Time auto-correlation function and Green-Kubo formula: A study on disordered harmonic chain

Abstract

We have considered heat conduction in a one-dimensional mass disordered harmonic chain of $N$ particles connected to two Langevin type reservoirs at different temperatures. An exact expression for the boundary heat current-current auto-correlation function in the non-equilibrium steady state (NESS) is obtained in terms of non-equilibrium phonon Green's functions. The time integral of the correlation function gives expected result, both in non-equilibrium as well as equilibrium cases. Using the form of this correlation function we show that asymptotic system size dependence of current fluctuation in NESS for a mass disordered harmonic chain is $N^{-\alpha }$ for different boundary conditions. For free and fixed boundary conditions we get $\alpha =1/2$ and 3/2 respectively, while for pinned case the fluctuation decays exponentially with system size.

References in corpus (5)

• Heat Transport in low-dimensional systems
• Fluctuation theorem in quantum heat conduction
• Green-Kubo formula for heat conduction in open systems
• Heat transport in ordered harmonic lattices
• Exact time-averaged thermal conductance for small systems: Comparison between direct calculation and Green-Kubo formalism

Cited by in corpus (3)

• The role of the nature of the noise in the thermal conductance of mechanical systems
• Ballistic Heat Conduction and Mass Disorder in One Dimension
• Stationary state of harmonic chains driven by boundary resetting