Vorträge in der Woche 11.09.2017 bis 17.09.2017

Dienstag, 12.09.2017: The Langlands Correspondence

Anton Deitmar

Mittwoch, 13.09.2017: New Approaches to Quantum Simulations: the Eigenpotential Variational Method

Lorenzo Fant (Trieste)

We will consider a possible new approach to quantum mechanical simulations. The method aims at solving the time independent Schroedinger equation, looking for an approximated analytical solution. It begins from an analytical guess of the wave function then trying to increase its precision by minimizing its energy, as standard variational methods. The main difference with existing variational methods consists in the minimization process which, instead of being done on the energy functional, is performed on the so called Eigenpotential. Such a quantity is defined for a generic wave function as the potential of which it is eigenstate of. It thus follows the idea of solving exactly an approximated potential as close as possible to the original one, instead of solving approximately the exact potential: By adjusting the wave function's parameters one reaches the best possible fit between the external potential and the eigenpotential. We developed such an algorithm to deal with one dimensional problems and began approaching to 2 dimensional ones looking for studying real systems in the near future. The hope is that such a method, when solidly developed in 2 and 3 dimensions, will give us an alternative to deal with nuclear quantum effects simulations, improving the existing approaches’ panorama.