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Seminario di Fisica Matematica: “The Quantum Fermi-Pasta-Ulam Problem”

Giovedì 17 Novembre 2016, ore 12:00 - Sala Riunioni IV piano - Matteo Stoppato

ARGOMENTI: Seminari

Giovedì 17 Novembre 2016 alle ore 12:00 in Sala Riunioni IV piano, Matteo Stoppato terrà un seminario dal titolo “The Quantum Fermi-Pasta-Ulam Problem”.

Abstract
In this talk we consider the quantum version of the classical Fermi-Pasta-Ulam problem, i.e. we study the quantum dynamics of a one-dimensional chain of particles interacting through nonlinear forces. Using the quantum analogue of the classical Hamiltonian perturbation theory, in the Heisenberg picture, we eliminate through a canonical transformation the nonresonant anharmonic terms, computing the quantum version of the Birkhoff normal form to second order. We then show that, for the initial excitation of long wavelength modes (acoustic modes), which is the case of low temperature lattices in thermal equilibrium, the dynamics of the system is close to that of the quantum Korteweg-de Vries equation.