Pedro Lamberti
Universidad Nacional de Córdoba, Physics, Faculty Member
Theory of diffusion in finite random media with a dynamic boundary condition. Manuel O. Cáceres Centro Atómico Bariloche and Instituto Balseiro, Comisión Nacional de Energía Atómica and Universidad Nacional de Cuyo, 8400 San Carlos de... more
Theory of diffusion in finite random media with a dynamic boundary condition. Manuel O. Cáceres Centro Atómico Bariloche and Instituto Balseiro, Comisión Nacional de Energía Atómica and Universidad Nacional de Cuyo, 8400 San Carlos de Bariloche, Ríο Negro, Argentina. ...
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In this work we investigate a generalization of the Jensen-Shannon divergence. This generalization is made in the context of the non-extensive Tsallis statistics. We study its basic properties and we applied it to the segmentation... more
In this work we investigate a generalization of the Jensen-Shannon divergence. This generalization is made in the context of the non-extensive Tsallis statistics. We study its basic properties and we applied it to the segmentation procedure in some particular cases. We also investigate the applicability of this generalized Jensen-Shannon divergence to the analysis of edge detection in digital images.
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A new formulation of the vacuum Einstein equations on asymptotically simple space-time is presented. This approach involves the introduction of two different non-local objects as the basic variables, rather than the usual (local) metric... more
A new formulation of the vacuum Einstein equations on asymptotically simple space-time is presented. This approach involves the introduction of two different non-local objects as the basic variables, rather than the usual (local) metric and connection, for general relativity. The first of these objects is the "light cone cut function", which analytically describes the intersection of the light cone from an arbitrary space-time point xa, with null infinity. The second non-local variable is the holonomy operator, i.e., the parallel propagator around closed curves, associated with a subclass of loops that arises naturally on asymptotically simple space-times. Some kinematical properties of these variables as well as the field equations satisfied by them are presented. Several implications of this formalism are discussed.
We show that the Cari\~{n}ena orthogonal polynomials are Jacobi polynomials; moreover, there exists a natural bijection between the negative and the positive curvature cases. These results hold only in the two dimensional case.
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We prove an $H-$theorem for the Brownian motion on the hyperbolic plane with a drift, as studied by Comtet and Monthus; the entropy used here is not the Boltzmann entropy but the R\'enyi entropy, the parameter of which being related in a... more
We prove an $H-$theorem for the Brownian motion on the hyperbolic plane with a drift, as studied by Comtet and Monthus; the entropy used here is not the Boltzmann entropy but the R\'enyi entropy, the parameter of which being related in a simple way to the value of the drift.
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Recent work indicates that the stochastic resonance phenomenon (SR) can have a strong signature in the neutron scattering cross section. Here we consider neutron scattering by a sample containing a random distribution of bistable... more
Recent work indicates that the stochastic resonance phenomenon (SR) can have a strong signature in the neutron scattering cross section. Here we consider neutron scattering by a sample containing a random distribution of bistable scattering centres. The robustness of the stochastic resonance signal is tested by performing suitable configurational averages over the potential parameters. By showing that the resonant line is not significantly weakened by the randomness, our results suggest that SR should be observable in a real glass.
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ABSTRACT Recently, Cariñena, et al. [Ann. Phys. 322, 434 (2007)] introduced a new family of orthogonal polynomials that appear in the wave functions of the quantum harmonic oscillator in two-dimensional constant curvature spaces. They are... more
ABSTRACT Recently, Cariñena, et al. [Ann. Phys. 322, 434 (2007)] introduced a new family of orthogonal polynomials that appear in the wave functions of the quantum harmonic oscillator in two-dimensional constant curvature spaces. They are a generalization of the Hermite polynomials and will be called curved Hermite polynomials in the following. We show that these polynomials are naturally related to the relativistic Hermite polynomials introduced by Aldaya et al. [Phys. Lett. A 156, 381 (1991)] , and thus are Jacobi polynomials. Moreover, we exhibit a natural bijection between the solutions of the quantum harmonic oscillator on negative curvature spaces and on positive curvature spaces. At last, we show a maximum entropy property for the ground states of these oscillators.
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We study the dynamics of fronts in ferroelectric smectic-C* liquid crystals under the influence of stochastic electric or magnetic fields. The order parameter (tilt angle) follows a stochastic partial differential equation with a... more
We study the dynamics of fronts in ferroelectric smectic-C* liquid crystals under the influence of stochastic electric or magnetic fields. The order parameter (tilt angle) follows a stochastic partial differential equation with a nonlinear noise which has a spatiotemporal structure.
