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Last update: T_FUUK (24.05.2004)
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Last update: LIPAVSKY/MFF.CUNI.CZ (15.05.2008)
advanced theory of transport in Fermi systems |
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Last update: prof. Pavel Lipavský, CSc. (30.10.2019)
examination |
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Last update: LIPAVSKY/MFF.CUNI.CZ (15.05.2008)
A. A. Abrokosov, L. P. Gorkov, I. E. Dzyaloshinski: Methods of Quantum Field Theory in Statistical Physics, 1975.
L. P. Kadanoff, G. Baym: Quantum Statistical Mechanins, 1962. |
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Last update: LIPAVSKY/MFF.CUNI.CZ (15.05.2008)
chalk talks |
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Last update: prof. Pavel Lipavský, CSc. (30.10.2019)
Required skills: Boltzmann equation (derivation, H-theorem, simple applications), Vlasov equation (classical linear response, two-stream instability), Landau concept of quasiparticles, quantum corrections to Boltzmann equation (Fermi Golden rule, Pauli exclussion principle, H-theorem for fermions), Wigner distribution (quantum linear response, Linhardt formula, Mermin formula), Green functions (adiabatic theorem, Dirac representation, Wick theorem, Feyman diagrams, selfenergy, Hartree-Fock approximation, screened Coulomb potential), nonequilibrium Green functions (analytic continuation for fermions, propagators, short-time expansion, quasiclassical expansion) |
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Last update: T_FUUK (13.04.2005)
Lectures deal with the Fermi liquid of electrons in crystals. First we return to the classical Boltzmann equation which we use to introduce the interplay of the free drift and collisions of particles. We demonstrate the implentation of the theory on the proof of the entropy production by collisions. Moreover, we evaluate the pressure and share viscosity in gasses. Second, we extend the Boltzmann equation to cover the plasma adding the Lorentz force from a mean electromagnetic field. We derive the classical linear response and discuss non-trivial aspects of the interaction of wave with particles in the regime of the two-stream instability. Our phenomenologic presentation of the idea of the mean field is closed by the Landau concept of quasiparticles. In the course of quantum generalization we first employ the Fermi Golden rule and Pauli exclussion principle in collisions. The quantum treatment of the drift requires to leave the Boltzmann distribution and handle the reduced density matrix instead. In this framework we derive the linear response and show that quantum systems reveal a classically prohibited feature ? at certain distances the repulsive Coulomb forces become attractive. This explains stability of metalic crystals. Systematic approach to non-equlibrium many-body systems we base on the method of non-equilibrium Greens functions. We first develop Greens functions for the ground state for which we introduce the Feynman diagrammatic approach. Derived rules apply also at finite temperatures and for non-equilibrium systems. We interlink these cases with the help of the complex time path. From equations for the Green function we recover the Boltzmann equation with all the above mentioned improovements.
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Last update: LIPAVSKY/MFF.CUNI.CZ (15.05.2008)
quantum mechanics, basics of the quantum statistics |