ﻻ يوجد ملخص باللغة العربية
A usual assumption in the so-called {it de Broglie - Bohm} approach to quantum dynamics is that the quantum trajectories subject to typical `guiding wavefunctions turn to be quite irregular, i.e. {it chaotic} (in the dynamical systems sense). In the present paper, we consider mainly cases in which the quantum trajectories are {it ordered}, i.e. they have zero Lyapunov characteristic numbers. We use perturbative methods to establish the existence of such trajectories from a theoretical point of view, while we analyze their properties via numerical experiments. Using a 2D harmonic oscillator system, we first establish conditions under which a trajectory can be shown to avoid close encounters with a moving nodal point, thus avoiding the source of chaos in this system. We then consider series expansions for trajectories both in the interior and the exterior of the domain covered by nodal lines, probing the domain of convergence as well as how successful the series are in comparison with numerical computations or regular trajectories. We then examine a H{e}non - Heiles system possessing regular trajectories, thus generalizing previous results. Finally, we explore a key issue of physical interest in the context of the de Broglie - Bohm formalism, namely the influence of order in the so-called {it quantum relaxation} effect. We show that the existence of regular trajectories poses restrictions to the quantum relaxation process, and we give examples in which the relaxation is suppressed even when we consider initial ensembles of only chaotic trajectories, provided, however, that the system as a whole is characterized by a certain degree of order.
De Broglie - Bohm (dBB) theory is a deterministic theory, built for reproducing almost all Quantum Mechanics (QM) predictions, where position plays the role of a hidden variable. It was recently shown that different coincidence patterns are predicted
This paper examines the nature of classical correspondence in the case of coherent states at the level of quantum trajectories. We first show that for a harmonic oscillator, the coherent state complex quantum trajectories and the complex classical tr
We use an alternative interpretation of quantum mechanics, based on the Bohmian trajectory approach, and show that the quantum effects can be included in the classical equation of motion via a conformal transformation on the background metric. We app
In this paper we present the Feynman-de Broglie-Bohm propagator for a semiclassical formulation of the Gross-Pitaeviskii equation.
A non-relativistic quantum mechanical theory is proposed that combines elements of Bohmian mechanics and of Everetts many-worlds interpretation. The resulting theory has the advantage of resolving known issues of both theories, as well as those of st