No classical limit of quantum decay for broad states

Abstract

Though the classical treatment of spontaneous decay leads to an exponential decay law, it is well known that this is an approximation of the quantum mechanical result which is a non-exponential at very small and large times for narrow states. The non exponential nature at large times is however hard to establish from experiments. A method to recover the time evolution of unstable states from a parametrization of the amplitude fitted to data is presented. We apply the method to a realistic example of a very broad state, the sigma meson and reveal that an exponential decay is not a valid approximation at any time for this state. This example derived from experiment, shows the unique nature of broad resonances.

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• Different manifestations of S-matrix poles
• The true quantum face of the "exponential" decay law
• The lowest resonance in QCD from low--energy data
• Regularities in the transformation of the oscillating decay rate in moving unstable quantum systems
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• Time dilation in the oscillating decay laws of moving two-mass unstable quantum states
• A universe born in a metastable false vacuum state needs not die
• On the velocity of moving relativistic unstable quantum systems
• From quantum unstable systems to the decaying dark energy: Cosmological implications
• Cosmological "constant" in a universe born in the metastable false vacuum state
• Quantum Corrections to the Decay Law in Flight