Analogue Hawking radiation from black hole solitons in quantum Josephson transmission lines

Abstract

The nonlinear LC circuit dual to the Toda lattice (voltage) soliton is studied using the reductive perturbation method. It is found that the current flowing through the circuit obeys the defocusing modified Korteweg--de Vries equation with shock-wave-type (current) solitons. The current soliton spatially modulates the nonlinear inductance, equivalently the spatial modulations of electromagnetic wave velocity in the circuit, resulting in the generation of analogue black holes. Hawking radiation from the black holes is also discussed based on the tunneling models.