29,680 research outputs found
Quantum Zeno dynamics: mathematical and physical aspects
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 system can evolve away from
its initial state, although it remains in the subspace defined by the
measurement. The continuing time evolution within the projected "quantum Zeno
subspace" is called "quantum Zeno dynamics:" for instance, if the measurements
ascertain whether a quantum particle is in a given spatial region, the
evolution is unitary and the generator of the Zeno dynamics is the Hamiltonian
with hard-wall (Dirichlet) boundary conditions. We discuss the physical and
mathematical aspects of this evolution, highlighting the open mathematical
problems. We then analyze some alternative strategies to obtain a Zeno dynamics
and show that they are physically equivalent.Comment: 52 pages, 10 figure
Quantum Zeno Dynamics
The evolution of a quantum system undergoing very frequent measurements takes
place in a subspace of the total Hilbert space (quantum Zeno effect). The
dynamical properties of this evolution are investigated and several examples
are considered.Comment: 12 pages, 1 figur
Disclosing hidden information in the quantum Zeno effect: Pulsed measurement of the quantum time of arrival
Repeated measurements of a quantum particle to check its presence in a region
of space was proposed long ago [G. R. Allcock, Ann. Phys. {\bf 53}, 286 (1969)]
as a natural way to determine the distribution of times of arrival at the
orthogonal subspace, but the method was discarded because of the quantum Zeno
effect: in the limit of very frequent measurements the wave function is
reflected and remains in the original subspace. We show that by normalizing the
small bits of arriving (removed) norm, an ideal time distribution emerges in
correspondence with a classical local-kinetic-energy distribution.Comment: 5 pages, 4 figures, minor change
Algebras of Measurements: the logical structure of Quantum Mechanics
In Quantum Physics, a measurement is represented by a projection on some
closed subspace of a Hilbert space. We study algebras of operators that
abstract from the algebra of projections on closed subspaces of a Hilbert
space. The properties of such operators are justified on epistemological
grounds. Commutation of measurements is a central topic of interest. Classical
logical systems may be viewed as measurement algebras in which all measurements
commute. Keywords: Quantum measurements, Measurement algebras, Quantum Logic.
PACS: 02.10.-v.Comment: Submitted, 30 page
Zeno dynamics yields ordinary constraints
The dynamics of a quantum system undergoing frequent measurements (quantum
Zeno effect) is investigated. Using asymptotic analysis, the system is found to
evolve unitarily in a proper subspace of the total Hilbert space. For spatial
projections, the generator of the "Zeno dynamics" is the Hamiltonian with
Dirichlet boundary conditions.Comment: 6 page
Non-Hermitian Dynamics in the Quantum Zeno Limit
Measurement is one of the most counter-intuitive aspects of quantum physics.
Frequent measurements of a quantum system lead to quantum Zeno dynamics where
time evolution becomes confined to a subspace defined by the projections.
However, weak measurement performed at a finite rate is also capable of locking
the system into such a Zeno subspace in an unconventional way: by Raman-like
transitions via virtual intermediate states outside this subspace, which are
not forbidden. Here, we extend this concept into the realm of non-Hermitian
dynamics by showing that the stochastic competition between measurement and a
system's own dynamics can be described by a non-Hermitian Hamiltonian. We
obtain an analytic solution for ultracold bosons in a lattice and show that a
dark state of the tunnelling operator is a steady state in which the
observable's fluctuations are zero and tunnelling is suppressed by destructive
matter-wave interference. This opens a new venue of investigation beyond the
canonical quantum Zeno dynamics and leads to a new paradigm of competition
between global measurement backaction and short-range atomic dynamics.Comment: Accepted in Phys. Rev.
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