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The temporal evolution of an unstable quantum mechanical system undergoing repeated measurements is investigated. In general, by changing the time interval between successive measurements, the decay can be accelerated (inverse quantum Zeno effect) or slowed down (quantum Zeno effect), depending on the features of the interaction Hamiltonian. A geometric… (More)

Received (received date) Revised (revised date) 1 2 Temporal behavior of quantum mechanical systems The temporal behavior of quantum mechanical systems is reviewed. We mainly focus our attention on the time development of the so-called " survival " probability of those systems that are initially prepared in eigenstates of the unperturbed Hamiltonian, by… (More)

If frequent measurements ascertain whether a quantum system is still in its initial state, transitions to other states are hindered and the quantum Zeno effect takes place. However, in its broader formulation, the quantum Zeno effect does not necessarily freeze everything. On the contrary, for frequent projections onto a multidimensional subspace, the… (More)

- Paolo Facchi, Saverio Pascazio
- Physical review letters
- 2002

The quantum Zeno effect is recast in terms of an adiabatic theorem when the measurement is described as the dynamical coupling to another quantum system that plays the role of apparatus. A few significant examples are proposed and their practical relevance discussed. We also focus on decoherence-free subspaces.

A pairwise clustering approach is applied to the analysis of the Dow Jones index companies, in order to identify similar temporal behavior of the traded stock prices. To this end, the chaotic map clustering algorithm is used, where a map is associated to each company and the correlation coefficients of the financial time series are associated to the… (More)

The quantum Zeno evolution of a quantum system takes place in a proper subspace of the total Hilbert space. The physical and mathematical features of the “Zeno subspaces” depend on the measuring apparatus: when this is included in the quantum description, the Zeno effect becomes a mere consequence of the dynamics and, remarkably, can be cast in terms of an… (More)

A quantum Zeno dynamics can be obtained by means of frequent measurements, frequent unitary kicks or a strong continuous coupling and yields a partition of the total Hilbert space into quantum Zeno subspaces, among which any transition is hindered. We focus on the “continuous” version of the quantum Zeno effect and look at several interesting examples. We… (More)

We investigate a few examples of quantum Zeno dynamics, when a system undergoes very frequent (projective) measurements that ascertain whether it is within a given spatial region. The evolution is found to be unitary and the generator of the Zeno dynamics is the Hamiltonian with hard-wall (Dirichlet) boundary conditions. This result is generalized to an… (More)

The interaction between an ultrarelativistic particle and a linear array made up of N two-level systems (“AgBr” molecules) is studied by making use of a modified version of the Coleman-Hepp Hamiltonian. Energy-exchange processes between the particle and the molecules are properly taken into account, and the evolution of the total system is calculated… (More)

An exponential behavior at all times is derived for a solvable dynamical model in the weak-coupling, macroscopic limit. Some implications for the quantum measurement problem are discussed, in particular in connection with dissipation. ‘Decoherence’ has become an important keyword in the quantum measurement theory [1] [2]. Many people ascribe the measurement… (More)