Fractal Dynamics in Chaotic Quantum Transport
arXiv:1210.3815 · doi:10.1103/PhysRevE.88.022913
Abstract
Despite several experiments on chaotic quantum transport in two-dimensional systems such as semiconductor quantum dots, corresponding quantum simulations within a real-space model have been out of reach so far. Here we carry out quantum transport calculations in real space and real time for a two-dimensional stadium cavity that shows chaotic dynamics. By applying a large set of magnetic fields we obtain a complete picture of magnetoconductance that indicates fractal scaling. In the calculations of the fractality we use detrended fluctuation analysis -- a widely used method in time series analysis -- and show its usefulness in the interpretation of the conductance curves. Comparison with a standard method to extract the fractal dimension leads to consistent results that, in turn, qualitatively agree with the previous experimental data.
to appear in Phys. Rev. E (2013)
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