Part II: Statistical Physics and elements of the solid state theory
Instructor: A.A.Varlamov
1.
The main principles of Statistical Physics
Statistical distribution, Liuville theorem, statistical matrix and statistical distributions in quantum
mechanics.
2.
G
ibbs distribution
Ideal gas: Boltzmann and Maxwell distributions. Quantum gases: Fermi

Dirac and Bose

Einstein
distributions. Fermi surface of the ideal Fermi gas. Heat capacity of the Fermi gas. Phenomenon of
the Bose

condensation. Black radiation.
3.
Soli
ds
Lattice heat capacity. Thermal expansion. Classical treatment of the lattice vibrations. Phonons.
4.
Phase transitions of the II order
Landau theory of phase transitions. Order parameter fluctuations.
5.
Superconductivity
General description and historical
review.
Ginzburg

Landau phenomenology.
Flux quantization.
Superconductivity of the second type. Evaluation of the lower and upper critical fields (8 hours).
Part III: Solid State Physics
Crystallographic lattice: Bravais lattices. Some practical crys
tal structures. The reciprocal lattice.
Brillouin zones. Diffraction from a crystallographic lattice.
Lattice vibrations: the harmonic approximation. Energy quantization: phonons. Acoustic and optical
phonons. Anelastic scattering of phonons.
Thermal pro
perties of crystals. Specific heat of solids: Einstein and Debye model. Anharmonic
contributions. Thermal expansion. Thermal conductivity: Umklapp scattering of phonons. Lattice
defects.
Free electron gas. Electrical resistance: Ohm law. Thermal conductivi
ty. Specific heat contribution
from the electron gas. Hall effect. Relationship between thermal conductivity and specific heat.
Electron

lattice interaction. Bands of energy. Metals, insulators and semiconductors. The Bloch
theorem. Equation of motion for
a Bloch electron. The Fermi surface. Quasi

free electron gas. The
effective mass. Electrons and holes. Electron

electron interaction. Intrinsic semiconductors. p

and n

doped semiconductors. The p

n junction.
Superconductivity: phenomenology and applicat
ions. I and II type superconductors. Meissner effect.
Critical field. London equations. Field quantization. DC and AC superconducting tunnel effect
(Josephson effect). Superconducting Quantum Interference Device (SQUID).
Textbook: C. Kittel “Introduction
to Solid State Physics”
Prerequisites: Mechanics, thermodynamics, electromagnetism, basic concepts of quantum
mechanics.
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