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Non-equilibrium dynamics in the fully connected Bose-Hubbard model: the emergence of dynamical phase transitions and synchronization

Andrea Pizzi

Non-equilibrium dynamics in the fully connected Bose-Hubbard model: the emergence of dynamical phase transitions and synchronization.

Rel. Fabrizio Dolcini. Politecnico di Torino, Corso di laurea magistrale in Physics Of Complex Systems (Fisica Dei Sistemi Complessi), 2018

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Abstract:

In the context of out of equilibrium dynamics of isolated interacting quantum many-body systems, we study the mean-field discretized and nonlinear Gross-Pitaevskii equation (GPE) of motion for a fully connected (or all-to-all coupled) Bose-Hubbard model describing a large population of bosons on a lattice of generic dimension V, with potential experimental applications ranging from ultra-cold atomic gases in optical traps to systems of Josephson junctions. Considering a quench on the system Hamiltonian, we describe the time evolution of a system initialized to the Mott insulating phase and taken in the strong superfluid regime, finding a sharp change in the dynamical behaviour when varying the quench intensity across a critical value, that is a dynamical phase transition. Our results generalize the study presented in some previous papers focusing on the particular cases of V = 2, V = 3 and 1D lattice, and place particular emphasis on the relaxation of some dynamical order parameters in the large V limit. On the side of the dynamical phase transition corresponding to the strong superfluid regime, we find such relaxation to consist of a π-synchronization of the mean field bosonic phases, that we find to compete against the eventual site-dependent disorder of the Hamiltonian in what, in analogy with the notorious Kuramoto model for nonlinear coupled oscillators, can be referred to as a synchronization transition. Additionally, in support of the validity of the mean field approximation far from the transition, we report a study beyond mean field based on the Bogolioubov-de Gennes method.

Relatori: Fabrizio Dolcini
Anno accademico: 2017/18
Tipo di pubblicazione: Elettronica
Numero di pagine: 90
Soggetti:
Corso di laurea: Corso di laurea magistrale in Physics Of Complex Systems (Fisica Dei Sistemi Complessi)
Classe di laurea: Nuovo ordinamento > Laurea magistrale > LM-44 - MODELLISTICA MATEMATICO-FISICA PER L'INGEGNERIA
Ente in cotutela: Université de Paris-Sud (Paris XI) (FRANCIA)
Aziende collaboratrici: NON SPECIFICATO
URI: http://webthesis.biblio.polito.it/id/eprint/8032
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