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Vaníček J and Heller EJ (2003), "Uniform semiclassical wave function for coherent two-dimensional electron flow", Physical Review E., January, 2003. Vol. 67(1), pp. 016211.
[Abstract] [BibTeX] [DOI]
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Abstract: We find a uniform semiclassical (SC) wave function describing coherent branched flow through a two-dimensional electron gas (2DEG), a phenomenon recently discovered
by direct imaging of the current using scanned probed microscopy [M.A. Topinka, B.J. LeRoy, S.E.J. Shaw, E.J. Heller, R.M. Westervelt, K.D. Maranowski, and A.C. Gossard, Science 289,
2323 (2000)]. The formation of branches has been explained by classical arguments [M.A. Topinka, B.J. LeRoy, R.M. Westervelt, S.E.J. Shaw, R. Fleischmann, E.J. Heller, K.D.
Maranowski, and A.C. Gossard, Nature (London) 410, 183 (2001)], but the SC simulations necessary to account for the coherence are made difficult by the proliferation of catastrophes
in the phase space. In this paper, expansion in terms of “replacement manifolds” is used to find a uniform SC wave function for a cusp singularity. The method is then generalized and
applied to calculate uniform wave functions for a quantum-map model of coherent flow through a 2DEG. Finally, the quantum-map approximation is dropped and the method is shown to work
for a continuous-time model as well.
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BibTeX:
@article{Vanicek2003,
author = {Vaníček, Jiří and Heller, Eric J.},
title = {Uniform semiclassical wave function for coherent two-dimensional electron flow},
journal = {Physical Review E},
year = {2003},
volume = {67},
number = {1},
pages = {016211},
note = {00028},
doi = {10.1103/PhysRevE.67.016211}
}
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Vaníček J and Heller EJ (2001), "Replacement manifolds: A method to uniformize semiclassical wave functions", Physical Review E., July, 2001. Vol. 64(2), pp. 026215.
[Abstract] [BibTeX] [DOI]
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Abstract: We present a semiclassical technique that relies on replacing complicated classical manifold structure with simpler manifolds, which are then evaluated by the usual
semiclassical rules. Under circumstances where the original manifold structure gives poor or useless results semiclassically the replacement manifolds can yield remarkable accuracy.
We give several working examples to illustrate the theory presented here.
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BibTeX:
@article{Vanicek2001,
author = {Vaníček, Jiří and Heller, Eric J.},
title = {Replacement manifolds: A method to uniformize semiclassical wave functions},
journal = {Physical Review E},
year = {2001},
volume = {64},
number = {2},
pages = {026215},
note = {00012},
doi = {10.1103/PhysRevE.64.026215}
}
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