LFU:online

Graduates of this course will have acquired a thorough understanding of fundamental aspects of the theory of ultracold quantum gases. They will be able to independently apply theoretical methods which are used to describe ultracold quantum gases, including microscopic modelling approaches and the functional integral formulation of quantum many-body systems.

Scales and microscopic modelling of interactions in ultracold quantum gases. Ultracold bosons: Gross-Pitaevski equation and Bogoliubov theory; condensation vs. superfluidity. Functional integral formulation, symmetry breaking, and the Goldstone theorem. Ultracold fermions: BCS theory, Feshbach resonances, and BEC-BCS crossover. Optical lattices: Microscopic derivation of Bose-Hubbard model, Mott-insulator to superfluid quantum phase transition. If time allows: Nonequilibrium dynamics in ultracold quantum gases. Anderson and many-body localization.

Oral exam.

Relevant literature will be discussed in the first lecture.

Statistical mechanics including second quantization.