Disturbance spreading in incommensurate and quasiperiodic systems

Details Disturbance spreading in incommensurate and quasiperiodic systems Disturbance spreading in incommensurate and quasiperiodic systems

2000-02-16

arxiv.org/abs/cond-mat/0002235v1

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1103/PhysRevB.61.9414

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.

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