Il quarto appuntamento della serie "A pranzo con la Fisica" è fissato per domani, mercoledì 19 dicembre 2007, ore 13.15-14.30, aula A del Dipartimento di Fisica.
Il seminario, aperto a tutti gli afferenti interessati ed anche agli studenti di Fisica, sarà svolto dal Prof. Carlo Presilla del Dipartimento di Fisica dell’ Università di Roma "La Sapienza", sul tema:
"Probabilistic representation of quantum systems, and not only"
The evolution of systems as varied as bosons or fermions in a lattice, classical dynamical systems, biological populations, networks, etc. are described by linear flows associated to a finite matrix operator H. It is a result established only few years ago that the solution of these flows, for real or imaginary time, admits an exact probabilistic representation in terms of Poisson processes.
On the basis of this Feynman-Kac–type formula, we have developed a Monte Carlo algorithm to perform unbiased numerical simulations at finite times and a method yielding semi-analytic results in the long-time limit. In the latter approach, we are able to determine the ground state of H in terms of a simple equation. A closed exact equation for the ground state is obtained and straightforwardly solved for a class of Hamiltonian models characterized, in the thermodynamic limit, by a multinomial probability density of the above multiplicities.
For this class of models we find a zero-temperature universal thermodynamic limit displaying a quantum phase transition between a normal phase and a frozen phase with zero hopping energy.