**abstract:**
We consider a dynamical quantum process starting at a pure state \phi. In
each step a fixed unitary operator U is applied followed by a projective
measurement whether or not the particle is back at the initial state.
The data are completely described by a measure on the unit circle, namely
the \phi-expectation of spectral measure of U. We find that the process is
recurrent (i.e., eventually returns with probability 1) if and only if the
measure has no absolutely continuous part. In the recurrent case the
expected return time is either infinite or an integer. This is paradoxical,
since it implies that the return time, unlike all probabilities pertaining
to experiments of finite duration, is a discontinuous function of the data.
This is resolved by interpreting the expected return time as a winding
number.
(joint work with A Grünbaum, L. Velázques, A.H. Werner)

Wed 13 Nov, 15:00 - 16:00, Sala Stemmi

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