Abstract
We present a numerical method which allows to efficiently calculate quantum transport through phase-coherent scattering structures, so-called “quantum billiards”. Our approach consists of an extension of the commonly used Recursive Green’s Function Method (RGM), which proceeds by a discretization of the scattering geometry on a lattice with nearest-neighbour coupling. We show that the efficiency of the RGM can be enhanced considerably by choosing symmetry-adapted grids reflecting the shape of the billiard. Combining modules with different grid structure to assemble the entire scattering geometry allows to treat the quantum scattering problem of a large class of systems very efficiently. We will illustrate the computational challenges involved in the calculations and present results that have been obtained with our method.
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Rotter, S., Weingartner, B., Libisch, F., Aigner, F., Feist, J., Burgdörfer, J. (2006). A Modular Method for the Efficient Calculation of Ballistic Transport Through Quantum Billiards. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2005. Lecture Notes in Computer Science, vol 3743. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11666806_67
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DOI: https://doi.org/10.1007/11666806_67
Publisher Name: Springer, Berlin, Heidelberg
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