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
Disorder and interaction in chiral chains: Majoranas versus complex fermions
TL;DR: In this article, the authors studied the low-energy physics of a chain of Majorana fermions in the presence of interaction and disorder, emphasizing the difference between Majoranas and conventional (complex) Fermions.
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Singularities in spectra of disordered systems
TL;DR: A review of singularities in the spectral density of random harmonic chains can be found in this article, where the singularity in the density of states near the low energy band edge for systems with arbitrary disorder in dimensions d = 1, 2, 3.
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Non-monotonic disorder-induced enhanced tunnelling
TL;DR: In this article, the quantum-mechanical transmission through a disordered tunnel barrier is investigated analytically in the following regime: (correlation range of the random potential) (penetration length) (barrier length).
Journal ArticleDOI
Mean-Field Phase Diagram for Bose-Hubbard Hamiltonians with Random Hopping
TL;DR: In this paper, the zero temperature phase diagram for ultracold bosons in a random 1D potential is obtained through a site decoupling mean-field scheme performed over a Bose-Hubbard (BH) Hamiltonian, whose hopping term is considered as a random variable.
Journal ArticleDOI
Transverse Meissner physics of planar superconductors with columnar pins
TL;DR: In this paper, the authors present exact results for the Bose glass phase transition in (1+1) dimensions, obtained by mapping the problem in the hard core limit onto one-dimensional fermions described by a non-Hermitian tight binding model.