Nature of the stochastic processes defined by Bohm’s momentum and quantum force

Abstract

The nature of the stochastic process defined by Bohm's momentum is elucidated for stationary energy eigenstates and nonstationary states in classically nonchaotic and chaotic Hamiltonian systems. In addition, the nature of the stochastic process defined by Bohm's quantum force is elucidated for stationary energy eigenstates in nonchaotic and chaotic systems, and for nonstationary states in nonchaotic systems. From these results, the following can be concluded. For stationary energy eigenstates, the process defined by the momentum is generically a stationary, Dirac-delta process in both nonchaotic and chaotic systems; in contrast, the process defined by the quantum force is nongeneric. For nonstationary states, the processes defined by the momentum and quantum force are both nongeneric in nonchaotic systems. Furthermore, for nonstationary states, the process defined by the momentum is, with a high level of confidence, a stationary, stable, brown (f - 2 power spectrum) process in the chaotic kicked pendulum. It is conjectured that this is also true for other chaotic systems. The preceding conclusion and conjecture complement those in [Phys. Rev. A 63. 042105 (2001)] for the process defined by the quantum force for nonstationary states in chaotic systems.