Square root of the monodromy map for the equation of RSJ model of Josephson junction

2018/12/02 by S. I. Tertychniy, Tertychniy, Sergey I.
Computer Science · Physics and Astronomy · #34A25 33E30 34A05 34M15 44A20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1901.01103

openalex publication_date 2018/12/02 · openalex created_date 2019/01/11 · openalex updated_date 2026/07/28

Abstract

Several noteworthy properties of the differential equation utilized for the modeling of Josephson junctions are considered. The explicit representation of the monodromy transform of the space of its solutions is given. In case of positive integer order, the transformation interpreted as the square root of the monodromy transformation noted is derived making use of a symmetry the associated linear second order differential equation possesses.

Related

• The interrelation of the special double confluent Heun equation and the equation of RSJ model of Josephson junction revisited
• Symmetries of the space of solutions to special double confluent Heun equation of negative integer order and its applications
• Representations of Josephson junction on the unit circle and the derivations of Mathieu operators and Fraunhofer patterns
• On monodromy eigenfunctions of Heun equations and boundaries of\n phase-lock areas in a model of overdamped Josephson effect
• The modelling of a Josephson junction and Heun polynomials