Distributed Approximating Functions for Real-Time Quantum Dynamics

Abstract

The application of path integrals to real-time quantum dynamics is of great interest because of the potential for circumventing severe difficulties which make standard scattering calculations for multiparticle systems unfeasible.1–22 These difficulties are consequences of the extremely large matrix dimensions encountered in systems involving more than 3 atoms, or even 3 atom systems involving only heavy atoms. In addition to the rapid increase in computational effort with matrix dimension, the extremely large memory required as basis size becomes large is also a serious problem. However, the Feynman path integral utilizes the coordinate representation, short real-time propagator, so that the local potentials (which are normally encountered in chemical physics) are diagonal, and the kinetic energy portion of the propagator is of a relatively simple form. By compounding the short real-time propagator N-times (for the step τ, so that t = Nτ), the full propagator is obtained approximately as an NG-dimensional integral (the discretized Feynman path integral1). Here, G represents the number of atoms in the system (or if the center of mass motion has been separated, G equals the number of atoms less one). Because N is typically large, such a result suggests that one resort to Monte Carlo methods for evaluating the Feynman amplitude, but the extremely oscillatory nature of the exact short real-time propagator makes such a procedure totally impossible.1–22 KeywordsCoherent StateHermite PolynomialCoordinate RepresentationHermite FunctionFree PropagatorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.