Quantum Josephson D/A converter driven by trains of short 2π-pulses

Buchstaber, Victor Matveevich; Karpov, O. V.; Tertychniy, S. I.

doi:10.1109/cpem.2002.1034942

Cited by 3 publications

(5 citation statements)

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“…• The next important point is the intimate connection (first mentioned by V. Buchstaber, see, e.g., Ref. [13]) between (1) and a simple linear system of the two first order ODEs (5). For (co)sinusoidal rhs function (2), the latter takes the form (3).…”

Section: Discussionmentioning

confidence: 92%

“…Next, the functions E(z) and E # (z) are linearly independent for nonzero κ. Indeed, utilizing (13), one finds…”

Section: Floquet Solutions Of Dche and Involutive Solution Mapsmentioning

confidence: 99%

“…(48) together with stipulation for the analyticity of E(z) can be considered as the equivalent to Eq. (13). Additionally, Eq.…”

Section: Floquet Solutions Of Dche and Involutive Solution Mapsmentioning

confidence: 99%

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General solution of overdamped Josephson junction equation in the case of phase-lock

Tertychniy

2007

Preprint

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The first order nonlinear ODE φ(t) + sin ϕ(t) = B + A cos ωt, (A, B, ω are real constants) which is commonly used as a simple model of an overdamped Josephson junction in superconductors is investigated. Its general solution is obtained in the case of the choice of parameters associated with one of three possible kinds of asymptotic behavior of solutions known as phase-lock where all but one solutions converge to a common 'essentially periodic' attractor. The general solution is represented in explicit form in terms of the Floquet solution of a particular instance of the double confluent Heun equation (DCHE). In turn, the solution of DCHE is represented through the Laurent series which defines an analytic function on the Riemann sphere with punctured poles. The Laurent series coefficients are given in explicit form in terms of infinite products of 2 × 2 matrices with a single zero element. The closed form of the phase-lock condition is obtained which is represented as the condition of existence of a real root of the transcendental function. The phase-lock criterion is conjectured whose plausibility is confirmed in numerical tests.

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Section: Discussionmentioning

confidence: 92%

“…Next, the functions E(z) and E # (z) are linearly independent for nonzero κ. Indeed, utilizing (13), one finds…”

Section: Floquet Solutions Of Dche and Involutive Solution Mapsmentioning

confidence: 99%

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General solution of overdamped Josephson junction equation in the case of phase-lock

Tertychniy

2007

Preprint

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“…Легко убедиться, что при выполнении (1) они удовлетворяют следующей системе линейных однородных уравнений c периодическими коэффициентами [15], [16]:…”

Section: голоморфные решения и их свойстваunclassified

“…В. М. БУХШТАБЕР, С. И. ТЕРТЫЧНЫЙ Уравнению (1) соответствует система из двух линейных дифференциальных уравнений с периодическими коэффициентами [15], [16]. На рис.…”

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