Cooperative Phenomena in Condensed Matter Physics

 

Lecture # 1                   05.02.07

 

Introduction. Symmetries of wave function for quantum particles. Pauli principle. Connection between spin and statistics.

Bose-Einstein statistics. Fermi-Dirac statistics. Distribution functions. Non-relativistic degenerate gases of fermions and bosons.

 

Notes 1

 

Lecture # 2                   07.02.07

 

Equation of State for fermions and bosons. Quantum correction to Clapeyron’s equation for Fermi and Bose statistics. 

Degenerate electron gas. Fermi surface. Equation of State.

 

Notes 2

Problems 1 & 2

 

Lecture # 3                   12.02.07

 

Bose Einstein Condensation. Equation of state. Thermodynamics. BEC transition. Jump in the specific heat.

 

Problem 3

Problem 4

 

Lecture # 4                   14.02.07

 

Phase Transitions I. Examples of phase transitions. Landau theory. Critical exponents. Ginzburg-Landau theory.

Correlation length. Ginzburg number.

 

Lecture # 5                   19.02.07

 

Phase Transitions II. Scaling invariance. Critical exponents. Upper critical dimension.

 

Tutorial  # 1                  20.02.07                      14:00       Room D

 

Electron in uniform magnetic field. Classical description. Equation of motion. Quantum description.

Schroedinger equation. Gauges. Landau levels.

 

Lecture # 6                   21.02.07

 

Discussion of  the 1st homework. Fermi gas with Dirac spectrum. Equation of state. Specific heat.

 

Lecture # 7                   26.02.07

 

Phase Transitions III. Fluctuations. Ornstein – Zernike theory. Classical vs Quantum phase transitions.

 

Notes 3

 

Lecture # 8                   26.02.07

 

Superfliudity I. Experimental facts. Hydrodynamics of two component liquid. Phonons. Rotons. Landau criterion.

 

Lecture # 9                   02.03.07

 

Superfluidity II.  Vortices. Thermodynamics of superfluids.

 

Tutorial  # 2                  03.03.07                      14:00       Room D

 

Thermodynamics. Black body radiation. Specific heat. Entropy. Electrons in metals. Specific heat. Sommerfeld constant.

 

Lecture # 10                 05.03.07

 

Magnetism I. Classical theory of magnetism. Langevin function. Molecular field. Curie and Curie-Weiss laws.

Quantum magnetism. Localized moments. Brillouin functions. Ferromagnets and Antiferromagnets.

 

Problem 5 & 6

 

Lecture # 11                 06.03.07   (This lecture was not recorded)

 

Magnetism II  Quantum magnetism: response functions. Susceptibility. Random Phase Approximation. Ornstein-Zernike theory.

Multi-component order parameters. Ferrimagnets. Spin Galsses

 

Lecture # 12                 09.03.07

 

Strongly correlated electron systems. High Temperature Superconductivity: main concepts, ideas and puzzles. Heavy Fermion compounds.

Strong correlations in low dimensions

 

Notes 4

 

Lecture # 13                 12.03.07

 

Cooperative phenomena at nanoscale. Quantum dots. Quantum wires. Molecular electronics.

 

Notes 5

 

Lecture # 14                 14.03.07

 

Discussion of the 2nd  homework

 

 

Meeting before exam     19.03.07     11:00                 Room D

 

Exam                                    23.03.07     10:00-13:00       Room D

Recommended literature:

 

1.           

N.W.Ashkroft and N.D.Mermin. Solid State Physics. (Holt, Richert and Winston, New York 1976)

 

2.           

L.D.Landau and E.M.Lifshitz, Quantum Mechanics, (Pergamon Press, 1977)

 

3.           

L.D.Landau and E.M.Lifshitz, Statistical Physics, (Pergamon Press, 1980)

 

4.

R.Feynman, Statistical Mechanics (W. A. Benjamin, Reading, 1972).

 

5.

C. Kittel, Introduction to Solid State Physics, (John Wiley and Sons 1995)