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# Find the critical c at which the constant solution

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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...
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