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 saddlepoint 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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 Fall '04
 LeonidLevitov
 Physics, Josephson junction, metastable state, cubic parabola, bounce path, nite temperature

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