Anomalous thermal conductivity and local temperature distribution on harmonic Fibonacci chains

TL;DR

This study investigates heat conduction in harmonic Fibonacci chains, revealing anomalous thermal conductivity and complex local temperature patterns, challenging the Fourier law due to their quasiperiodic structure and critical eigenstates.

Contribution

It demonstrates that harmonic Fibonacci chains exhibit non-standard heat conduction behavior, with heat current diminishing as (ln N)^{-1} and non-uniform temperature distributions, highlighting the impact of quasiperiodicity.

Findings

Heat current scales as (ln N)^{-1} with system size.

Local temperature oscillates strongly along the chain.

Fourier law does not hold in harmonic Fibonacci chains.

Abstract

The harmonic Fibonacci chain, which is one of a quasiperiodic chain constructed with a recursion relation, has a singular continuous frequency-spectrum and critical eigenstates. The validity of the Fourier law is examined for the harmonic Fibonacci chain with stochastic heat baths at both ends by investigating the system size N dependence of the heat current J and the local temperature distribution. It is shown that J asymptotically behaves as (ln N)^{-1} and the local temperature strongly oscillates along the chain. These results indicate that the Fourier law does not hold on the harmonic Fibonacci chain. Furthermore the local temperature exhibits two different distribution according to the generation of the Fibonacci chain, i.e., the local temperature distribution does not have a definite form in the thermodynamic limit. The relations between N-dependence of J and the frequency-spectrum, and between the local temperature and critical eigenstates are discussed.