Thermal Rectification in Graded Nonlinear Transmission Lines

We consider heat conduction in a nonlinear inductance-capacitance(LC)transmission line with an inductance gradient by adding white-noise signals.It is found that the heat flux in the direction of inductance decrease is larger than that in the direction of inductance increase.When the low-inductance end is at higher temperature,the phonon density decreases due to conversion to high-frequency phonons,which can not move to the high-inductance end due to its lower cutoff frequency.However,when the high-inductance end is at higher temperature,the loss of phonon density can be compensated for because some high-frequency phonons can move to the low-inductance end dur to its higher cutoff frequency.This leads to the asymmetry of energy transfer.Discussion shows that this asymmetry exists in a particular range of temperatures,and increases with the increase of the difference between heat baths and the inductance gradient.