Geodesic
Basic modeling of openness, quantum states and transport in two- and three-dimensional ballistic cavities
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 3 (2010) no. 3, pp. 280-288.

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A basic model for particle states and current flow in open quantum dots/billiards are investigated. The model is unconventional and extends the use of complex potentials first introduced in phenomenological nuclear inelastic scattering theory (the optical model). Attached leads/source drain are represented by complex potentials. Probability densities and currents flows for open 2D quantum dots/billiards are calculated and the results are compared with microwave measurements used to emulate the dot. We also apply the model to a rectangular enclosure and report on helical flows guided by nodal lines and disc-like accumulations of flow lines. The model is of conceptual as well as practical and educational interest.
Keywords: nano-scale systems, quantum dots, microwave billiards, quantum transport, vortices, helical motion, streamlines. 
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Karl-Fredrik Berggren; Iryna I. Yakimenko. Basic modeling of openness, quantum states and transport in two- and three-dimensional ballistic cavities. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 3 (2010) no. 3, pp. 280-288. http://geodesic.mathdoc.fr/item/JSFU_2010_3_3_a1/

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