Washboard potential

In previous work, the iGLE and WiGLE models have been illustrated through the use of free-particle, biased, and biased-washboard potentials. Rather than repeat these calculations, in this section we illustrate the dramatic role that the asymmetry in the nonstationary friction can play in the dynamics of the symmetric double-well potential. The specific question to be explored is whether the equilibrium position of the double-well particles is affected by the asymmetry in the nonstationary friction. 

The circuit under consideration consists of a normal coherent conductor with conductance G in series with the Josephson junction(system) (Fig. 1). The system is biased with voltage source V k T/e. This assures that the normal conductor is in the shot noise regime. In addition, we inject extra current p that controls the slope of the Josephson washboard potential. 

If fluctuations are neglected, this system can be described with the celebrated model of resistively shunted junction [5], The normal conductor is a source of non-gaussian current fluctuations that instantly tilt the washboard potential and can lead to an escape of from the minimum. The escape gives rise to an observable voltage pulse. The escape rate in the same or similar systems has been studied for a variety of noise sources and potentials [6, 7, 8, 9],... 

Let us now consider the more interesting case > 1. The simplest realization of such a barrier comprises N 1 Josephson junctions connected in series, this gives U() = NIcsin(/N), 4>o — N. However, this system is formally metastable the vortices can traverse the junction providing phase slips A = 27r. To eliminate this, one would increase the barrier for the vortex formation, for instance, by making several parallel chains of junctions. This would further complicate the concrete function U(4>). We notice that any function U() can be approximated by a cubic parabola if the tilting of the washboard potential is close to the critical value. This is why we choose the cubic parabola form... 

Washboard potential) Here s another way to visualize the dynamics of an overdamped Josephson junction. As in Section 2.7, imagine a particle sliding down a suitable potential. 

The potential in (b) is often called the washboard potential (Van Duzer and... 

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