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March 2010 A coherent semiclassical transport model for pure-state quantum scattering
Shi Jin, Kyle A. Novak
Commun. Math. Sci. 8(1): 253-275 (March 2010).


We present a time-dependent semiclassical transport model for coherent pure-state scattering with quantum barriers. The model is based on a complex-valued Liouville equation, with interface conditions at quantum barriers computed from the steady-state Schrödinger equation. By retaining the phase information at the barrier, this coherent model adequately describes quantum scattering and interference at quantum barriers, with a computational cost comparable to that of classical mechanics. We construct both Eulerian and Lagrangian numerical methods for this model, and validate it using several numerical examples, including multiple quantum barriers.


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Shi Jin. Kyle A. Novak. "A coherent semiclassical transport model for pure-state quantum scattering." Commun. Math. Sci. 8 (1) 253 - 275, March 2010.


Published: March 2010
First available in Project Euclid: 23 February 2010

zbMATH: 1191.82043
MathSciNet: MR2655909

Primary: 65M06 , 65Z05 , 81Q20 , 81S30 , 81T80

Keywords: Coherent , Liouville , Multiscale method , quantum barrier , semiclassical limit

Rights: Copyright © 2010 International Press of Boston

Vol.8 • No. 1 • March 2010
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