Shock wave in series connected Josephson transmission line: Theoretical foundations and effects of resistive elements

TL;DR

This paper provides a theoretical analysis of shock wave behavior in Josephson transmission lines with ohmic dissipation, revealing how different resistor placements affect shock broadening and propagation velocity.

Contribution

It introduces a comprehensive theoretical framework for understanding shock waves in dissipative Josephson transmission lines, including the effects of various resistor configurations.

Findings

Shock broadening occurs when resistors are shunted across junctions or ground capacitors.

Shock propagation velocity remains unaffected by ohmic resistors.

An alternative expansion fan solution is formulated for dissipative JTLs.

Abstract

We analytically study shock wave in the Josephson transmission line (JTL) in the presence of ohmic dissipation. When ohmic resistors shunt the Josephson junctions (JJ) or are introduced in series with the ground capacitors the shock is broadened. When ohmic resistors are in series with the JJ, the shock remains sharp, same as it was in the absence of dissipation. In all the cases considered, ohmic resistors don't influence the shock propagation velocity. We study an alternative to the shock wave - an expansion fan - in the framework of the simple wave approximation for the dissipationless JTL and formulate the generalization of the approximation for the JTL with ohmic dissipation.