Disturbance spreading in incommensurate and quasiperiodic systems

Abstract

The propagation of an initially localized excitation in one dimensional incommensurate, quasiperiodic and random systems is investigated numerically. It is discovered that the time evolution of variances ${\sigma }^2(t)$ of atom displacements depends on the initial condition. For the initial condition with nonzero momentum, ${\sigma }^2(t)$ goes as $t^{\alpha }$ with $\alpha =1$ and 0 for incommensurate Frenkel-Kontorova (FK) model at $V$ below and above $V_c$ respectively; and $\alpha =1$ for uniform, quasiperiodic and random chains. It is also found that $\alpha =1-\beta$ with $\beta$ the exponent of distribution function of frequency at zero frequency, i.e., $\rho (\omega )\sim {\omega }^{\beta }$ (as $\omega \to 0$). For the initial condition with zero momentum, $\alpha =0$ for all systems studied. The underlying physical meaning of this diffusive behavior is discussed.

8 Revtex Pages, 5 PS figures included, to appear in Phys. Rev. B April 2000

References in corpus (7)

• Formation and manipulation of a metallic wire of single gold atoms
• Heat conduction in one dimensional chains
• Anomalous Thermal Transport in Quantum Wires
• Energy transport and correlation between two attractors connected by Fermi-Pasta-Ulam chain
• The quantum Frenkel-Kontorova model: a squeezed state approach
• Ground state wavefunction of the quantum Frenkel-Kontorova model
• Conductance of a Mott Quantum Wire

Cited by in corpus (5)

• Bulk and boundary zero-bias anomaly in multi-wall carbon nanotubes
• Nonlinear lattice waves in heterogeneous media
• Wave interactions in localizing media - a coin with many faces
• Electronic properties of the 1D Frenkel-Kontorova model
• Nonclassical properties of electronic states of aperiodic chains in a homogeneous electric field