The Josephson effect and the requirements of causality

✍ Scribed by Richard A. Ferrell

• Publisher: Elsevier Science
• Year: 1988
• Tongue: English
• Weight: 518 KB
• Volume: 152
• Category: Article
• ISSN: 0921-4534
• DOI: 10.1016/0921-4534(88)90068-8

✦ Synopsis

A general treatment is given of the complex conductance, a(to, 0), which describes the linear response of a Josephson junction, biased at phase ~, to an applied voltage oscillating at frequency to. By calculating the transition rate for to larger than tog, the gap frequency, we determine Re a(to, ¢0. The Kramers-Kronig relations then yield a simple expression, in terms of elliptic integrals, for a(to, c)) at all to. This expression includes, in a unified form, both the Josephson effect and the effect of self-capacitance. An explicit result is obtained for the dependence of the Josephson plasma frequency on bias current for very small junctions.