Are quantum trajectories suitable for semiclassical approximations?

TL;DR

This paper examines whether quantum trajectories in the de Broglie-Bohm interpretation are suitable for semiclassical approximations, highlighting their differences from classical trajectories and implications for understanding quantum-classical transition.

Contribution

It analyzes the properties of quantum trajectories in the de Broglie-Bohm framework and their suitability for semiclassical methods, especially in systems with classical chaos.

Findings

Quantum trajectories depend on quantum potential, altering classical trajectory characteristics.

Quantum trajectories can be chaotic even in integrable systems.

The discrepancy challenges the classical-quantum transition understanding.

Abstract

The quantum trajectories in the de Broglie-Bohm formulation of quantum mechanics depend on an additional quantum potential derived from the full wave solution of Schr\"odinger's equation. The task of supplying collectively all the correct quantum results strongly alters the characteristics of the corresponding classical trajectories, which underlie semiclassical approximations to the evolving wave function. Both classical and quantum trajectories are here considered to be conservative with no influence of an external environment, even though this is the source of eventual classicality in quantum systems, that is, decoherence. The concept of integrability, closely correspondent in classical and quantum mechanics, is not preserved by the quantum trajectories. General systems, in which classical chaotic motion participates, are much harder to treat semiclassically, but quantum trajectories can be chaotic even for integrable systems. This discrepancy between the character of classical and quantum trajectories in the de Broglie-Bohm interpretation does not clarify the singular classical-quantum transition.