2002/01/25 by Wojciech Hubert Zurek · 3 citations
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1038/35089017
published as Nature 412, 712-717 (2001) · Published in Nature 412, 712-717 (2001)
arxiv created 2002/01/25 · arxiv updated 2009/12/01
Heisenberg's principle1 states that the product of uncertainties of position and momentum should be no less than Planck's constant ℏ. This is usually taken to imply that phase space structures associated with sub-Planck (≪ ℏ) scales do not exist, or, at the very least, that they do not matter. I show that this deeply ingrained prejudice is false: Non-local "Schrödinger cat" states of quantum systems confined to phase space volume characterized by `the classical action' A ≫ ℏ develop spotty structure on scales corresponding to sub-Planck a = ℏ2 / A ≪ ℏ. Such structures arise especially quickly in quantum versions of classically chaotic systems (such as gases, modelled by chaotic scattering of molecules), that are driven into nonlocal Schrödinger cat -- like superpositions by the quantum manifestations of the exponential sensitivity to perturbations2. Most importantly, these sub-Planck scales are physically significant: a determines sensitivity of a quantum system (or of a quantum environment) to perturbations. Therefore sub-Planck a controls the effectiveness of decoherence and einselection caused by the environment3-8. It may also be relevant in setting limits on sensitivity of Schrödinger cats used as detectors.