A deep connection between the ubiquity of Lévy distributions in nature and the nonextensive thermal statistics introduced a decade ago has been established recently ͓Tsallis et al., Phys. Rev. Lett. 75, 3589 ͑1995͔͒, by using unnormalized q-expectation values. It has just been argued on physical grounds that normalized q-expectation values should be used instead. We revisit, within this more appropriate scheme, the Lévy problem and verify that the relevant analytic results become sensibly simplified, whereas the basic physics remains unchanged.
We discuss an alternative to relative entropy as a measure of distance between mixed quantum states. The proposed quantity is an extension to the realm of quantum theory of the Jensen-Shannon divergence ͑JSD͒ between probability distributions. The JSD has several interesting properties. It arises in information theory and, unlike the Kullback-Leibler divergence, it is symmetric, always well-defined, and bounded. We show that the quantum JSD shares with the relative entropy most of the physically relevant properties, in particular those required for a "good" quantum distinguishability measure. We relate it to other known quantum distances and we suggest possible applications in the field of the quantum information theory.
An analytical soluble model based on a Continuous Time Random Walk (CTRW) scheme for the adsorption-desorption processes at interfaces, called bulk-mediated surface diffusion, is presented.The time evolution of the effective probability distribution width on the surface is calculated and analyzed within an anomalous diffusion framework. The asymptotic behavior for large times shows a sub-diffusive regime for the effective surface diffusion but, depending on the observed range of time, other regimes may be obtained. Montecarlo simulations show excellent agreement with analytical results. As an important byproduct of the indicated approach, we present the evaluation of the time for the first visit to the surface.
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