On the adjacency quantization in an equation modeling the Josephson effect

DOI10.1007/s10688-014-0070-zzbMath1370.37143arXiv1301.7159OpenAlexW2124071088MaRDI QIDQ2342089

Yanyan Li

Publication date: 8 May 2015

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.7159

zbMATH Keywords

monodromyordinary differential equationrotation numberStokes operatorArnold tongueirregular singularityJosephson effect

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Dynamical systems in solid mechanics (37N15) Statistical mechanics of superconductors (82D55) Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain (34M40) Linear ordinary differential equations and systems in the complex domain (34M03)

Related Items (11)

On families of constrictions in model of overdamped Josephson junction and Painlevé 3 equation* ⋮ The Hess-Appelrot case and quantization of the rotation number ⋮ Solution space monodromy of a special double confluent Heun equation and its applications ⋮ On monodromy eigenfunctions of Heun equations and boundaries of phase-lock areas in a model of overdamped Josephson effect ⋮ On constrictions of phase-lock areas in model of overdamped Josephson effect and transition matrix of the double-confluent Heun equation ⋮ On determinants of modified Bessel functions and entire solutions of double confluent Heun equations ⋮ On spectral curves and complexified boundaries of the phase-lock areas in a model of Josephson junction ⋮ Unnamed Item ⋮ The rotation number integer quantization effect in braid groups ⋮ On families of constrictions in the model of an overdamped Josephson junction ⋮ Holomorphic solutions of the double confluent Heun equation associated with the RSJ model of the Josephson junction

Cites Work

• Phase-lock effect for equations modeling resistively shunted Josephson junctions and for their perturbations
• Birkhoff invariants and Stokes' multipliers for meromorphic linear differential equations
• Birkhoff invariants and effective calculations for meromorphic linear differential equations. I
• Geometry of the Prytz planimeter
• Rotation number quantization effect
• Galois groups, Stokes operators and a theorem of Ramis
• Asymptotic properties of Arnold tongues and Josephson effect
• A system on a torus modelling the dynamics of a Josephson junction
• Stokes phenomena
• On properties of the differential equation describing the dynamics of an overdamped Josephson junction
• Unnamed Item
• Unnamed Item

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