problemset10

this requires the external current to be in the

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Unformatted text preview: ion.) This requires the external current to be in the range ;Jc < I < Jc. In such a case, the decay of supercurrent is controlled by quantum and thermal uctuations. The decay is described by the system (4) tunneling out a local minimum of U ( ) ; I . To determine the decay rate, one has to nd a classical bounce trajectory in imaginary time, as it was done in problem 1 in the absence of dissipation, = 0. How are these results modi ed for tunneling in a dissipative system? Caldeira and Leggett pointed out that the bounce solution can be constructed in an analytic form for the highly overdamped regime, � m= , where is the time of tunneling (3). In this case, by a dimensional estimate, one shows that the kinetic energy term m _2 =2 is small compared to the dissipative term and thus can be dropped. Further simpli cation can be achieved near the classical stability threshold, where the e ective potential can be replaced by a cubic parabola (1) with a = Jc ; I , b = 1...
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