A hybrid Schrödinger/Gaussian beam solver for quantum barriers and surface hopping

Pages: 1097 - 1120, Volume 4, Issue 4, December 2011

doi:10.3934/krm.2011.4.1097       Abstract        References        Full Text (1803.7K)       Related Articles

Shi Jin - Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, WI 53706, United States (email)
Peng Qi - Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, WI 53706, United States (email)

Abstract: In this paper, we propose a hybrid method coupling a Schrödinger solver and the Gaussian beam method for the numerical simulation of quantum tunneling through potential barriers or surface hopping across electronic potential energy surfaces. The idea is to use a Schrödinger solver near potential barriers or zones where potential energy surfaces cross, and the Gaussian beam method--which is much more efficient than a direct Schrödinger solver--elsewhere. Buffer zones are used to convert data between the Schrödinger solver and the Gaussian beam solver. Numerical examples show that this method indeed captures quantum tunneling and surface hopping accurately, with a computational cost much lower than a direct quantum solver in the entire domain.

Keywords:  Gaussian beam, Time-splitting spectral method, Surface hopping, quantum tunneling.
Mathematics Subject Classification:  Primary: 58F15, 58F17; Secondary: 53C35.

Received: May 2011;      Revised: October 2011;      Published: November 2011.

 References