Energy transport in a one-dimensional harmonic ternary chain with Ornstein–Uhlenbeck disorder

Abstract

In this paper we study a one-dimensional ternary harmonic chain with the mass distribution constructed from an Ornstein–Uhlenbeck process. We generate a ternary mass disordered distribution by generating the correlated Ornstein–Uhlenbeck process and mapping it into a sequence of three different values. The probability of each value is controlled by a fixed parameter b. We analyze the localization aspect of the above model by numerical solution of the Hamilton equations and by the transfer matrix formalism. Our results indicate that the correlated ternary mass distribution does not promote the appearance of new extended modes. In good agreement with previous work, we obtain extended modes for b → ∞; however, we explain in detail the main issue behind this apparent localization– delocalization transition. In addition, we obtain the energy dynamics for this classical chain.