# Time auto-correlation function and Green-Kubo formula: A study on disordered harmonic chain - Condensed Matter > Statistical Mechanics

Time auto-correlation function and Green-Kubo formula: A study on disordered harmonic chain - Condensed Matter > Statistical Mechanics - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: We have considered heat conduction in a one-dimensional mass disorderedharmonic chain of $N$ particles connected to two Langevin type reservoirs atdifferent temperatures. An exact expression for the boundary heatcurrent-current auto-correlation function in the non-equilibrium steady stateNESS is obtained in terms of non-equilibrium phonon Green-s functions. Thetime integral of the correlation function gives expected result, both innon-equilibrium as well as equilibrium cases. Using the form of thiscorrelation function we show that asymptotic system size dependence of currentfluctuation in NESS for a mass disordered harmonic chain is $N^{-\alpha}$ fordifferent boundary conditions. For free and fixed boundary conditions we get$\alpha=1-2$ and 3-2 respectively, while for pinned case the fluctuation decaysexponentially with system size.

Autor: Anupam Kundu

Fuente: https://arxiv.org/