rede (modelo de Ising e generalizações): An introduction to lattice gauge theory and spin systems - John B. Kogut
-Termodinâmica quântica: The role of quantum information in thermodynamics—a topical review - John Goold, Marcus Huber, Arnau Riera, Lídia del Rio and Paul Skrzypczyk (veja também The Quantum Thermodynamics Revolution), Thermodynamics of quantum systems with multiple conserved quantities - Yelena Guryanova, Sandu Popescu, Anthony J. Short, Ralph Silva & Paul Skrzypczyk
- Transições de fase topológicas: Nobel Lecture: Topological defects and phase transitions - John Michael Kosterlitz
- Máquina de Carnot com potência finita: Approaching the Carnot Limit at Finite Power: An Exact Solution - Clifford V. Johnson
- Buracos negros e termodinâmica: Black Holes and Entropy - Jacob D. Bekenstein, Black holes and thermodynamics - S. W. Hawking
- Estrelas de Neutron e anãs brancas: Neutron stars for undergraduates - Richard R. Silbar and Sanjay Reddy
- Dualidade: Duality in field theory and statistical systems - Robert Savit