Related papers: Study of the localization-delocalization transitio…
We study numerically the disorder-induced localization-delocalization phase transitions that occur for mass and spring constant disorder in a three-dimensional cubic lattice with harmonic couplings. We show that, while the phase diagrams…
We analytically study phonon transmission and localization in random superlattices by using a Green's function approach. We derive expressions for the average transmission rate and localization length, or Lyapunov exponent, in terms of the…
We study, theoretically and numerically, a minimal model for phonons in a disordered system. For sufficient disorder, the vibrational modes of this classical system can become Anderson localized, yet this problem has received significantly…
Anderson transition of the phonon modes is studied numerically. The critical exponent for the divergence of the localization length is estimated using the transfer matrix method, and the statistics of the modes is analyzed. The latter is…
We study the localization properties of normal modes in harmonic chains with mass and spring weak disorder. Using a perturbative approach, an expression for the localization length is obtained, which is valid for arbitrary correlations of…
The diatomic linear chain of masses coupled by harmonic springs is a textboook model for vibrational normal modes (phonons) in crystals. In addition to propagating acoustic and optic branches, this model is known to support a ``gap mode''…
The Anderson transitions in a random magnetic field in three dimensions are investigated numerically. The critical behavior near the transition point is analyzed in detail by means of the transfer matrix method with high accuracy for…
The principle and the efficiency of the Monte Carlo transfer-matrix algorithm are discussed. Enhancements of this algorithm are illustrated by applications to several phase transitions in lattice spin models. We demonstrate how the…
We introduce transfer matrices to describe the motion of particles in the vicinity of the stable and unstable fixed points of longitudinal phase space and use them to analyze the transfer of bunches between radio-frequency systems operating…
Using a quantum map version of one-dimensional Anderson model, the localization-delocalization transition of quantum diffusion induced by coherent dynamical perturbation is investigated in comparison with quantum standard map. Existence of…
We consider the localization properties of a lattice of coupled masses and springs with random mass and spring constant values. We establish the full phase diagrams of the system for pure mass and pure spring disorder. The phase diagrams…
Localizing linearly moving sound sources using microphone arrays is challenging as the transient nature of the signal leads to relatively short observation periods. Commonly, a moving focus is used and most methods operate at least…
Density functional perturbation theory calculations of alpha-quartz using extended norm conserving pseudopotentials have been used to study the elastic properties and phonon dispersion relations along various high symmetry directions as a…
The density matrix renormalization group method is used to investigate the spin-Peierls transition for Heisenberg spins coupled to quantized phonons. We use a phonon spectrum that interpolates between a gapped, dispersionless (Einstein)…
In this paper, we present an asymptotic model describing localised flexural vibrations along a structured ring containing point masses or spring-mass resonators in an elastic plate. The values for the required masses and stiffnesses of…
It was previously found that at high temperature the lowest part of the QCD Dirac spectrum consists of localized modes obeying Poisson statistics. Higher up in the spectrum, modes become delocalized and their statistics can be described by…
We study the hopping transport of a quantum particle through randomly diluted percolation clusters in two dimensions realized both on the square and triangular lattices. We investigate the nature of localization of the particle by…
We examine quantum percolation on a square lattice with random dilution up to $q=38%$ and energy $0.001 \le E \le 1.6$ (measured in units of the hopping matrix element), using numerical calculations of the transmission coefficient at a much…
Quasiperiodic long range order is intermediate between spatial periodicity and disorder, and the excitations in 1D quasiperiodic systems are believed to be transitional between extended and localized. These ideas are tested with a numerical…
This paper presents a simple ball-and-spring model for the propagation of small amplitude vibrations in a granular material. In this model, the positional disorder in the sample is ignored and the particles are placed on the vertices of a…