Dynamics, kinetics, and transport properties of the one-dimensional mass-disordered harmonic lattice.

In the present paper we thoroughly investigated the dynamics, kinetics, and the transport properties of the one-dimensional (1D) mass-disordered lattice of harmonic oscillators with the number of particles N < or =5000. The thermostat is simulated by the Langevin sources. Our method is adequate to any 1D lattice with linear equations of motion. Two accurate methods to calculate the temporal behavior of pair correlation functions were developed. The feature of the considered disordered model is an existence of localized states with great relaxation times tau to their stationary states. The exponential growth tau proportional variant exp(N) is observed. A method which allows us to extend the range of computed relaxation times up to tau approximately =(10)300 is suggested. The stationary state is unique. The thermal conduction x has the nonmonotonic character versus N: for the number of particles N < 300 the thermal conduction increases as x proportional variant ln N and reaches the maximal value at N approximately =300. At larger values the decreasing asymptotic is observed: x proportional variant N -alpha, and alpha approximately 0.27. An influence of parameters on the calculated properties was analyzed. Mathematical problems associated with the computation of very large times of establishing the stationary states were extensively studied.