  A very weakly coupled linear oscillator is proposed as a detector for
observing time-irreversible characteristics of a quantum system, and it is used
to measure the lifetime during which a classically chaotic quantum system shows
decay of correlation. Except for a particular case where the lifetime agrees
with the conventional Heisenberg time, which is proportional to the Hilbert
space dimension $N$, it is in general much longer: the lifetime increases in
proportion to the product of $N$ and the number of superposed eigenstates, and
is proportional to $N^2$ in the case of full superposition.
