Showing papers on "Quantum evolution published in 1997"
TL;DR: In this article, a pseudo or quantal entropy of a pure state reveals significant dynamical features during a unitary evolution, in a way with the entropy of "basis mixing" and can be used as a dynamic descriptor for the onset of quantum chaos.
13 citations
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TL;DR: The quantum view of dynamical chaos, as an attempt to resolve these contradictions guided by the correspondence principle and based upon the characteristic time scales of quantum evolution, is explained in this paper.
Abstract: Interrelations between dynamical and statistical laws in physics, on the one hand, and between the classical and quantum mechanics, on the other hand, are discussed with emphasis on the new phenomenon of dynamical chaos. The principal results of the studies into chaos in classical mechanics are presented in some detail, including the strong local instability and robustness of the motion, continuity of both the phase space as well as the motion spectrum, and time reversibility but nonrecurrency of statistical evolution, within the general picture of chaos as a specific case of dynamical behavior. Analysis of the apparently very deep and challenging contradictions of this picture with the quantum principles is given. The quantum view of dynamical chaos, as an attempt to resolve these contradictions guided by the correspondence principle and based upon the characteristic time scales of quantum evolution, is explained. The picture of the quantum chaos as a new generic dynamical phenomenon is outlined together with a few other examples of such a chaos including linear (classical) waves and digital computer. I conclude with discussion of the two fundamental physical problems: the quantum measurement (\psi-collapse), and the causality principle which both appear to be related to the phenomenon of dynamical chaos.
9 citations
TL;DR: Wu et al. as mentioned in this paper showed that the analysis and the main result of the article by L-A. Wu [Phys. Rev. A 53, 2053] are completely erroneous.
Abstract: It is shown that the analysis and the main result of the article by L-A. Wu [Phys. Rev. A 53, 2053 (1996)] are completely erroneous.
5 citations
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TL;DR: In this article, the nonadiabatic geometric phase in a time dependent quantum evolution is shown to provide an intrinsic concept of time having dual properties relative to the external time, and a nontrivial extension of the ordinary quantum mechanics is thus obtained with interesting scaling laws.
Abstract: The nonadiabatic geometric phase in a time dependent quantum evolution is shown to provide an intrinsic concept of time having dual properties relative to the external time. A nontrivial extension of the ordinary quantum mechanics is thus obtained with interesting scaling laws. A fractal like structure in time is thus revealed.