On germs of constriction curves in model of overdamped Josephson junction, dynamical isomonodromic foliation and Painlev\'e 3 equation

A Glutsyuk - arxiv preprint arxiv:2308.04310, 2023 - arxiv.org
B. Josephson (Nobel Prize, 1973) predicted tunnelling effect for a system (called Josephson
junction) of two superconductors separated by a narrow dielectric: existence of a …

Holomorphic solutions of the double confluent Heun equation associated with the RSJ model of the Josephson junction

VM Buchstaber, SI Tertychnyi - Theoretical and Mathematical Physics, 2015 - Springer
This work is a continuation of research on a first-order nonlinear differential equation applied
in the overshunted model of the Josephson junction. The approach is based on the relation …

On monodromy eigenfunctions of Heun equations and boundaries of phase-lock areas in a model of overdamped Josephson effect

VM Buchstaber, AA Glutsyuk - Proceedings of the Steklov Institute of …, 2017 - Springer
We study a family of double confluent Heun equations of the form LE= 0, where L= L λ, μ, n
is a family of second-order differential operators acting on germs of holomorphic functions of …

On determinants of modified Bessel functions and entire solutions of double confluent Heun equations

VM Buchstaber, AA Glutsyuk - Nonlinearity, 2016 - iopscience.iop.org
We investigate the question on existence of entire solutions of well-known linear differential
equations that are linearizations of nonlinear equations modeling the Josephson effect in …

On families of constrictions in model of overdamped Josephson junction and Painlevé 3 equation

Y Bibilo, AA Glutsyuk - Nonlinearity, 2022 - iopscience.iop.org
The tunnelling effect predicted by Josephson (Nobel Prize, 1973) concerns the Josephson
junction: two superconductors separated by a narrow dielectric. It states existence of a …

Chiral tunneling through generic one-dimensional potential barriers in bilayer graphene

V Kleptsyn, A Okunev, I Schurov, D Zubov… - Physical Review B, 2015 - APS
We study tunneling of charge carriers in single-and bilayer graphene. We propose an
explanation for nonzero “magic angles” with 100% transmission for the case of symmetric …

On the adjacency quantization in an equation modeling the Josephson effect

AA Glutsyuk, VA Kleptsyn, DA Filimonov… - Functional Analysis and …, 2014 - Springer
We study a two-parameter family of nonautonomous ordinary differential equations on the 2-
torus. This family models the Josephson effect in superconductivity. We study its rotation …

On constrictions of phase-lock areas in model of overdamped Josephson effect and transition matrix of the double-confluent Heun equation

AA Glutsyuk - Journal of Dynamical and Control Systems, 2019 - Springer
In 1973, B. Josephson received a Nobel Prize for discovering a new fundamental effect
concerning a Josephson junction,—a system of two superconductors separated by a very …

Extended Model of Josephson Junction, Linear Systems with Polynomial Solutions, Determinantal Surfaces, and Painlevé III Equations

AA Glutsyuk - Proceedings of the Steklov Institute of Mathematics, 2024 - Springer
We consider a three-parameter family of linear special double confluent Heun equations
introduced and studied by VM Buchstaber and SI Tertychniy, which is an equivalent …

Josephson effect and slow-fast systems

V Kleptsyn, O Romaskevich, I Schurov - arxiv preprint arxiv:1305.6755, 2013 - arxiv.org
In order to model the processes taking place in systems with Josephson contacts, a
differential equation on a torus with three parameters is used. One of the parameters of the …