Lecturer:
Course Type:
PhD Course
Academic Year:
2020-2021
Period:
October - June
Duration:
60 h
Description:
- The course will discuss rigorous results in quantum mechanics and in statistical mechanics, relevant for condensed matter physics. Topics to be covered include:
- Elements of spectral theory, with applications to lattice Schroedinger operators.
- Effect of disorder on quantum dynamics. The Anderson model, and its phase diagram.
- Relation between spectra and dynamics: the RAGE theorem.
- Anderson localization through path expansions.
- Quantum transport, heuristic linear response theory. Making it rigorous: the adiabatic theorem.
- Quantum Hall effect. Bulk-edge correspondence.
- Time-reversal invariant systems. Example: Kane-Mele model. Z2 classification and bulk-edge duality.
- Interacting lattice models. Grand canonical formulation, Fock space, perturbation theory.
- Cluster expansion, convergence of fermionic perturbation theory, analyticity of the Gibbs state.
- Approach to criticality: the rigorous renormalization group. Applications: interacting graphene, nonintegrable perturbations of the 2d Ising model. Construction of a nontrivial RG fixed point: lattice models with long range hoppings.
- Universality of transport in quantum Hall systems and semimetals.
- References:
- M. Aizenman and S. Warzel. Random Operators. American Mathematical Society.
- G. M. Graf. Aspects of the integer quantum Hall effect. Proceedings of Symposia in Pure Mathematics (2007).
- G. M. Graf and M. Porta. Bulk-edge correspondence for two-dimensional topological insulators. Comm. Math. Phys. 324, 851-895, (2013).
- M. Porta. Mathematical Methods of Condensed Matter Physics. Lecture notes.
- A. Giuliani, V. Mastropietro and S. Rychkov. Gentle introduction to rigorous Renormalization Group: a worked fermionic example. arXiv:2008.04361
Research Group:
Location:
A-136 and Zoom, sign in to get the link
Next Lectures:
Friday, January 22, 2021 - 09:00 to 11:00
Friday, January 29, 2021 - 09:00 to 11:00
Friday, February 5, 2021 - 09:00 to 11:00
Friday, February 12, 2021 - 09:00 to 11:00
Friday, February 19, 2021 - 09:00 to 11:00
Friday, February 26, 2021 - 09:00 to 11:00
Friday, March 5, 2021 - 09:00 to 11:00
Friday, March 12, 2021 - 09:00 to 11:00
Friday, March 19, 2021 - 09:00 to 11:00
Friday, March 26, 2021 - 09:00 to 11:00
Friday, April 2, 2021 - 09:00 to 11:00
Friday, April 9, 2021 - 09:00 to 11:00
Friday, April 16, 2021 - 09:00 to 11:00
Friday, April 23, 2021 - 09:00 to 11:00
Friday, April 30, 2021 - 09:00 to 11:00
Friday, May 7, 2021 - 09:00 to 11:00
Friday, May 14, 2021 - 09:00 to 11:00
Friday, May 21, 2021 - 09:00 to 11:00
Friday, May 28, 2021 - 09:00 to 11:00
Friday, June 4, 2021 - 09:00 to 11:00
Friday, June 11, 2021 - 09:00 to 11:00
Friday, June 18, 2021 - 09:00 to 11:00
Friday, June 25, 2021 - 09:00 to 11:00