Thermal Transport in Phononic Cayley Tree Networks

Abstract

We analytically investigate the heat current $I$ and its thermal fluctuations $\Delta$ in a branching network without loops (Cayley tree). The network consists of two type of harmonic masses: vertex masses $M$ placed at the branching points where phononic scattering occurs and masses $m$ at the bonds between branching points where phonon propagation take place. The network is coupled to thermal reservoirs consisting of one-dimensional harmonic chains of coupled masses $m$. Due to impedance missmatching phenomena, both $\mathcal{I}$ and $\Delta$, are non-monotonic functions of the mass ratio $\mu =M/m$. In particular, there are cases where they are strictly zero below some critical value ${\mu }^{\ast }$.

References in corpus (14)

• Thermal conduction in classical low-dimensional lattices
• Phononics: Manipulating heat flow with electronic analogs and beyond
• Heat Transport in low-dimensional systems
• Thermal conductivity of graphene flakes: Comparison with bulk graphite
• Negative Differential Conductance and Hot Phonons in Suspended Nanotube Molecular Wires
• Berry-Phase induced Heat Pumping and its Impact on the Fluctuation Theorem
• Fluctuation theorem in quantum heat conduction
• Heat conduction in the disordered harmonic chain revisited
• Cayley Trees and Bethe Lattices, a concise analysis for mathematicians and physicists
• Effect of phonon scattering by surface roughness on the universal thermal conductance
• Fourier law in the alternate mass hard-core potential chain
• Generating Function Formula of Heat Transfer in Harmonic Networks
• Cumulant generating function formula of heat transfer in ballistic system with lead-lead coupling
• Random Matrix Theory approach to Mesoscopic Fluctuations of Heat Current

Cited by in corpus (1)

• Resistor-network anomalies in the heat transport of random harmonic chain