Journal ArticleDOI
The Dynamics of a Disordered Linear Chain
TLDR
In this paper, the distribution function of the frequencies of normal modes of vibration of a disordered chain of one-dimensional harmonic oscillators is calculated analytically, in the limit when the chain becomes infinitely long.Abstract:
By a disordered chain we mean a chain of one-dimensional harmonic oscillators, each coupled to its nearest neighbors by harmonic forces, the inertia of each oscillator and the strength of each coupling being a random variable with a known statistical distribution law. A method is presented for calculating exactly the distribution-function of the frequencies of normal modes of vibration of such a chain, in the limit when the chain becomes infinitely long. For some special examples, in which the distribution law of the oscillator parameters is assumed to be of exponential form, the frequency spectra are calculated analytically. The theory applies equally well to a chain of masses connected by elastic springs and making mechanical vibrations, or to an electrical transmission line composed of alternating inductances and capacitances with random characteristics.read more
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Journal ArticleDOI
Об одном классе случайных возмущений иерархического лапласиана@@@On a class of random perturbations of the hierarchical Laplacian
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Ma-Dasgupta renormalization studies of various disordered systems
TL;DR: In this article, the authors describe exact results that can be obtained in various one-dimensional models, either classical or quantum, either for dynamics or statics, with special attention to the off-equilibrium dynamics of a particle diffusing in a Brownian potential or in a trap landscape.
Book ChapterDOI
Anderson Localization of Light: Disorder-Induced Linear, Nonlinear, and Quantum Phenomena
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Noncrossing partition flow and random matrix models.
TL;DR: In this paper, the authors study a generating function flowing from enumerating a set of partitions to the one enumerating the corresponding set of noncrossing partitions; numerical simulations indicate that its limit in the Adjacency random matrix model on bipartite Erdos-Renyi graphs gives a good approximation of the spectral distribution for large average degrees.
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Localization persisting under aperiodic driving
TL;DR: In this article, a disordered spin-1/2 XX chain driven quasi-periodically via a Thue-Morse sequence was identified as a system exhibiting persistent localization under aperiodic driving.