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Abstract: If frequent measurements ascertain whether a quantum system is still in agiven subspace, it remains in that subspace and a quantum Zeno effect takesplace. The limiting time evolution within the projected subspace is calledquantum Zeno dynamics. This phenomenon is related to the limit of a productformula obtained by intertwining the time evolution group with an orthogonalprojection.By introducing a novel product formula we will give a characterization of thequantum Zeno effect for finite-rank projections, in terms of a spectral decayproperty of the Hamiltonian in the range of the projections. Moreover, we willalso characterize its limiting quantum Zeno dynamics and exhibit its notnecessarily lower-bounded generator as a generalized mean value Hamiltonian.

Author: Paolo Facchi, Marilena Ligabò

Source: https://arxiv.org/


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