Monday 12:00, 31.10.11
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, building 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 (BM) as a numerical tool because of its apparently local dynamics. 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 the 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 are able to obtain one- and two-dimensional tunneling, interference, thermal rate constants and eigenvalues. Recently we have extended the method to non-adiabatic transitions, where rather than hopping from surface to surface the trajectories affect their counterparts on the other surfaces via the difference in their complex phase. On the formal side, the approach is shown to be a rigorous extension of generalized Gaussian wavepacket methods to obtain exact quantum mechanics, and has intriguing implications for fundamental quantum mechanics.