Item

Abstract

Fermi's golden rule describes the decay dynamics of unstable quantum
systems coupled to a reservoir, and predicts a linear decay in time.
Although it arises at relatively short times, the Fermi regime does not
take hold in the earliest stages of the quantum dynamics. The standard
criterion in the literature for the onset time of the Fermi regime is
t(F)similar to 1/Delta omega, with Delta omega the frequency interval
around the resonant transition frequency omega (0) of the system, over
which the coupling to the reservoir does not vary appreciably. In this
work, this criterion is shown to be inappropriate in general for
broadband reservoirs, where the reservoir coupling spectrum takes the
form R (omega)proportional to omega (eta), and for which it is found
that for eta >1, the onset time of the Fermi regime is given by
t(F)proportional to(omega (X)/omega (0))(eta -1)x1/omega (0) where omega
(X) is the high-frequency cutoff of the reservoir. Therefore, the onset
of the Fermi regime can take place at times orders of magnitude larger
than those predicted by the standard criterion. This phenomenon is shown
to be related to the excitation of the off-resonant frequencies of the
reservoir at short times. For broadband reservoirs with eta <= 1, and
for narrowband reservoirs, it is shown that the standard criterion is
correct.