Speaker: Prof. David J. Tannor, Weizmann Institute of Science

Title:  How did Pauli Miss It: An Exact Formulation of Quantum Mechanics with Complex Trajectories

Abstract: Ever since the advent of Quantum Mechanics, there has been a quest for a trajectory based formulation of quantum theory that is exact. In the 1950's, David Bohm, buiding on earlier work of Madelung and de Broglie, developed an exact formulation of quantum mechanics in which trajectories evolve in the presence of the usual Newtonian force plus an additional quantum force. In recent years, there has been a resurgence of interest in Bohmian Mechanics as a numerical tool because of its apparently local dynamics, which could lead to a significant computational advantages for the simulation of large  quantum systems. However, closer inspection of the Bohmian formulation reveals that the nonlocality of quantum mechanics has not disappeared - it has simply been swept under the rug into quantum force. In this work, we present a new formulation of Bohmian mechanics in which the quantum action, S, is taken to be complex. This requires the propagation of complex trajectories, but with the reward of a significantly higher degree of localization. For example, using strictly localized trajectories (no communication with their neighbors) we obtain extremely accurate quantum mechanical transmission probabilities down to 10^{-7}. We have recently extended the formulation to include interference effects, which has been one of the major obstacles in conventional Bohmian mechanics. Applications to one- and two-dimensional transmission, thermal rate constants in one and two dimensions, the calculation of eigenvalues and nonadiabatic transitions will be presented. A variation on the method allows for the calculation of thermal rate constants and eigenvalues using just one or two zero-velocity trajectories. On the formal side, the approach is shown to be a rigorous extension of generalized Gaussian wavepacket methods to give exact quantum mechanics, and has intriguing implications for fundamental quantum mechanics.

For more information, please contact:

Svetlana Malinovskaya
Associate Professor
Burchard
Room 509
Phone: 201.216.8094
Fax: 201.216.5638
smalinov@stevens.edu

flyer David Tannor