The project aims to investigate the analytic and spectral properties of some effective models commonly used in condensed matter physics, and their derivation from more fundamental models, in an appropriate scale limit.
We plan to investigate the derivation of tight-binding models in solids state physics via well-localized Wannier bases, and the topological obstruction to the existence of the latter; the spectral properties of Schrödinger and Dirac operators with non-Hermitian potentials; the self-adjointness and the spectral properties of zero-range N-body Hamiltonian operators; the topological properties of the minimizers of the Landau-de Gennes functional governing the phase transitions of liquid crystals.
We expect that the solution to these problems will require the interplay of different mathematical techniques, so the team involves experts in Calculus of Variations, Real Analysis, Spectral Theory and Mathematical Physics.
