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
Citations
More filters
Journal ArticleDOI
On the spectrum of the hierarchical Laplacian
Alexander Bendikov,Paweł Krupski +1 more
TL;DR: The hierarchical Laplacian (L_C) as mentioned in this paper is a non-negative definite, self-adjoint operator in the hierarchical lattice of F.J. Dyson.
Journal ArticleDOI
Magic-angle semimetals with chiral symmetry
TL;DR: In this article, a two-dimensional, chirally symmetric model of Dirac electrons subjected to a quasiperiodic modulation is introduced, which harbors a rich phase diagram at the Dirac node energy: a semimetal phase with Dirac dispersion, a ''chiral metal'' phase with a nontrivial real space structure, and subdiffusive dynamics and Chalker scaling.
Journal ArticleDOI
A unification of the Holstein polaron and dynamic disorder pictures of charge transport in organic semiconductors
TL;DR: In this article, a unified and nonperturbative method for calculating spectral and transport properties of Hamiltonians with simultaneous Holstein and Peierls (off-diagonal) electron-phonon coupling is presented.
Journal ArticleDOI
The classical β-ensembles with β proportional to 1/N: From loop equations to Dyson’s disordered chain
Peter J. Forrester,G. Mazzuca +1 more
TL;DR: In this article, the Gauss hypergeometric differential equation determining the Stieltjes transform of the limiting density in the Jacobi case is identified, and the moments and covariances of monomial linear statistics are characterized through recurrence relations.
Journal ArticleDOI
Coherent potential theory for interacting bands: Phonons and excitons in substitutionally disordered molecular crystals
Hwei-Kwan Hong,Raoul Kopelman +1 more
TL;DR: A coherent potential approximation (CPA) theory for disordered molecular solids with interacting bands is proposed in this article, which has a wide range of applications including electronic states coupled via vibronic or spin-orbit couplings, vibrational states with degeneracies in the gas phase or coupled by Fermi resonance, triplet magnetic sublevels coupled via exciton interactions, and phonons in general.