Statistics and Quantum Chaos
We use multi-time correlation functions of quantum systems to construct random variables with statistical properties that reflect the degree of complexity of the underlying quantum dynamics.
quant-ph↗
arXiv subjects
F. Benatti
Publications and source records attributed to F. Benatti.
Multi-time correlations in relaxing quantum dynamical systems
In this paper, we consider the long time asymptotics of multi-time correlation functions for quantum dynamical systems that are sufficiently random to relax to a ``reference state''. In particular, the evolution of such systems must have a continuous spectrum. Special attention is paid to general dynamical clustering conditions and their consequences for the structure of fluctuations of temporal averages.
quant-ph↗
Non-Standard neutral kaons dynamics from D-brane statistics
The neutral kaon system can be effectively described by non-unitary, dissipative, completely positive dynamics that extend the usual treatment. In the framework of open quantum systems, we show how the origin of these non-standard time evolutions can be traced to the interaction of the kaon system with a large environment. We find that D-branes, effectively described by a heat-bath of quanta obeying infinite statistics, could constitute a realistic example of such an environment.
hep-th↗
Comment on ``Searching for Evolutions of Pure States into Mixed States in the Two-State System K-K''
It has been recently proposed to study generic dynamical evolutions of the neutral kaon system that go beyond quantum mechanics. We explicitly show that, unless the condition of complete positivity is enforced, those dynamics are physically inconsistent and should be rejected.
hep-ph↗
On the decay law for unstable open systems
We use (nonconservative) dynamical semigroups to investigate the decay law of a quantum unstable system weakly coupled with a large environment. We find that the deviations from the classical exponential law are small and can be safely ignored in any actual experiment.
hep-th↗
epsilon'/epsilon violates Bell's inequality
We formulate a set of Bell's inequalities for the system of two correlated neutral kaons coming from the decay of a phi-meson, without assuming CP and CPT invariance. We show that a non-vanishing value of the phenomenological parameter epsilon' would violate such inequalities, ruling out Bell's locality.
hep-ph↗
Completely positive dynamics of correlated neutral kaons
We study the behaviour of correlated neutral kaons produced in phi-meson decays under the hypothesis that the quantum mechanical time-evolution is completely positive. We show that planned experiments at phi-factories could give precise bounds on the phenomenological parameters of the model.
hep-ph↗
Testing complete positivity
We study the modified dynamical evolution of the neutral kaon system under the condition of complete positivity. The accuracy of the data from planned future experiments is expected to be sufficiently precise to test such a hypothesis.
quant-ph↗
Experimental limits on complete positivity from the K-K system
Available data on measured observables allow deriving estimates for some of the phenomenological parameters that characterize the time-evolution and decay of the neutral kaon system based on the hypothesis of complete positivity. The present experimental uncertainties are still too large to permit a full test of complete positivity.
hep-ph↗
Complete Positivity and the K K-bar system
Models that provide experimentally testable violations of ordinary Quantum Mechanics have been recently proposed. These models are based on non-unitary time evolutions of density matrices that are generated by linear positive maps. We discuss the consequences of imposing a stronger condition on those maps, known as complete positivity. It turns out that experimental data on the neutral kaon system giving upper bounds to the parameters characterizing positive maps, also give bounds to those determining completely positive ones.
hep-th↗