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Unconventional decay law for excited states in closed many-body systems

V. V. Flambaum·F. M. Izrailev
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Abstract

We study the time evolution of an initially excited many-body state in a finite system of interacting Fermi-particles in the situation when the interaction gives rise to the ``chaotic'' structure of compound states. This situation is generic for highly excited many-particle states in quantum systems, such as heavy nuclei, complex atoms, quantum dots, spin systems, and quantum computers. For a strong interaction the leading term for the return probability $W(t)$ has the form $W(t)\simeq \exp (-Δ_E^2t^2)$ with $Δ_E^2$ as the variance of the strength function. The conventional exponential linear dependence $W(t)=C\exp (-Γt)$ formally arises for a very large time. However, the prefactor $C$ turns out to be exponentially large, thus resulting in a strong difference from the conventional estimate for $W(t)$.

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V. V. Flambaum, F. M. Izrailev. 2001-02-17. Unconventional decay law for excited states in closed many-body systems. https://doi.org/10.1103/physreve.64.026124

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