Brownian motion and classical potential theory by Sidney C. Port

By Sidney C. Port

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60. 61. 62. 63. M. J. M. de Jong and C. W. J. Beenakker, Physica A 230,219 (1996). X. Jehl, M. Sanquer, R Calemczuk and D. Mailly, Nature (London) 405 50 (2000). A. Kozhevnikov, RJ. E. Prober, Phys. Rev. Lett. 84 3398 (2000). X. Jehl and M. Sanquer, Phys. Rev. B 63, 052511 (2001). B. Reulet, A. A. Kozhevnikov, D. E. Prober, W. Belzig, Yu. V. Nazarov, "Phase Sensitive Shot Noise in an Andreev Interferometer", cond-matl0208089 F. Lefloch, C. Hoffmann, M. Sanquer and D. Quirion, "Doubled Full Shot Noise in Quantum Coherent Superconductor - Semiconductor Junctions", cond-matl0208126 M.

In the basis of eigenchannels the transport problem becomes a simple superposition of independent single mode problems without any coupling, and the conductance can be written as 2e 2 G=h~Ti. (2) 2 At this point the definition of eigenchannels may seem somewhat arbitrary and dependent on the number of channels of the perfect leads attached to the sample. For instance, the dimension of the transmission matrix it i can be arbitrarily large depending on the number of modes introduced to represent the leads, which suggests that the number of eigenchannels is not a well defined quantity for a given sample.

Current-current correlation of the chaotic dot junction coupled to the superconductor with M open channels and with normal contacts of N open channels as a function of 2N/ M. In the presence of the proximity effect (solid line) the correlation is positive for 2N < M. Application of a magnetic flux of the order of a flux quantum suppresses the proximity effect and leads to negative correlations (broken line) independent of the ratio of Nand M. After P. Samuelsson and M. Btittiker [41]. (50) is the cross-correlation averaged over an ensemble of cavities.

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