Quantum Systems: A Mathematical Journey from Few to Many Particles

Wigner transformation approach to surface hopping problem

Qin Li

California Institute of Technology

In quantum molecular dynamics, Born-Oppenheimer approximation breaks down when energy surfaces get close, and transitions between them may happen. We use the Wigner transformation to study to the transition rate near such surface crossing points. We specialize to the case of avoided crossing, and develop a domain decomposition method to solve the numerical problem efficiently.