Gardellin, Arianna (2018) Dynamics of the quantum nonlinear Klein-Gordon chain. [Magistrali biennali]
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The aim of this work is to study the dynamics of one-dimensional Klein-Gordon anharmonic chains of interacting bosons. Especially, we focus our attention on the quantum version of Hamiltonian perturbation theory, which allows us to achieve the Hamiltonian of our bosonic system written in normal form. More precisely we show that Hamiltonian normal form of the quoted system consists in a Bose-Hubbard-like Hamiltonian. We consider both the case of short-range and long-range (all-to-all) interaction. We also treat the case of disordered chains with a distribution of the local potentials.
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