B. Elattari et Sa. Gurvitz, Influence of measurement on the lifetime and the linewidth of unstable systems - art. no. 032102, PHYS REV A, 6203(3), 2000, pp. 2102
We investigate the quantum Zeno effect in the case of electron tunneling ou
t of a quantum dot in the presence of continuous monitoring by a detector.
It is shown that the Schrodinger equation for the-whole system can be reduc
ed to Bloch-type rate equations describing the combined time development of
the detector and the measured system. Using these equations we find that c
ontinuous measurement of the unstable system does not affect its exponentia
l decay to a reservoir with a constant density of states. The width of the
energy distribution of the tunneling electron, however, is not equal to the
inverse lifetime-it increases due to the decoherence generated by the dete
ctor. We extend the analysis to the case of a reservoir described by an ene
rgy-dependent density of states, and we show that continuous measurement of
such quantum systems affects both the exponential decay rate and the energ
y distribution, The decay does not always slow down, but might be accelerat
ed The energy distribution of the tunneling electron may reveal the lines i
nvisible before the measurement.