Related papers: Zeno product formula revisited
A discussion of the quantum Zeno effect and paradox is given. The quantum Zeno paradox claims that a continuously observed system, prepared in a state which is not an eigenstate of the Hamiltonian operator, never decays. To recover the…
Frequent applications of a mixing quantum operation to a quantum system slow down its time evolution and eventually drive it into the invariant subspace of the named operation. We prove this phenomenon, the quantum Zeno effect, and its…
We report the first observation of the Quantum Zeno and Anti-Zeno effects in an unstable system. Cold sodium atoms are trapped in a far-detuned standing wave of light that is accelerated for a controlled duration. For a large acceleration…
Quantum Zeno effect shows that frequent observations can slow down or even stop the unitary time evolution of an unstable quantum system. This effect can also be regarded as a physical consequence of the the statistical indistinguishability…
The problem of inverting a system in presence of a series-defined output is analyzed. Inverse models are derived that consist of a set of algebraic equations. The inversion is performed explicitly for an output trajectory functional, which…
A Hermite type formula is introduced and used to study the zeta function over the real and complex n-projective space. This approach allows to compute the residua at the poles and the value at the origin as well as the value of the…
The quantum Zeno effect is described in geometric terms. The quantum Zeno time (inverse standard deviation of the Hamiltonian) and the generator of the quantum Zeno dynamics are both given a geometric interpretation.
Building on the mapping relations between analytic functions and periodic functions using the abstract operators $\cos(h\partial_x)$ and $\sin(h\partial_x)$, and by defining the Zeta and related functions including the Hurwitz Zeta function…
Our basic structure is a finite-dimensional complex Hilbert space $H$. We point out that the set of effects on $H$ form a convex effect algebra. Although the set of operators on $H$ also form a convex effect algebra, they have a more…
Making use of inverse Mellin transform techniques for analytical continuation, an elegant proof and an extension of the zeta function regularization theorem is obtained. No series commutations are involved in the procedure; nevertheless the…
The evolution of a quantum system is supposed to be impeded by measurement of an involved observable. This effect has been proven indistinguishable from the effect of dephasing the system's wave function, except in an individual quantum…
The dynamics of a quantum system undergoing frequent "measurements", leading to the so-called quantum Zeno effect, is examined on the basis of a neutron-spin experiment recently proposed for its demonstration. When the spatial degrees of…
We consider the evolution of an arbitrary quantum dynamical semigroup of a finite-dimensional quantum system under frequent kicks, where each kick is a generic quantum operation. We develop a generalization of the Baker-Campbell-Hausdorff…
We study the dynamics of the populations of a model molecule endowed with two sets of rotational levels of different parity, whose ground levels are energy degenerate and coupled by a constant interaction. The relaxation rate from one set…
Quantum mechanics predicts that the decay rate of unstable systems could be effectively modified by the process of the measurement of the survival probability. Depending on the intrinsic properties of the unstable system and the…
In this note, we study the dynamics and associated zeta functions of conformally compact manifolds with variable negative sectional curvatures. We begin with a discussion of a larger class of manifolds known as convex co-compact manifolds…
It is shown that in a simple coupler where one of the waveguides is subject to controlled losses of the electric field, it is possible to observe optical analog of the linear and nonlinear quantum Zeno effects. The phenomenon consists in a…
Quantum Zeno and anti-Zeno effects on pure dephasing are studied using exactly solvable microscopic models. The crossover between these two opposite effects is investigated. The case of a single two-level system undergoing dephasing is…
We formulate a parametrized uniformly absolutely globally convergent series of $\zeta$(s) denoted by Z(s, x). When expressed in closed form, it is given by Z(s, x) = (s -- 1)$\zeta$(s) + 1 x Li s z z -- 1 dz, where Li s (x) is the…
Prevention of a quantum system's time evolution by repetitive, frequent measurements of the system's state has been called the quantum Zeno effect (or paradox). Here we investigate theoretically and numerically the effect of repeated…