École Nationale Supérieure de
Techniques Avancées

Abstract

During this internship, I studied the notion of resonance in quantum systems modeling molecules and solids. Finding resonances is useful in chemistry and material science. They are poles in the analytic continuation of the Green function of the Hamiltonian, and physically manifest as finite-lifetime states, neither bound nor scattering. When located close to the real axis, they cause lumps in frequency dependent quantities. They can also provide a basis on which to expand states. We develop an approach for Hamiltonians of the form H = H0 + V , composed of an homogeneous or periodic part H0, locally perturbed by a localized potential V . This choice is motivated by the use of such Hamiltonians in DFT (Density Functional Theory) to compute electronic structures. We study the properties of the Green function and its continuation. We suggest a new method to find resonances of the Green function, thereby providing information on the electronic distribution in the system. We show the results obtained and we study the convergence of the method comparatively to complex scaling.