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The question of distinguishability of quantum states is at the heart of quantum information processing, an issue is here addressed with reference to different distances in probability space vis-a-vis metrics in Hilbert's one. We provide... more
The question of distinguishability of quantum states is at the heart of quantum information processing, an issue is here addressed with reference to different distances in probability space vis-a-vis metrics in Hilbert's one. We provide further reconfirmation of Wootters' hypothesis: the possibility that statistical fluctuations in the outcomes of measurements be regarded as responsible for the Hilbert-space structure of quantum mechanics, a view that becomes here considerably strengthened. We show that distances between neighboring states, whether of statistical or Hilbert's metric origin, have as a lower bound Fisher's measure, up to second-order approximation. As a consequence, the structure of the vicinity of a given quantum state is to a large extent determined by the fluctuations of the pertinent observables. It is also shown that Tsallis' non-extensivity parameter q can be used as a tool for increasing discernibility between wave functions.
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Information theoretic quantities are useful tools to characterize symbolic sequences. In this paper, we use the Jensen-Shannon divergence to study symbolic binary sequences that represent the stationary state of a lattice-gas model... more
Information theoretic quantities are useful tools to characterize symbolic sequences. In this paper, we use the Jensen-Shannon divergence to study symbolic binary sequences that represent the stationary state of a lattice-gas model describing the traffic of monomeric kinesin KIF1A. More specifically, the constructed binary sequences represent the state of a microtubule protofilament at different adenosine triphosphate (ATP) and KIF1A motor concentrations in the cytosol. The model presents some stationary regimes with phase coexistence. By using the Jensen-Shannon divergence, we develop a method of analysis that allows us to identify cases in which phase coexistence occurs and, for these cases, to locate the position of the interphase that separates the regions with different phase.
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The Einstein-Langevin equations for a Robertson-Walker universe in which a small stochastic perturbation is introduced in the deterministic equations of motion for the radius of the universe are analysed. We solve the associated nonlinear... more
The Einstein-Langevin equations for a Robertson-Walker universe in which a small stochastic perturbation is introduced in the deterministic equations of motion for the radius of the universe are analysed. We solve the associated nonlinear Fokker-Planck equation in the small noise limit using the Ω expansion and find that the cosmological constant plays an essential role in the long time stability of the model. Fellowship holder at CONICET.
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The correlation between potential shape and specific heat is generally absent from textbook discussions. We present a detailed analysis of the specific heat contribution due to independent particles subject to one-dimensional classical... more
The correlation between potential shape and specific heat is generally absent from textbook discussions. We present a detailed analysis of the specific heat contribution due to independent particles subject to one-dimensional classical and quantum model potentials. For the classical models, we use phase space concepts to develop a clear physical interpretation of the temperature dependence of the specific heat. For the quantum models, we make the interpretation in terms of the differences in quantum levels.
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We discuss different statistical distances in probability space, with emphasis on the Jensen-Shannon divergence, vis-a-vis {\it metrics} in Hilbert space and their relationship with Fisher's information measure. This study provides... more
We discuss different statistical distances in probability space, with emphasis on the Jensen-Shannon divergence, vis-a-vis {\it metrics} in Hilbert space and their relationship with Fisher's information measure. This study provides further reconfirmation of Wootters' hypothesis concerning the possibility that statistical fluctuations in the outcomes of measurements be regarded (at least partly) as responsible for the Hilbert-space structure of quantum mechanics.
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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... more
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.
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We develop a quantitative method of analysis of EEG records. The method is based on the wavelet analysis of the record and on the capability of the Jensen–Shannon divergence (JSD) to identify dynamical changes in a time series. The JSD is... more
We develop a quantitative method of analysis of EEG records. The method is based on the wavelet analysis of the record and on the capability of the Jensen–Shannon divergence (JSD) to identify dynamical changes in a time series. The JSD is a measure of distance between probability distributions. Therefore for its evaluation it is necessary to define a (time dependent) probability distribution along the record. We define this probability distribution from the wavelet decomposition of the associated time series. The wavelet JSD provides information about dynamical changes in the scales and can be considered a complementary methodology reported earlier [O.A. Rosso, S. Blanco, A. Rabinowicz, Signal Processing 86 (2003) 1275; O.A. Rosso, S. Blanco, J. Yordanova, V. Kolev, A. Figliola, M. Schürmann, E. Başar, J. Neurosci. Methods 105 (2001) 65; O.A. Rosso, M.T. Martin, A. Figliola, K. Keller, A. Plastino, J. Neurosci. Methods 153 (2006) 163]. In the present study we have demonstrated it by analyzing EEG signal of tonic–clonic epileptic seizures applying the JSD method. The display of the JSD curves enables easy comparison of frequency band component dynamics. This would, in turn, promise easy and successful comparison of the EEG records from various scalp locations of the brain.
