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Josephson junctions were theoretically proposed as threshold detectors of the Full Counting Statistics (FCS) several years ago [1, 2]. Since then there have been increasing efforts to implement the concept [3, 4] as well as to refine and extend the original theory to experimentally more relevant cases [5-7]. Despite this intensive effort, the initial promises associated with the method haven't been realized yet.
I will present a theory for the evaluation of the exponential part of non-equilibrium escape rates due to the non-Gaussian noise which unifies and extends the previous attempts [5-7]. It's based on the semiclassical calculation of the action of an effective dynamical system representing the stochastic problem in the limit of the weak noise. Further, I will review the present experimental status of the field and compare the experimental findings with the theoretical predictions. I will argue that the persistent discrepancy is most likely due to insufficient precision of the theoretical evaluation of the escape rates. Evaluation of the exponential prefactor of the escape rates, i.e. going beyond the lowest order approximation to the quasi-classical action seems to be the next goal which should be addressed by the theorists in order to achieve quantitative comparison with the experimental results. This task is, however, very difficult to achieve due to non-analyticities of the involved action [8]. Possible atttitudes towards this problem will be discussed including the evaluation of the suitability of the threshold detection of FCS, especially with Josephson junctions. References [1] J. Tobiska and Yu.V. Nazarov, Phys. Rev. Lett. 93, 106801 (2004) [2] J. Pekola, Phys. Rev. Lett. 93, 206601 (2004) [3] A. V. Timofeev et al., Phys. Rev. Lett. 98, 207001 (2007) [4] B. Huard et al., Annalen der Physik 16, 10-11 (2007) 736 [5] J. Ankerhold, Phys. Rev. Lett. 98, 036601 (2007) [6] E. V. Sukhorukov and A. N. Jordan, Phys. Rev. Lett. 98, 136803 (2007) [7] H. Grabert, Phys. Rev. B 77, 205315 (2008) [8] P. Hänggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990) |
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