Depinning of kinks in a Josephson-junction ratchet array

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 61, Issue 3, 2000, Pages 2257-2266

  Trias E ^a   Mazo, J J ^a,b   Falo, F ^b   Orlando, T P ^a  

^a Department of Electrical Engineering and Computer Science   (United States)

^b CSIC   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

LOCAL AREA NETWORKS; QUANTUM OPTICS;

APPLIED CURRENT; APPLIED FIELD; CIRCULAR ARRAYS; JOSEPHSON-JUNCTION; OTHER PROPERTIES; PARALLEL ARRAYS; RATCHET POTENTIAL; REFLECTION SYMMETRY;

JOSEPHSON JUNCTION DEVICES;

EID: 0038158647     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.61.2257     Document Type: Article

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18. To derive the circuit equations we need to apply both Kirchhoff’s current law (KCL) at the nodes and Kirchhoff’s voltage law (KVL) for each loop. In circuits with Josephson junctions, KVL is superseded by the more stringent requirement of flux quantization. Flux quantization gives a constraint on the flux of a loop while KVL only constrains the derivative of the flux, i.e. the voltage. Satisfying flux quantization automatically satisfies KVL.
19. We have used the Josephson-voltage relation (Formula presented) and set the damping (Formula presented) to (Formula presented). The damping is usually referred to as the Stewart-McCumber parameter (Formula presented).
20. In the case of an open array, where open boundary conditions must be imposed, (Formula presented) (Formula presented) and (Formula presented) otherwise.
21. There are several ways of calculating the periodicity in M of the sine-Gordon equation (regular array). Probably the most straightforward is to find a transformation that moves the M dependence from the boundary conditions to the sine term. In the case of the regular discrete sine-Gordon equation the new phases are just (Formula presented). Then M appears only in (Formula presented) and the periodicity of the equations in M is just (Formula presented). Though this approach can also be used in an inhomogeneous ring, it is not trivial to guess the correct transformation.
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