Energy transport in one-dimensional harmonic chains

Abstract

We study the spatial evaluation of a localized energy pulse in one-dimensional perfect as well as mass-disordered (uncorrelated and correlated) harmonic chains. In the classical case the behavior of the second moment ${\mathit{M}}_{2}$(t) of energy distribution strongly depends on the initial excitations, especially in disordered systems. Two types of initial excitations are considered here, namely (a) impulse excitation and (b) displacement excitation. The excitation is applied at a particular mass of the chain. We have shown that ${\mathit{M}}_{2}$(t) can be expressed in terms of the velocity-velocity correlation function in the case of impulse excitation. On the other hand, it is the energy-current--energy-current correlation function for the displacement excitation. The origin of these results has been shown to appear due to the different kinds of initial occupation probability of the modes of the system. For a perfect harmonic chain the difference is seen at the amplitude of ${\mathit{M}}_{2}$(t). On the other hand, the effect is observed in the time exponent of ${\mathit{M}}_{2}$(t) in disordered systems. The effect of mass correlation on the energy transport is investigated. Our numerical calculations support the analytical results. The possible implications of these results are also mentioned.