Journal Articles

Permanent URI for this collectionhttps://mro.massey.ac.nz/handle/10179/7915

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Author: search.filters.author.Kottos TSubject: search.filters.subject.01 Mathematical Sciences

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Now showing 1 - 5 of 5
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    Probing localization in absorbing systems via Loschmidt echos.
    (26/06/2009) Bodyfelt JD; Zheng MC; Kottos T; Kuhl U; Stöckmann H-J
    We measure Anderson localization in quasi-one-dimensional waveguides in the presence of absorption by analyzing the echo dynamics due to small perturbations. We specifically show that the inverse participation number of localized modes dictates the decay of the Loschmidt echo, differing from the Gaussian decay expected for diffusive or chaotic systems. Our theory, based on a random matrix modeling, agrees perfectly with scattering echo measurements on a quasi-one-dimensional microwave cavity filled with randomly distributed scatterers.
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    Observation of asymmetric transport in structures with active nonlinearities.
    (7/06/2013) Bender N; Factor S; Bodyfelt JD; Ramezani H; Christodoulides DN; Ellis FM; Kottos T
    A mechanism for asymmetric transport which is based on parity-time-symmetric nonlinearities is presented. We show that in contrast to the case of conservative nonlinearities, an increase of the complementary conductance strength leads to a simultaneous increase of asymmetry and transmittance intensity. We experimentally demonstrate the phenomenon using a pair of coupled Van der Pol oscillators as a reference system, each with complementary anharmonic gain and loss conductances, connected to transmission lines. An equivalent optical setup is also proposed.
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    Critical Fidelity at the Metal-Insulator Transition
    (2006) Bodyfelt JD; Ng G; Kottos T
    Using a Wigner Lorentzian random matrix ensemble, we study the fidelity, F(t), of systems at the Anderson metal-insulator transition, subject to small perturbations that preserve the criticality. We find that there are three decay regimes as perturbation strength increases: the first two are associated with a Gaussian and an exponential decay, respectively, and can be described using linear response theory. For stronger perturbations F(t) decays algebraically as F(t)∼t-D2μ, where D2μ is the correlation dimension of the local density of states
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    Scaling theory of heat transport in quasi-one-dimensional disordered harmonic chains.
    (2013-02) Bodyfelt JD; Zheng MC; Fleischmann R; Kottos T
    We introduce a variant of the banded random matrix ensemble and show, using detailed numerical analysis and theoretical arguments, that the phonon heat current in disordered quasi-one-dimensional lattices obeys a one-parameter scaling law. The resulting β function indicates that an anomalous Fourier law is applicable in the diffusive regime, while in the localization regime the heat current decays exponentially with the sample size. Our approach opens a new way to investigate the effects of Anderson localization in heat conduction based on the powerful ideas of scaling theory.
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    Engineering fidelity echoes in Bose-Hubbard Hamiltonians
    (1/06/2007) Bodyfelt JD; Hiller M; Kottos T
    We analyze the fidelity decay for a system of interacting bosons described by a Bose-Hubbard Hamiltonian. We find echoes associated with "non-universal" structures that dominate the energy landscape of the perturbation operator. Despite their classical origin, these echoes persist deep into the quantum (perturbative) regime and can be described by an improved random matrix modeling. In the opposite limit of strong perturbations (and high enough energies), classical considerations reveal the importance of self-trapping phenomena in the echo efficiency. © Europhysics Letters Association.