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Fluctuation of heat flow along one dimensional linear conducting chain

Welles Antonio Martinez Morgado 1 ; Michael Moraes Cândido 1 ; Silvio Manuel Duarte Queirós 2
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Anomalous conductivity is a strong characteristic of linear chains. The main reason for it is the ballistic way phonons propagate in these systems. It would be expected that non-linear systems would fix that problem due to the phonon-phonon coupling present in them. However, due to their crumpled one dimensional topology, non-linearity is not sufficient to effectively diffuse heat under non-equilibrium conditions, namely under distinct temperatures at its extremities. Indeed, it is well known that even non-linear higher dimensional systems do not satisfy Fourier law as well.

The one dimensional model is thus a source of intriguing anomalies that might be of interest due to its applicability to experimental nano-scale systems such as nano-wires, nanotubes (as objects that make the crossover between 1D and 2D), and many more. In fact, thermal properties for these systems are still quite hard to access experimentally.

The use of classical models might give us insight on some of the more important properties for these systems. The heat flux has already been extensively studied for them, in special how to eliminate the anomalous behaviour mentioned earlier and make them obey Fourier Law. Several techniques have been developed such as self-consistent thermal reservoirs along the chain, effective interactions with external particles, and mass dispersion among others.

However, higher moments of the heat flux have not been extensively explored despite the fact that they bring important information about the organization of the energy transport throughout the chain.

In this spirit, we have studied them by means of exactly solving the coupled Langevin equations that define the dynamics of the system. We have found interesting properties, such as the non-dependence of chain length for the transmission of higher order fluctuations. We are going to report on these results and show how they are necessary to form a complete and consistent picture of heat conduction for the harmonic chain.