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ABSTRACT
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We study in detail a very natural metric for quantum states. This new proposal has two basic ingredients: entropy and purification. The metric for two mixed states is defined as the square root of the entropy of the average of... more
We study in detail a very natural metric for quantum states. This new proposal has two basic ingredients: entropy and purification. The metric for two mixed states is defined as the square root of the entropy of the average of representative purifications of those states. Some basic properties are analyzed and its relation with other distances is investigated. As an illustrative application, the proposed metric is evaluated for 1-qubit mixed states.
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ABSTRACT
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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... more
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.
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We introduce a complexity measure for symbolic sequences. Starting from a segmentation procedure of the sequence, we define its complexity as the entropy of the distribution of lengths of the domains of relatively uniform composition in... more
We introduce a complexity measure for symbolic sequences. Starting from a segmentation procedure of the sequence, we define its complexity as the entropy of the distribution of lengths of the domains of relatively uniform composition in which the sequence is decomposed. We show that this quantity verifies the properties usually required for a ``good'' complexity measure. In particular it satisfies the one hump property, is super-additive and has the important property of being dependent of the level of detail in which the sequence is analyzed. Finally we apply it to the evaluation of the complexity profile of some genetic sequences.
The observability of the stochastic resonance phenomenon in a neutron scattering experiment is investigated, considering that the scatterer can hop between two sites. Under stochastic resonance conditions scattered intensity is... more
The observability of the stochastic resonance phenomenon in a neutron scattering experiment is investigated, considering that the scatterer can hop between two sites. Under stochastic resonance conditions scattered intensity is transferred from the quasielastic region to two inelastic peaks. The magnitude of the signal-to-noise ratio is shown to be similar to that arising in the corresponding power spectrum. Effects of potential asymmetry are discussed in detail. Asymmetry leads to a reduction of the signal-to-noise ratio by a factor of 1-xi(2), where xi is an asymmetry parameter which is zero for symmetric problems and equal to unity in a completely asymmetric case.
The quantum dynamics of a semi-infinite homogeneous harmonic chain is studied. Assuming the system to be in its ground state, a harmonic motion, A sin(ωt), is imposed on the mass at the beginning of the chain. The quantum state of the... more
The quantum dynamics of a semi-infinite homogeneous harmonic chain is studied. Assuming the system to be in its ground state, a harmonic motion, A sin(ωt), is imposed on the mass at the beginning of the chain. The quantum state of the system for t>0 is calculated by means of the evolution operator.Two different regimes occur: one for angular frequencies ω outside the allowed band ω>ω0 and the other one for ω inside the band. After a transient the time derivative of the total energy of the chain vanishes for the first regime and tends to a constant for the second one. The mean values of the displacements from their equilibrium position are also calculated for masses along the chain. These averaged displacements and the time derivative of the total energy are shown to give exactly the same expression as in the classical case.
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We construct solutions to the Einstein equations and their sources with a high asphericity using kinetic theory. In particular, we consider all the solutions associated with disk like sources of counter rotating collisionless particles,... more
We construct solutions to the Einstein equations and their sources with a high asphericity using kinetic theory. In particular, we consider all the solutions associated with disk like sources of counter rotating collisionless particles, and find that the hoop conjecture is satisfied.
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In the context of the study of diffusion in disordered media we present an alternative way to obtain the Terwiel cumulants expansion. Our approach starts from a formal solution of the master equation (ME) associated with the model of the... more
In the context of the study of diffusion in disordered media we present an alternative way to obtain the Terwiel cumulants expansion. Our approach starts from a formal solution of the master equation (ME) associated with the model of the nearest-neighbour random walk in a one-dimensional disordered chain. We apply our formalism to the analysis of a finite-effective-medium-like approximation.
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Many problems of statistical and quantum mechanics can be established in terms of a distance; in the first case the distance is usually defined between probability distributions; in the second one, between quantum states. The present work... more
Many problems of statistical and quantum mechanics can be established in terms of a distance; in the first case the distance is usually defined between probability distributions; in the second one, between quantum states. The present work is devoted to review the main properties of a distance known as the Jensen-Shannon divergence (JSD) in its classical and quantum version. We present two examples of application of this distance: in the first one we use it as a quantifiers of the stochastic resonance phenomenon in ion channels; in the second one we use the JSD to propose a geometrical view of entanglement for two qubits states.
