Details
| Original language | English |
|---|---|
| Pages (from-to) | 543-569 |
| Number of pages | 27 |
| Journal | Comm. Math. Phys. |
| Volume | 320 |
| Publication status | Published - 2013 |
Abstract
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In: Comm. Math. Phys., Vol. 320, 2013, p. 543-569.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Recurrence for discrete time unitary evolutions
AU - Grünbaum, F. A.
AU - Velázquez, L.
AU - Werner, A. H.
AU - Werner, R. F.
PY - 2013
Y1 - 2013
N2 - We consider quantum dynamical systems specified by a unitary operator U and an initial state vector phi. In each step the unitary is followed by a projective measurement checking whether the system has returned to the initial state. We call the system recurrent if this eventually happens with probability one. We show that recurrence is equivalent to the absence of an absolutely continuous part from the spectral measure of U with respect to for which we give a topological interpretation. A key role in our theory is played by the first arrival amplitudes, which turn out to be the (complex conjugated) Taylor coefficients of the Schur function of the spectral measure. On the one hand, this provides a direct dynamical interpretation of these coefficients; on the other hand it links our definition of first return times to a large body of mathematical literature.
AB - We consider quantum dynamical systems specified by a unitary operator U and an initial state vector phi. In each step the unitary is followed by a projective measurement checking whether the system has returned to the initial state. We call the system recurrent if this eventually happens with probability one. We show that recurrence is equivalent to the absence of an absolutely continuous part from the spectral measure of U with respect to for which we give a topological interpretation. A key role in our theory is played by the first arrival amplitudes, which turn out to be the (complex conjugated) Taylor coefficients of the Schur function of the spectral measure. On the one hand, this provides a direct dynamical interpretation of these coefficients; on the other hand it links our definition of first return times to a large body of mathematical literature.
U2 - 10.1007/s00220-012-1645-2
DO - 10.1007/s00220-012-1645-2
M3 - Article
VL - 320
SP - 543
EP - 569
JO - Comm. Math. Phys.
JF - Comm. Math. Phys.
SN - 1432-0916
ER -