COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > An Eulerian surface hopping method for the Schr"{o}dinger equation with conical crossings

## An Eulerian surface hopping method for the Schr"{o}dinger equation with conical crossingsAdd to your list(s) Download to your calendar using vCal - Jin, S (Wisconsin-Madison)
- Monday 13 December 2010, 10:00-11:00
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact Mustapha Amrani. Partial Differential Equations in Kinetic Theories In a nucleonic propagation through conical crossings of electronic energy levels, the codimension two conical crossings are the simplest energy level crossings, which affect the Born-Oppenheimer approximation in the zeroth order term. The purpose of this paper is to develop the surface hopping method for the Schr”{o}dinger equation with conical crossings in the Eulerian formulation. The approach is based on the semiclassical approximation governed by the Liouville equations, which are valid away from the conical crossing manifold. At the crossing manifold, electrons hop to another energy level with the probability determined by the Landau-Zener formula. This hopping mechanics is formulated as an interface condition, which is then built into the numerical flux for solving the underlying Liouville equation for each energy level. While a Lagrangian particle method requires the increase in time of the particle numbers, or a large number of statistical samples in a Monte Carlo setting, the advantage of an Eulerian method is that it relies on fixed number of partial differential equations with a uniform in time computational accuracy. We prove the positivity and $l^{1}$-stability and illustrate by several numerical examples the validity and accuracy of the proposed method. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
- Featured lists
- INI info aggregator
- Isaac Newton Institute Seminar Series
- School of Physical Sciences
- Seminar Room 1, Newton Institute
Note that ex-directory lists are not shown. |
## Other listsCambridge Language Sciences Early-Career Researchers Events Empowered Employability Cambridge Social Ontology Group (CSOG)## Other talksDiversity of the human response to malaria The Revolution and Legacy of 1918 in Ukraine Quaternary Discussion Group seminar TO A TRILLION AND BEYOND: THE FUTURE OF COMPUTING AND THE INTERNET OF THINGS - The IET Cambridge Prestige Lecture Development of a Broadly-Neutralising Vaccine against Blood-Stage P. falciparum Malaria Experimental modelling of waves in ice cover |