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In a recent paper, the generalization of the Jensen Shannon divergence (JSD) in the context of quantum theory has been studied (Phys. Rev. A 72, 052310 (2005)). This distance between quantum states has shown to verify several of the... more
In a recent paper, the generalization of the Jensen Shannon divergence (JSD) in the context of quantum theory has been studied (Phys. Rev. A 72, 052310 (2005)). This distance between quantum states has shown to verify several of the properties required for a good distinguishability measure. Here we investigate the metric character of this distance. More precisely we show, formally for pure states and by means of simulations for mixed states, that its square root verifies the triangle inequality.
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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 (JSD) between probability... more
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 (JSD) 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 (QJSD) 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.
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We discuss the paradigmatic bipartite spin- system having the probabilities (1+3x)/4 of being in the Einstein–Podolsky–Rosen fully entangled state and 3(1−x)/4 of being orthogonal. This system is known to be separable if and only if... more
We discuss the paradigmatic bipartite spin- system having the probabilities (1+3x)/4 of being in the Einstein–Podolsky–Rosen fully entangled state and 3(1−x)/4 of being orthogonal. This system is known to be separable if and only if (Peres criterion). This critical value has been recently recovered by Abe and Rajagopal through the use of the nonextensive entropic form which has enabled a current generalization of Boltzmann–Gibbs statistical mechanics. This result has been enrichened by Lloyd, Baranger and one of the present authors by proposing a critical-phenomenon-like scenario for quantum entanglement. Here, we further illustrate and discuss this scenario through the calculation of some relevant quantities.
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In a recent paper, we have studied a generalization of the Jensen–Shannon divergence (JSD) (Physica A 329 (2003) 81). This generalization was made in the context of Tsallis’ statistical mechanics. The present work is devoted to an... more
In a recent paper, we have studied a generalization of the Jensen–Shannon divergence (JSD) (Physica A 329 (2003) 81). This generalization was made in the context of Tsallis’ statistical mechanics. The present work is devoted to an investigation of the metric character of the JSD generalization.
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The global behavior of light cone cuts at null infinity, i.e., the intersection of light cones of interior point, with null infinity, is investigated. In particular, it is shown that the topological structure of these cuts, for the case... more
The global behavior of light cone cuts at null infinity, i.e., the intersection of light cones of interior point, with null infinity, is investigated. In particular, it is shown that the topological structure of these cuts, for the case of an asymptotically flat space-time, is very simple. The nature of the light cone cuts singularities is also analyzed. Generically, only two different types of singularities occur and their local description is given.
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The Jensen–Shannon divergence is a symmetrized and smoothed version of the Kullback–Leibler divergence. Recently it has been widely applied to the analysis and characterization of symbolic sequences. In this paper we investigate a... more
The Jensen–Shannon divergence is a symmetrized and smoothed version of the Kullback–Leibler divergence. Recently it has been widely applied to the analysis and characterization of symbolic sequences. In this paper we investigate a generalization of the Jensen–Shannon divergence. This generalization is done in the framework of the non-extensive Tsallis statistics. We study its basic properties and we investigate its applicability as a tool for segmentating symbolic sequences.
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We discuss a way of characterizing probability distributions, complementing that provided by the celebrated notion of information measure, with reference to a measure of complexity that we call a “nontriviality measure”. Our starting... more
We discuss a way of characterizing probability distributions, complementing that provided by the celebrated notion of information measure, with reference to a measure of complexity that we call a “nontriviality measure”. Our starting point is the “LMC” measure of complexity advanced by López-Ruiz et al. (Phys. Lett. A 209 (1995) 321) and its analysis by Anteneodo and Plastino (Phys. Lett. A 223 (1997) 348). An improvement of some of their troublesome characteristics is thereby achieved. Basically, we replace the Euclidean distance to equilibrium by the Jensen–Shannon divergence. The resulting measure turns out to be (i) an intensive quantity and (ii) allows one to distinguish between different degrees of periodicity. We apply the “cured” measure to the logistic map so as to clearly exhibit its advantages.
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A very simple numerical method for solving boundary problems in electrostatics is presented. The approximation scheme is based on the substitution of a series expansion of the electrostatic potential by a finite sum and a discretization... more
A very simple numerical method for solving boundary problems in electrostatics is presented. The approximation scheme is based on the substitution of a series expansion of the electrostatic potential by a finite sum and a discretization of the boundary where the conditions are given. These boundary conditions may be of the mixed type. In this way the original problem is reduced to the solution of a system of linear equations. As an application of the method proposed, the problem of a hollow cap of a sphere set to a constant potential is treated.