Possible curvature effects in the Josephson junction

Dobrowolski, Tomasz

doi:10.1140/epjb/e2013-30222-6

Cited by 10 publications

(5 citation statements)

References 44 publications

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“…The equations (20) are the starting point for the derivation of the Fokker -Planck equation described in appendix A. The stationary solution of this equation is the following…”

Section: The Influence Of Thermal Fluctuations On the Kink Motionmentioning

confidence: 99%

“…where we used formula (7) and bias current mean value (8). Similarly, formula (20) leads to the expression…”

Section: Acknowledgementsmentioning

confidence: 99%

“…The effects of arbitrary curvature on fluxon motion in curved Josephson junctions were studied in articles [17,18,19,20,21] with curvatures playing the role of potential barriers for kink motion. In particular in [22] the different simplified effective descriptions were compared in order to choose the most suitable for the considered system.…”

Section: Introductionmentioning

confidence: 99%

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The impact of thermal noise on kink propagation through a heterogeneous system

Gatlik¹,

Dobrowolski²

2022

Preprint

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“…The equations (20) are the starting point for the derivation of the Fokker -Planck equation described in appendix A. The stationary solution of this equation is the following…”

Section: The Influence Of Thermal Fluctuations On the Kink Motionmentioning

confidence: 99%

“…where we used formula (7) and bias current mean value (8). Similarly, formula (20) leads to the expression…”

Section: Acknowledgementsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The impact of thermal noise on kink propagation through a heterogeneous system

Gatlik¹,

Dobrowolski²

2022

Preprint

Self Cite

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“…The particle motion on a given curved surface M 2 is an interesting problem in a wide range fields in physics, for example, the diffusion or brownian motion [1], [2], the fluid dynamics [3], the pattern formation [4], Josephson effect [5], morphogenesis of melanoma in medical science [6], chemical biology [7], quantum mechanics [8], [9], [10], [11], and so on. In our study we first explain the diffusion process, and then study the quantum mechanics on such a manifold.…”

Section: Geometrical Toolsmentioning

confidence: 99%

Geometric Flow Appearing in Conservation Law in Classical and Quantum Mechanics

Ogawa¹

2019

GIQ

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The appearance of a geometric flow in the conservation law of particle number in classical particle diffusion and in the conservation law of probability in quantum mechanics is discussed in the geometrical environment of a two-dimensional curved surface with thickness ǫ embedded in R3. In such a system with a small thickness ǫ, the usual two-dimensional conservation law does not hold and we find an anomaly by using the equation ∂ρ/∂t + ∇ (2) i J i = 0, where ρ is the two-dimensional density, J i is the two-dimensional flow, and ∇(2) i is the two-dimensional covariant derivative. The anomalous term is obtained by the expansion of ǫ. We find that this term has a Gaussian and mean curvature dependence and can be written as the total divergence of some geometric flow J i G . In total, we have ∂ρ ∂t + ∇(2) i (J i + J i G ) = 0. This fact holds in both classical and quantum mechanics when we confine particles to a curved surface with a small thickness.

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“…In consideration of these facts and since some quantum-mechanical models in non-Euclidean space are used for construction of phenomenological models of component particles and nanoparticles [6][7][8], we suppose that nonlinear model could help to improve some of them. In addition, non-trivial curvature, which is not originated by geometry of space, have an effect on some physical processes [9]. Moreover, some models of a superconductor in a non-Euclidean space † y.kurochkin@dragon.bas-net.by play significant role for field-theoretic models with a dynamically break symmetry [10,11] and for models that are constructed on holographic methods for condensed matter [12].…”

Section: Introductionmentioning

confidence: 99%

Ginzburg--Landau Model in Three Dimensional Lobachevsky Space

Kurochkin¹,

Rybak²

2014

Acta Phys. Pol. B

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We consider the Ginzburg-Landau model of a superconductor in three dimensional Lobachevsky space. Generally, covariant Ginzburg-Landau equations were derived and two types of solutions of these equations were obtained: with a flat and cylindrically symmetric boarders of superconductors. The first case is considered in the quasi-Cartesian coordinates system and it is shown that when the radius of curvature of Lobachevsky space ρ is less than a double quantity of the London penetration depth λ, magnetic field might increase with penetration depth. In the second case, which studies cylindrically symmetric superconductor, it is shown that magnetic field depends on two coordinates: depth penetration and coordinate along the surface of the superconductor. When radius of curvature ρ of Lobachevsky space goes to infinity, derived solutions and equations will go to the usual Ginzburg-Landau model in flat space.

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Possible curvature effects in the Josephson junction

Cited by 10 publications

References 44 publications

The impact of thermal noise on kink propagation through a heterogeneous system

The impact of thermal noise on kink propagation through a heterogeneous system

Geometric Flow Appearing in Conservation Law in Classical and Quantum Mechanics

Ginzburg--Landau Model in Three Dimensional Lobachevsky Space

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