Elméleti Fizika szeminárium-sorozat
Professor Stefan Teufel (Tübingen): Non-equilibrium almost-stationary states and linear response for gapped quantum systems
in: Novobátzky-room (Északi Tömb, 2.54)
I report on recent mathematical results concerning the validity of linear response theory at zero temperature for perturbations of gapped Hamiltonians describing interacting fermions on a lattice, e.g. quantum Hall systems. The challenge here is to prove Kubo's formula uniformly in the volume and also for perturbations (like a small constant electric field) that close the spectral gap. Our justification of linear response theory is based on a novel extension of the adiabatic theorem to situations where a time-dependent perturbation closes the gap. According to the standard version of the adiabatic theorem, when the perturbation is switched on adiabatically and as long as the gap does not close, the initial ground state evolves into the ground state of the perturbed operator. The new adiabatic theorem states that for perturbations that are either slowly varying potentials or small quasi-local operators, once the perturbation closes the gap, the adiabatic evolution follows non-equilibrium almost-stationary states (NEASS) that we construct explicitly.