Monte Carlo Bohmian Dynamics from Trajectory Stability Properties

• Published in: The journal of physical chemistry. A, Molecules, spectroscopy, kinetics, environment, & general theory Molecules, spectroscopy, kinetics, environment, & general theory, 2004-06, Vol.108 (25), p.5408-5416
• Main Authors: Liu, Jian, Makri, Nancy
• Format: Article
• Language: English
• ISSN: 1089-5639; 1520-5215
• DOI: 10.1021/jp040149n

It is shown that the quantum force in the Bohmian formulation of quantum mechanics can be related to the stability properties of the given trajectory. In turn, the evolution of the stability properties is governed by higher order derivatives of the quantum potential, leading to an infinite hierarchy of coupled differential equations whose solution specifies completely all aspects of the dynamics. Neglecting derivatives of the quantum potential beyond a certain order allows truncation of the hierarchy, leading to approximate Bohmian trajectories. Use of the method in conjunction with Bohmian initial value formulations [J. Chem. Phys. 2003, 119, 60] gives rise to simple position-space representations of observables or time correlation functions. These are analogous to approximate quasiclassical expressions based on the Wigner or Husimi phase space density but involve lower dimensional integrals with smoother integrands and avoid the costly evaluation of phase space transforms. The lowest-order version of the truncated hierarchy can capture large corrections to classical mechanical treatments and yields (with fewer trajectories) results that are somewhat more accurate than those based on quasiclassical phase space treatments.