{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Find the critical c at which the constant solution

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: dinate. Find the critical c at which the constant solution becomes unstable and turns into an oscillatory solution. Make a schematic plot of ln W vs. , identify the Arrhenius and the tunneling regimes. 3. Decay of supercurrent in a Josephson junction. Consider a Josephson junction shunted by an Ohmic resistor and biased by an external current I . The imaginary time action for this problem is Z m _2 + U ( ) ; I dt + ZZ ( (t) ; (t0 ))2 dt dt0 (4) 2 4 (t ; t0 )2 with U ( ) = Jc(1 ; cos ). a) Write down the saddle-point equation S= = 0. By comparing with the classical _ equations of motion, C V + R;1V + Jc sin = I , 2eV = h _ nd the relation between m and and the junction capacitance and resistance. b) Classically, the supercurrent can ow as long as the e ective potential U ( ) ; I has a local minimum. (For a stationary solution of Jc sin = I , since _ = 0, there is no voltage, and hence no dissipat...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online