Speaker: Giovanna Marcelli (Aalborg University)

Title: Adiabatic evolution of low-temperature many-body quantum systems

Abstract:
We consider finite-range, many-body fermionic lattice models and we study the evolution of their thermal equilibrium state after introducing a weak and slowly varying time-dependent perturbation. Under suitable assumptions on the external driving, we derive a representation for the average of the evolution of local observables via a convergent expansion in the perturbation, for small enough temperatures. Convergence holds for a range of parameters that is uniform in the size of the system. Under a spectral gap assumption on the unperturbed Hamiltonian, convergence is also uniform in temperature. As an application, our expansion allows to prove closeness of the time-evolved state to the instantaneous Gibbs state of the perturbed system, in the sense of expectation of local observables, at zero and at small temperatures. Our strategy is based on a rigorous version of the Wick rotation and fermionic cluster expansion.
This talk is based on a joint work with R. L. Greenblatt, M. Lange and M. Porta.