• Login
    View Item 
    •   Home
    • Massey Documents by Type
    • Theses and Dissertations
    • View Item
    •   Home
    • Massey Documents by Type
    • Theses and Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Advances in classical and quantum wave dynamics on quasiperiodic lattices : a dissertation submitted for the degree of Doctor of Philosophy in Physics, Centre for Theoretical Chemistry and Physics, New Zealand Institute for Advanced Study, Massey University, Albany, New Zealand

    Icon
    View/Open Full Text
    01_front.pdf (114.7Kb)
    02_whole.pdf (2.621Mb)
    Export to EndNote
    Abstract
    Lattices and discrete networks are cornerstones of a number of scientific subjects. In condensed matter, optical lattices allowed the experimental realization of several theoretically predicted phenomena. Indeed, these structures constitute ideal benchmarks for light and wave propagation experiments involving interacting particles, such as clouds of ultra-cold atoms that Bose-Einstein condensate. Moreover, they allow experimental design of particular lattice topologies, as well as the implementation of several classes of spatial perturbations. For example, Anderson localization being observed for the first time in atomic Bose-Einstein condensate experiments and Aubry-André localization discovered with light propagating through networks of optical waveguide. This thesis considers different types of lattices in the presence of quasiperiodic modulations, mainly the celebrated Aubry-André potential. Particular attention will be given to spectral properties of models, localization features of eigenmodes and the transition from delocalized (metallic) eigenstates to localized (insulating) ones within the energy spectrum. We additionally discuss the relation between the model’s properties and the dynamics of particles hopping along the lattice. After introducing the linear discrete Schrödinger equation, we first discuss the spectral properties of the Aubry-André model. We then study the transition between metallic and insulating regimes of a class of quasiperiodic potentials constructed as an iterative superposition of periodic potentials with increasing spatial period. Next, we discuss the Aubry-André perturbation of flat-band topologies, their energy-dependent transition (mobility edge), which can be expressed in analytical forms in case of specific onsite energy correlations, highlighting existence of zeroes, singularities and divergences. We then discuss two cases of driven one-dimensional lattices, namely an Aubry-André chain with a weak time-space periodic driving and an Anderson chain with a quasiperiodic multi-frequency driving. We show anaytically and numerically how drivings can lift the respective localization and generate delocalization by design. Finally we discuss the problem of the possible generation of correlated metallic states of two interacting particles problem in one dimensional Aubry-André chains, under a coherent drive of the interaction.
    Date
    2016
    Author
    Danieli, Carlo
    Rights
    The Author
    Publisher
    Massey University
    URI
    http://hdl.handle.net/10179/11307
    Collections
    • Theses and Dissertations
    Metadata
    Show full item record

    Copyright © Massey University
    | Contact Us | Feedback | Copyright Take Down Request | Massey University Privacy Statement
    DSpace software copyright © Duraspace
    v5.7-2020.1-beta1
     

     

    Tweets by @Massey_Research
    Information PagesContent PolicyDepositing content to MROCopyright and Access InformationDeposit LicenseDeposit License SummaryTheses FAQFile FormatsDoctoral Thesis Deposit

    Browse

    All of MROCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

    My Account

    LoginRegister

    Statistics

    View Usage Statistics

    Copyright © Massey University
    | Contact Us | Feedback | Copyright Take Down Request | Massey University Privacy Statement
    DSpace software copyright © Duraspace
    v5.7-2020.1-beta1