Physics 540: Statistical Mechanics


1.Thursday, January 24 First meeting. Introduction. Macroscopic systems. Classical statistical mechanics. Phase space. Distribution function. Statistical independence of subsystems. Fluctuations of additive observables. LL 1-2
2.Tuesday, January 29 Statistical ensemble. Liouville theorem. Microcanonical distribution. Quantum statistical mechanics. Statistical matrix. Density of states. Statistical weight of the system. LL 3-7
3.Thursday, January 31 Entropy. Level spacing of macroscopic system. The law of increase of entropy. LL 7-8
4.Tuesday, February 5 HW 1 given. Thermodynamic quantities. Temperature. Adiabatic processes. LL 9,11
5.Thursday, February 7 Pressure. First law of thermodynamics. Specific heat. Thermodynamic potentials: energy, enthalpy, Helmholtz free energy, and Gibbs free energy. Maxwell relations between thermodynamic derivatives and Jacobians. LL 12-16
6.Tuesday, February 12 HW 2 given. Relations between thermodynamic coefficients. Equation of state and specific heats. Adiabatic expansion. Thermodynamic inequalities. LL 16,21
7.Thursday, February 14 Maximal work and Carnot cycle. Nernst's theorem. Thermodynamic potentials in the presence of external fields. Curie's law for independent 1/2 spins in magnetic field. LL 19, 23,15 K.1 ex 4,10
8.Tuesday, February 19 HW 3 given. Number of particles as an external parameter. Chemical potential. Solving problems in thermodynamics. LL 24-25
9.Thursday, February 21 Microcanonical distribution. Canonical (Gibbs) distribution. T-P distribution. LL 28, 36
10.Tuesday, February 26 HW 4 given. Grand canonical distribution. Fluctuations of thermodynamic quantities. LL 35-36
11.Thursday, February 28 Thermodynamics and Gibbs distribution in the presence of external fields. LL 25, K.2 pr 3,4
12.Tuesday, March 5 HW 5 given. Thermodynamics and Gibbs distribution of rotating bodies. Thermodynamic perturbation theory (classical). LL 26, 34, 32
13.Thursday, March 7 Thermodynamic perturbation theory (quantum). Boltzmann distribution. LL 32, 37, 38
14.Tuesday, March 12 HW 6 given. Boltzmann distribution for classical system. Comparison of partition funcitons for 1d quantum and classical oscillators. 'Frozen degrees of freedom'. Ideal Boltzmann gas. Equation of state. Ideal gas with constant specific heat. LL 38, 41-43
15.Thursday, March 14 The law of equipartition. Monoatomic gases. Rotation of molecules. Polyatomic gases. LL 44, 45, 46, 47-51, K.3 ex 2
16.Tuesday, March 19 HW 7 given. Symmetry factors, identical atoms, nuclear spins, electronic states, anharmonicity etc. Ideal gases not in equilibrium. Gibbs paradox. Mixture of ideal gases. Chemical equilibrium. LL 46-51, 40, 101
17.Thursday, March 21 Chemical equilibrium. Chemical equilibrium between ideal gases. The law of mass action. Equilibrium constant. Non-ideal gases. Virial expansion. LL 101-103, 74-75
Tuesday, March 26 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Spring Break !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Thursday, March 28 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Spring Break !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
18.Tuesday, April 2 HW 8 given. Van der Waals equation. Ideal quantum gases. Fermi and Bose statistics. Ideal quantum gases not in equilibrium. LL 76, 53-55
19.Thursday, April 4 Fermi and Bose gases of elementary particles. A degenerate electron gas. LL 56-57
20.Tuesday, April 9 HW 9 given. A degenerate electron gas. Specific heat. Magnetism of an electron gas. Bohr-van Leeuwen theorem. LL 57-59
21.Thursday, April 11 Magnetism of an electron gas. Pauli paramagnetism. Landau diamagnetism. De Haas-van Alphen effect. LL 59
22.Tuesday, April 16 HW 10 given. A degenerate relativistic electron gas. Electrons and holes in semiconductors. A degenerate Bose gas. Bose condensation. LL 61-62, K.4 ex 3-4
23.Thursday, April 18 Bose condensation. Singularities in thermodynamic potentials. Black body radiation. Planck's distribution. Planck's formula. Rayleigh-Jeans formula. LL 62-63
24.Tuesday, April 23 HW 11 given. Black body radiation. Kirchhoff's law. Phonons in crystals. Debye's law. Debye's interpolation formula. LL 63, 64, 66
25.Thursday, April 25 Phase equilibrium. Phase diagrams. Metastable states. Triple points. Latent heat of a transition. The Clapeyron-Clausius formula. The pressure of a saturated vapor. The phase transitions of the first kind and free energy landscape. The critical point. LL 81-84
26.Tuesday, April 30 HW 12 given. Phase transitions of the second type. Spontaneous symmetry breaking. Order parameter. The discontinuity of specific heat. Effect of an external field on a phase transition. LL 142-144
27.Thursday, May 2 Effect of an external field on a phase transition. Fluctuations of the order parameter. Applicability of Landau theory of phase transitions. Levanyuk-Ginzburg criterion. LL 144-149
28.Tuesday, May 7 Fluctuation range. Critical indices. Scaling hypothesis. Critical phenomena. What next?
Final. Thursday,
May 9,
This is an open book examination. You are allowed to use a textbook (only one, please), your lecture notes, and homeworks with solutions. Each problem is worth 25 points. Only four problems out of six will be graded. You have to indicate which problems you want to have graded. LL 1-16, 21, 23-32, 34-51, 53-64, 66, 74-76, 81-84, 101-103, 142-149