Using semiclassical trajectories for the time-evolution of interacting quantum-mechanical systems

Abstract

We have developed a method that recasts the time-propagation of dynamic, mutually interacting quantum-mechanical wavefunctions principally as the time-evolution of many classical particles. Our approach utilizes an approximation of Feynman path integrals, known as the semiclassical method, to reduce the path integral to only the “classical” paths connecting the wavefunction at one time step to the next. In exchange for simplifying the path sampling, each classical path’s contribution gains a determinant term dependent on the path and its environment. Like virtual particles in quantum field theory, “virtual classical particles” are said to follow these classical paths. Pushing these virtual classical particles provides the necessary data to evolve quantum wavefunctions in time. Particle-based techniques implemented on parallel computers can then be used to propagate quantum systems using this alternative method.