Critical points and trajectories of the Bohmian quantum flow

A. Tzemos, G. Contopoulos
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Abstract

In the present work we study the critical points of the Bohmian quantum flow, namely the nodal point and its associated X-point, which are responsible for the generation of chaos in Bohmian trajectories. In the first part of the paper we find an analytical equation for the position of the X-point in a planar 2-d Bohmian system with a single nodal point and test its accuracy numerically. We then calculate its asymptotic curves and comment on the way they affect the evolution of the nearby Bohmian trajectories. In the second part we present our first results on the position of the X-point and its asymptotic curves in a 3d partially integrable system, where the Bohmian trajectories evolve on spherical surfaces.
波西米亚量子流的临界点和轨迹
在本工作中,我们研究了波希曼量子流的临界点,即节点及其相关的x点,它们负责波希曼轨迹中混沌的产生。本文第一部分给出了平面二维单节点波西米亚系统x点位置的解析方程,并对其精度进行了数值验证。然后,我们计算了它的渐近曲线,并评论了它们如何影响附近波西米亚轨迹的演变。在第二部分中,我们给出了在球面上波西米亚轨迹演化的三维部分可积系统中x点的位置及其渐近曲线的初步结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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