【摘 要】
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Recent experiments and numerical simulations have shown that disorder in mesoscopic systems can be of fractal(self-similar)type.Conductance of such systems
【机 构】
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Ulyanovsk State University,Department of Theoretical Physics,Russia
【出 处】
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The 5th International Conference on Nonlinear Science and Co
论文部分内容阅读
Recent experiments and numerical simulations have shown that disorder in mesoscopic systems can be of fractal(self-similar)type.Conductance of such systems can not be described in frames of the quasi-one-dimensional(1D)Dorokhov-Mello Pereyra-Kumar(DMPK)approach and its multidimentional generalizations.We derive a fractional analogue of the DMPK-equation for the joint probability distribution of the transmission eigenvalues in case of fractal disorder characterized by a heavytailed distribution of distances between scatterers.The equation contains fractional derivative describing the non-locality of the process,its solutions are related to the Levy stable statistics.Analytical results agree with Monte-Carlo simulations of disordered wires and with particular results obtained in [C.W.J.Beenakker et al.,Phys.Rev.B 79,024204(2009)] and [F.Falceto & V.Gopar,Europhys.Lett.92,57014(2010)].The results are also applicable to description of conductance through 1D system with sublocalized electrons and light transmission through fractal photonic quasi-1D wires.
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