Time evolution of unstable quantum states and a resolution of Zeno's paradox

C. B. Chiu, E. C. G. Sudarshan, and B. Misra
Phys. Rev. D 16, 520 – Published 15 July 1977
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Abstract

The time evolution of quantum states for unstable particles can be conveniently divided into three domains: the very short time where Zeno's paradox is relevant, the intermediate interval where the exponential decay holds more or less, and the very long time where the decay is governed by a power law. In this work, we reexamine several questions relating to the deviations from the simple exponential decay law. On the basis of general considerations, we demonstrate that deviations from exponential decay near t=0 are inevitable. We formulate general resonance models for the decay. From analytic solutions to specific narrow-width models, we estimate the time parameters T1 and T2 separating the three domains. The parameter T1 is found to be much much less than the lifetime Γ1, while T2 is much greater than the lifetime. For instance, for the charged pion decay, T11014Γ and T2190Γ. A resolution of Zeno's paradox provided by the present consideration and its limitaions are discussed.

  • Received 29 October 1976

DOI:https://doi.org/10.1103/PhysRevD.16.520

©1977 American Physical Society

Authors & Affiliations

C. B. Chiu* and E. C. G. Sudarshan*

  • Center for Particle Theory, Department of Physics, The University of Texas, Austin, Texas 78712

B. Misra

  • Service de Chimie Physique II, Brussels 1050, Belgium
  • Center for Statistical Mechanics and Thermodynamics, Department of Physics, The University of Texas, Austin, Texas 78712

  • *Work supported in part by the Energy Research and Development Administration under Contract No. E(40-1)3992.

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Vol. 16, Iss. 2 — 15 July 1977

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