Learning objectives
Understanding the bases of quantum statistical mechanics and learning some important applications.
Learning to use the second quantization formalism for many body systems.
Prerequisites
Basic knowledge of quantum mechanics and classical statistical mechanics
Course unit content
Main results in classical statistical mechanics.
Mixed states in quantum statistical mechanics, density operator, statistical entropy.
Fundamental principle of statistical mechanics, quantum ensembles (microcanonical, canonical, T-P, gran-canonical). Paramagnets, molecular vibro-rotations, specific heat of solids.
Identical particles, Fock spoace, second quantization, photons, ideal quantum gases, Hubbard model, spin-waves.
Fluctuations. Phase transitions. Mean-field approximation. MonteCarlo method.
Computer simulations (Matlab): Heisenberg model in canonical ensemble. MonteCarlo method for the 2d Ising model. Exact-diagonalization study of the Hubbard model.
Full programme
Main results in classical statistical mechanics.
Mixed states in quantum statistical mechanics, density operator, statistical entropy.
Fundamental principle of statistical mechanics, quantum ensembles (microcanonical, canonical, T-P, gran-canonical). Paramagnets, molecular vibro-rotations, specific heat of solids.
Identical particles, Fock spoace, second quantization, photons, ideal quantum gases, Hubbard model, spin-waves.
Fluctuations. Phase transitions. Mean-field approximation. MonteCarlo method.
Computer simulations (Matlab): Heisenberg model in canonical ensemble. MonteCarlo method for the 2d Ising model. Exact-diagonalization study of the Hubbard model.
Bibliography
Lecture notes.
Huang - Statistical Mechanics
Yeomans - Statistical Mechanics of Phase Transitions
Bruus and Flensberg - Introduction to Quantum field theory in condensed matter physics
Teaching methods
Lectures and computer simulations.
Assessment methods and criteria
Oral examination. The student can also expose a topic of his choice. This can be a topic treated in the course or in a closely related field.
Other information
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