$t$ as a result, although it seems to need to assume that each measurement is an instantaneous ideal measurement. The decay of the system can be slowed down or even prevented. This is called quantum Zeno eect. The problem was discussed in Beskow-Nilsson [BN], Misra-Sudarshan [MS]. Zeno is a Greek philosopher who said something like “A flying arrow does not fly”. The aim of this talk is to present the following product formula on quantum Zeno dynamics. This note is mainly based on the joint work with P.Exner [EI]. Theorem. Let $H$ be a nonnegative selfadjoint operator in a separable Hilbert space $ \mathcal{H}$$t$ as a result, although it seems to need to assume that each measurement is an instantaneous ideal measurement. The decay of the system can be slowed down or even prevented. This is called quantum Zeno eect. The problem was discussed in Beskow-Nilsson [BN], Misra-Sudarshan [MS]. Zeno is a Greek philosopher who said something like “A flying arrow does not fly”. The aim of this talk is to present the following product formula on quantum Zeno dynamics. This note is mainly based on the joint work with P.Exner [EI]. Theorem. Let $H$ be a nonnegative selfadjoint operator in a separable Hilbert space $ \mathcal{H}$

Jan 1, 20060 citations

Bell and Zeno

Karl Gustafson

International Journal of Theoretical PhysicsNov 1, 20055 citations

Zeno and Anti-Zeno Dynamics

Gershon Kurizki, Abraham G. Kofman, V. M. Akulin +2 more

NATO science series. Series II, Mathematics, physics and chemistryJan 1, 20050 citations

Quantum Zeno effect and dynamics

Paolo Facchi A, Marilena Ligabò

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 bounded from below) generator as a generalized mean value Hamiltonian.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 bounded from below) generator as a generalized mean value Hamiltonian.

arXiv:0911.2201Journal of Mathematical PhysicsFeb 1, 201042 citations

t

as a result, although it seems to need to assume that each measurement is an instantaneous ideal measurement. The decay of the system can be slowed down or even prevented. This is called quantum Zeno eect. The problem was discussed in Beskow-Nilsson [BN], Misra-Sudarshan [MS]. Zeno is a Greek philosopher who said something like “A flying arrow does not fly”. The aim of this talk is to present the following product formula on quantum Zeno dynamics. This note is mainly based on the joint work with P.Exner [EI]. Theorem. Let

H

be a nonnegative selfadjoint operator in a separable Hilbert space $ \mathcal{H}$