Parameter-free ansatz for inferring ground state wave functions of even potentials

Schr\"odinger's equation (SE) and the information-optimizing principle based on Fisher's information measure (FIM) are intimately linked, which entails the existence of a Legendre transform structure underlying the SE. In this comunication we show that the existence of such an structure allows, via the virial theorem, for the formulation of a parameter-free ground state's SE-ansatz for a rather large family of potentials. The parameter-free nature of the ansatz derives from the structural information it incorporates through its Legendre properties

A Schroedinger link between non-equilibrium thermodynamics and Fisher information

It is known that equilibrium thermodynamics can be deduced from a constrained Fisher information extemizing process. We show here that, more generally, both non-equilibrium and equilibrium thermodynamics can be obtained from such a Fisher treatment. Equilibrium thermodynamics corresponds to the ground state solution, and non-equilibrium thermodynamics corresponds to excited state solutions, of a Schroedinger wave equation (SWE). That equation appears as an output of the constrained variational process that extremizes Fisher information. Both equilibrium- and non-equilibrium situations can thereby be tackled by one formalism that clearly exhibits the fact that thermodynamics and quantum mechanics can both be expressed in terms of a formal SWE, out of a common informational basis.Comment: 12 pages, no figure

Jensen Shannon divergence as a measure of the degree of entanglement

The notion of distance in Hilbert space is relevant in many scenarios. In particular, distances between quantum states play a central role in quantum information theory. An appropriate measure of distance is the quantum Jensen Shannon divergence (QJSD) between quantum states. Here we study this distance as a geometrical measure of entanglement and apply it to different families of states.Comment: 5 pages, 2 figures, to appear in the special issue of IJQI "Noise, Information and Complexity at Quantum Scale", eds. S. Mancini and F. Marcheson

Convex politopes and quantum separability

We advance a novel perspective of the entanglement issue that appeals to the Schlienz-Mahler measure [Phys. Rev. A 52, 4396 (1995)]. Related to it, we propose an criterium based on the consideration of convex subsets of quantum states. This criterium generalizes a property of product states to convex subsets (of the set of quantum-states) that is able to uncover a new geometrical property of the separability property

On a conjecture about Dirac's delta representation using q-exponentials

A new representation of Dirac's delta-distribution, based on the so-called q-exponentials, has been recently conjectured. We prove here that this conjecture is indeed valid

Power-law random walks

We present some new results about the distribution of a random walk whose independent steps follow a $q-$Gaussian distribution with exponent $\frac{1}{1-q}; q \in \mathbb{R}$. In the case $q>1$ we show that a stochastic representation of the point reached after $n$ steps of the walk can be expressed explicitly for all $n$. In the case $q<1,$ we show that the random walk can be interpreted as a projection of an isotropic random walk, i.e. a random walk with fixed length steps and uniformly distributed directions.Comment: 5 pages, 4 figure

Relativistic Klein-Gordon charge effects by information-theoretic measures

The charge spreading of ground and excited states of Klein-Gordon particles moving in a Coulomb potential is quantitatively analyzed by means of the ordinary moments and the Heisenberg measure as well as by use of the most relevant information-theoretic measures of global (Shannon entropic power) and local (Fisher's information) types. The dependence of these complementary quantities on the nuclear charge Z and the quantum numbers characterizing the physical states is carefully discussed. The comparison of the relativistic Klein-Gordon and non-relativistic Schrodinger values is made. The non-relativistic limits at large principal quantum number n and for small values of Z are also reached.Comment: Accepted in New Journal of Physic

Wootters' distance revisited: a new distinguishability criterium

The notion of distinguishability between quantum states has shown to be fundamental in the frame of quantum information theory. In this paper we present a new distinguishability criterium by using a information theoretic quantity: the Jensen-Shannon divergence (JSD). This quantity has several interesting properties, both from a conceptual and a formal point of view. Previous to define this distinguishability criterium, we review some of the most frequently used distances defined over quantum mechanics' Hilbert space. In this point our main claim is that the JSD can be taken as a unifying distance between quantum states.Comment: 15 pages, 3 figures, changed content, added reference for last sectio

Crustal blocks and seismicity in the Central Apennines of Italy

Kinematics and geodynamics of crustal-block structures separated by compliant zones with viscoelastic rheology play an important role in defining the conditions for many deformation events such as ordinary seismic ruptures, silent and slow earthquakes and aseismic fault creep phenomena. New seismological data from the Latium-Abruzzi carbonatic platform of central Italy fit a block-tectonic modelling previously proposed for this area on the basis of structural and paleomagnetic evidences