Quantum Zeno effect and dynamics

Details Quantum Zeno effect and dynamics Quantum Zeno effect and dynamics

2009-11-11

arxiv.org/abs/0911.2201v1

J. Math. Phys. 51, 022103 (2010)

Physics

Mathematical Physics

15 pages, 1 figure

Scientific paper

10.1063/1.3290971

If frequent measurements ascertain whether a quantum system is still in a given subspace, it remains in that subspace and a quantum Zeno effect takes place. The limiting time evolution within the projected subspace is called quantum Zeno dynamics. This phenomenon is related to the limit of a product formula obtained by intertwining the time evolution group with an orthogonal projection. By introducing a novel product formula we will give a characterization of the quantum Zeno effect for finite-rank projections, in terms of a spectral decay property of the Hamiltonian in the range of the projections. Moreover, we will also characterize its limiting quantum Zeno dynamics and exhibit its (not necessarily lower-bounded) generator as a generalized mean value Hamiltonian.

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