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波米安轨迹是真的吗？半经典系统中de Broglie-Bohm与经典动力学的动力学失配

Are Bohmian trajectories real? On the dynamical mismatch between de Broglie-Bohm and classical dynamics in semiclassical systems

A. Matzkin, V. Nurock

备注：
Figures downgraded to low resolution. V2:Minor changes
发表信息：
Studies in Hist. and Philosophy of Science B, 39, 17, 2008. [Published version is slightly different and carries the title "Classical and Bohmian trajectories in semiclassical systems: Mismatch in dynamics, mismatch in reality?" ]
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摘要：

德布罗意-玻姆对量子力学的解释旨在通过点状粒子遵循明确轨道的运动来给出量子现象的实在论描述。这项工作是由德布罗意玻姆帐户的性质的半经典系统。半经典系统是表现出经典轨迹的量子系统：这种系统的波函数和可观测性质取决于量子系统的经典对应物的轨迹。例如，量子性质有规则或无序的方面，这取决于底层的经典系统是否具有规则或混沌动力学。相比之下，半经典系统中的玻姆轨线与经典对应物的轨线几乎没有共同之处，相对于这些系统中可见的量子-经典对应，产生了动力学失配。我们的目的是描述这种不匹配（明确的插图），解释其起源，并检查一些后果的状态Bohmian轨迹在半经典系统。我们认为，特别是半经典系统把更强的约束的经验接受性和可接受性的Bohmian轨迹，因为通常的参数，以消除经典和德布罗意-玻姆运动之间的不匹配被削弱的发生在量子波函数的经典轨迹，这样的系统。

英文摘要：

The de Broglie-Bohm interpretation of quantum mechanics aims to give a realist description of quantum phenomena in terms of the motion of point-like particles following well-defined trajectories. This work is concerned by the de Broglie-Bohm account of the properties of semiclassical systems. Semiclassical systems are quantum systems that display the manifestation of classical trajectories: the wavefunction and the observable properties of such systems depend on the trajectories of the classical counterpart of the quantum system. For example the quantum properties have a regular or disordered aspect depending on whether the underlying classical system has regular or chaotic dynamics. In contrast, Bohmian trajectories in semiclassical systems have little in common with the trajectories of the classical counterpart, creating a dynamical mismatch relative to the quantum-classical correspondence visible in these systems. Our aim is to describe this mismatch (explicit illustrations are given), explain its origin, and examine some of the consequences on the status of Bohmian trajectories in semiclassical systems. We argue in particular that semiclassical systems put stronger constraints on the empirical acceptability and plausibility of Bohmian trajectories because the usual arguments given to dismiss the mismatch between the classical and the de Broglie-Bohm motions are weakened by the occurrence of classical trajectories in the quantum wavefunction of such systems.

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