Sylabus:The course is devoted to the study of statistical mechanics and thermodynamics. A basic theory is given. Different examples and problems are presented.
Statistical Mechanics 83964
- Lecture 1 Introduction to statistical mechanics. The macroscopic and the microscopic states. Equilibrium and observation time. Equilibrium and molecular motion. Relaxation time. Local equilibrium. Phase space of a classical system. Statistical ensemble. Liouville’s theorem. Density matrix in statistical mechanics and its properties. Liouville’s-Neiman equation.
- Lecture 2 The microcanonical ensemble. Quantum states and the phase space. Some paradoxes in statistical physics. Ergodic hypothesis. Quasi-ergodic systems. Some model systems in statistical physics: Spin system, classical and quantum consideration.
- Lecture 3 Entropy in statistical mechanics. Thermodynamic contacts: Mechanical contact, heat contact, diffusion contact. Equilibrium. Chemical potential. The main distributions in statistical mechanics. A system in the canonical ensemble. Thermostat.
- Lecture 4 Thermodynamics. Equilibrium (reversible) and noequilibrium ( nonrevrsible) processes. Adiabatic, isotermic, isobaric and isochoric processes. Connection between statistical and thermodynamic quantities. Helmholtz free energy F. Enthalpy H. Gibbs Free Energy G. Thermodynamic potentials. Heat capacity. The lows of thermodynamics. Thermodynamic functions for the canonical ensemble. Partition functions. Alternative expression for the partition function. Density of states. A system of harmonic oscillators.
- Lecture 5 The grand canonical ensemble. Grand partition function. Connection with Thermodynamic functions. Density and energy fluctuations in the grand canonical ensemble: correspondence with other ensembles. Fermi-Dirac statistics. Classical limit. Bose-Einstein statistics.
- Lecture 6 Ideal gases. Entropy. Sackur-Tetrode formula. De Broglie wavelength. Chemical potential. Ideal gas in canonical ensemble. Entropy of a system in a canonical ensemble. Free Energy. Maxwell Velocity Distribution. Principle of equipartition of energy. Heat capacity. Ideal gas in the grand canonical ensemble.
- Lecture 7 Gaseous systems composed of molecules with internal motion: Monatomic molecules, Diatomic molecules. Electron, Vibartional and Rotational contribution. Fermi gas. Electron gas in metals. Heat capacity of electron gas.
- Lecture 8 Ideal Bose gas. Thermodynamic behavior of an ideal Bose gas. The temperature of condensation. Elementary excitation in liquid helium II. Thermodynamics of black-body radiation. Planck’s formula for the distribution of energy over the black-body spectrum. Stefan-Boltzmann law of black-body radiation.
- Lecture 9 Thermodynamics of crystal lattice. The field of sound waves. Phonons and second sound. The Debye model. The Debye temperature. Specific heat of the solid in the Debye model.
- Lecture 10 Non Ideal systems. Intermolecular interactions. Lenard-Jones potential. Corrections to the Ideal Gas Law. Van der Waals equation. Short Distance and Long Distance Interaction. The Plasma Gas and Ionic Solutions. The Debye-Huckel radius.
- Lecture 11 Phase transition. Critical point. First-order phase transition. Phase diagrams. The theory of Yang and Lee. A dynamical model for phase transition. Weiss theory of ferromagnetism. Second order phase transition. Landau theory. Critical point exponents. Chemical equilibrium and chemical reactions.
- Lecture 12 Ising model as a macroscopic model of phase transition. Why the Ising model is very important? Relationship between lattice models, models of ferroelectrics and Ising model. The classical formulation of the problem. Exact solutions. Drawbacks of the mean field approximation. The Static Fluctuation Approximation as new method of the solving the Ising problem.
- Lecture 13 Fluctuations. Fluctuations of macroscopic variables. Correlation functions. Response and Fluctuation. Density correlation function. Theory of random processes. Spectral analysis of fluctuations: the Wiener-Khintchine theorem. The Nyquist theorem. Applications of Nyquist theorem.
- Lecture 14 Brownian motion. Einstein-Smoluhowski theory of the Brownian motion. Langevin theory of the Brownian motion Approach to equilibrium: Foker-Planck equation. The fluctuation-dissipation theorem.
R.K.Pathria, Statistical Mechanics, Pergamon Press, 1986
- R.Kubo, Statistical Mechanics, Interscience Publishers, New York, 1965.
- L.D. Landau and E.M. Lifshitz, Statistical Physics, Pergamon Press, 1980.
- Shang-Keng Ma, Statistical Mechanics, World Scientific, 1985.
- C.Kittel, Elementary Statistical Physics, John Wiley & Sons, Inc. New York, 1958.
- J.M.Yomans, Statistical Mechanics of Phase Transitions, Clarendon Press, Oxford, 1992.
- R.P.Feynman, Statistical Mechanics, A Set of Lectures., Addison-Wesley Publishing Company, 1972
- F.Reif, Statistical Physics, Berkeley Physics Course , V5, Mgraw-Hill Book Company, 1965.
- C.J. Thompson, Classical equilibrium Statistical Mechanics, Clarendon Press, Oxford, 1988.