Zeno dynamics and constraints

Abstract

We investigate some examples of quantum Zeno dynamics, when a system undergoes very frequent (projective) measurements that ascertain whether it is within a given spatial region. In agreement with previously obtained results, the evolution is found to be unitary and the generator of the Zeno dynamics is the Hamiltonian with hard-wall (Dirichlet) boundary conditions. By using a new approach to this problem, this result is found to be valid in an arbitrary $N$-dimensional compact domain. We then propose some preliminary ideas concerning the algebra of observables in the projected region and finally look at the case of a projection onto a lower dimensional space: in such a situation the Zeno ansatz turns out to be a procedure to impose constraints.

21 pages

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Cited by in corpus (8)

• Quantum Zeno dynamics: mathematical and physical aspects
• Quantum Zeno dynamics and quantum Zeno subspaces
• Disclosing hidden information in the quantum Zeno effect: Pulsed measurement of the quantum time of arrival
• Non-Markovianity during quantum Zeno effect
• Zeno dynamics in wave-packet diffraction spreading
• Sufficient conditions for the anti-Zeno effect
• Entropy of the Information Retrieved from Black Holes
• The geometry of the quantum Zeno effect