Seminarium Fizyki Materii Skondensowanej

A pedagogical introduction to solving classical and quantum mechanical interaction problems in infinite spatial dimensions is given. As a warm-up Bohr's atomic model is derived by solving the Schrodinger equation in infinite dimensions. Then we solve classical many-body problems (Ising model, Ising model with random coupling, hard sphere fluids) in this limit. Regarding quantum particles, the solution of the Hubbard model in infinite dimensions is discussed in detail. It corresponds to a dynamical mean-field theory, which allows to compute the properties of correlated electrons in models and materials. Finally, strategies to go beyond mean-field theory are presented.