# Physics and applications of Josephson effect by Antonio Barone

By Antonio Barone

This ebook surveys all points of the Josephson effect-from the underlying actual conception to genuine and proposed engineering purposes. either ends of this spectrum are fascinating. The actual concept is novel and critical for plenty of macroscopic quantum results, that have a wealthy and but untapped power for technical improvement. we try right here to offer greater than a survey and no more than an exhaustive exposition of this extensive box. instead of to hide every little thing, we have now attempted to discover these facets of thought, fabrication know-how, and equipment program that might be of lasting worth.

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1), wn,n+1 is the probability that per unit time interval a primary building unit is added to a cluster consisting initially of n such units. The clusters are assumed to be of spherical shape with a radius R. ∆Φ in Eq. 1) is the change of the (relevant for the given boundary conditions) thermodynamic potential resulting from the formation of a cluster consisting of n building units. The cluster-size distribution function f (n, t) obeys the boundary condition f (n → 0, t) = c(t). 3) 42 3 Kinetics of Nucleation–Growth Processes: The First Stages The actual concentration c(t) of single particles is given hereby by the mass-balance equation ∞ c0 = c(t) + nf (n, t) dn.

77) with νiα and taking the sum over all components, we get with Eqs. 78) and dn =− dt 1 d∆G(n) . 79) A comparison with Eq. 80) with 1 (+) wn,n+1 = k . 81) (+) wni ;ni +1 i=1 Similarly, we can also express the change of the volume of a cluster of the new phase consisting of n ambient phase units. The change of the volume of a cluster of the new phase can generally be written as k dVα = −4πR2 ωiα ji . 82) With Eq. 70), we get dVα = dt k ωiα i=1 dni . 84) resulting in dVα dn = dt dt k ωiα νiα i=1 .

62) with similar consequences. Finally, in the derivation of the basic equations for the determination of the emission coefﬁcients, it was not utilized that the temperature in the cluster has to be the same as in the surrounding ambient phase. Therefore, the method is equally well applicable to phase formation under nonisothermal conditions. In this case, the values of the chemical potential have to be taken at the respective temperatures of the clusters and the ambient phase. , Ref. [306]).