Ensayos sobre la Percepcion-Creación artística, 2010
Marco teórico del Proyecto de investigacion "Sobre los paradigmas dualistas en el proceso de la p... more Marco teórico del Proyecto de investigacion "Sobre los paradigmas dualistas en el proceso de la percepción-creación artística" UNA- Dto Artes Visuales. Drs Manuel O.Cáceres y A. Cáceres- R 0306/07 2007/2009
We study a linear Langevin dynamics driven by an additive non-Markovian symmetrical dichotomic no... more We study a linear Langevin dynamics driven by an additive non-Markovian symmetrical dichotomic noise. It is shown that when the statistics of the time intervals between noise transitions is characterized by two well differentiated timescales, the stationary distribution may develop multimodality (bi-and trimodality). The underlying effects that lead to a probability concentration in different points include intermittence and also a dynamical locking of realizations. Our results are supported by numerical simulations as well as by an exact treatment obtained from a Markovian embedding of the full dynamics, which leads to a third-order differential equation for the stationary distribution.
We described the first passage time distribution associated to the stochastic evolution from an u... more We described the first passage time distribution associated to the stochastic evolution from an unstable uniform state to a patterned one (attractor of the system), when the time evolution is given by an integro-differential equation describing a population model. In order to obtain analytical results we used the Stochastic Path Perturbation Approach introducing a minimum coupling approximation into the nonlinear dynamics, and a stochastic multiscale perturbation expansion. We show that the stochastic multiscale perturbation is a necessary tool to handle other problems like: nonlinear instabilities and multiplicative stochastic partial differential equations. A small noise parameter was introduced to define the random escape of the stochastic field. We carried out Monte Carlo simulations in a non-local Fisher like equation, to show the agreement with our theoretical predictions.
Bath-induced correlations in an infinite dimension Hilbert space has been shown. Quantum correlat... more Bath-induced correlations in an infinite dimension Hilbert space has been shown. Quantum correlations between two free spinless dissipative distinguishable particles (initially uncorrelated) are studied analytically using the quantum master equation. We show that for temperature $T>0$ the time-evolution of the reduced density matrix cannot be written as the direct product of two independent particles. We found a time-scale that characterizes the time when the bath-induced correlation is maximum before being wipe out by dissipation (purity, spatial, and mirror correlations are studied). We introduce a Wigner function associated to the Wannier lattice where the dissipative quantum walks move. Thus we discuss the peculiarities of the scenario of enlarging the lattice to the semi-integers in order to fulfilll all the fundamental properties of the Wigner function. We have supported the quantum character of the correlations by analyzing the negativity of the Wigner function.
The first passage time (FPT) problem is studied for superstatistical models assuming that the mes... more The first passage time (FPT) problem is studied for superstatistical models assuming that the mesoscopic system dynamics is described by a Fokker-Planck equation. We show that all moments of the random intensive parameter associated to the superstatistical approach can be put in one-to-one correspondence with the moments of the FPT. For systems subjected to an additional uncorrelated external force, the same statistical information is obtained from the dependence of the FPT-moments on the external force. These results provide an alternative technique for checking the validity of superstatistical models. As an example, we characterize the mean FPT for a forced Brownian particle.
A theory is presented for the transient process of decay from the state of marginal stability occ... more A theory is presented for the transient process of decay from the state of marginal stability occurring in a subcritical pitchfork bifurcation. We introduce an approximation for the stochastic paths that allows the calculation of a generating function for the statistics of the escape time. The timedependent moments and transient fluctuations are calculated from the distribution of passage times by a scaling transformation that is associated with initial non-Gaussian statistics. Our results are in agreement with numerical simulations reported also here.
The attenuation in the propagation of a plane wave in conducting media has been studied. We analy... more The attenuation in the propagation of a plane wave in conducting media has been studied. We analyzed a wave motion suffering dissipation by the Joule effect in its propagation in a medium with global disorder. We solved the stochastic telegrapher's equation in the Fourier-Laplace representation allowing us to find the space penetration length of a plane wave in a complex conducting medium. Considering fluctuations in the loss of energy, we found a critical value k c for Fourier's modes, thus if |k| < k c the waves are localized. We showed that the penetration length is inversely proportional to k c. Thus, the penetration length L = k −1 c becomes an important piece of information for describing wave propagation with Markovian and non-Markovian fluctuations in the rate of the absorption of energy τ −1. In addition, intermittent fluctuations in this rate have also been studied.
We investigated a diffusion-like equation with a bounded speed of signal propagation (the so call... more We investigated a diffusion-like equation with a bounded speed of signal propagation (the so called telegrapher’s equation) in a random media. We discuss some properties of the mean-value solution in a well-defined perturbation theory. The frequency-dependent effective-velocity of propagation is studied in the long and short time regime. We show that due to the wave-like character of telegrapher’s equation the effective-velocity is a complex dispersive function in time. Exact results and asymptotic perturbative long-time behaviors (for an exponential space-correlated binary disorder) are presented, showing their agreement and corroborating the goodness of the effective medium approximation in continuous system.
The 1D random Boltzmann-Lorentz equation has been connected with a set of stochastic hyperbolic e... more The 1D random Boltzmann-Lorentz equation has been connected with a set of stochastic hyperbolic equations. Therefore, the study of the Boltzmann-Lorentz gas with disordered scattering centers has been transformed into the analysis of a set of stochastic telegrapher's equations. For global binary disorder (Markovian and non-Markovian) exact analytical results for the second moment, the velocity autocorrelation function, and the selfdiffusion coefficient are presented. We have demonstrated that time-fluctuations in the lost of energy in the telegrapher's equation, can delay the entrance to the diffusive regime, this issue has been characterized by a timescale t c which is a function of disorder parameters. Indeed, producing a longer ballistic dynamics in the transport process. In addition, fluctuations of the space probability distribution have been studied, showing that the mean value of a stochastic telegrapher's Fourier mode is a good statistical object to characterize the solution of the random Boltzmann-Lorentz gas. In a different context, the stochastic telegrapher's equation has also been related to the run-and-tumble model in Biophysics. Then a discussion devoted to the potential applications when swimmers' speed and tumbling rate have time fluctuations has been pointed out.
From the exact solution of the stochastic telegrapher's equation, Fourier plane-wave-like modes a... more From the exact solution of the stochastic telegrapher's equation, Fourier plane-wave-like modes are introduced. Then the time evolution of the plane-wave modes are analyzed when the absorption of energy in the telegrapher's equation has strong time fluctuations. We demonstrate that fluctuations in the loss of energy introduce a localized gap with a size that depends on the correlation timescale of the fluctuations. We prove that for a large time correlation the gap is strongly reduced, which means that there is delocalization in the plane-wave modes with respect to the plane waves in the ordinary telegrapher's equation. This result is of relevance in the study of the transport of electromagnetic waves in a conducting medium, and sheds light on the functional role of the fluctuations in the loss of energy in the telegrapher's dynamics.
Journal of Physics A: Mathematical and Theoretical, 2017
Quantum correlations and coherence generated between two free spinless particles in the lattice, ... more Quantum correlations and coherence generated between two free spinless particles in the lattice, interacting with a common quantum phonon bath are studied. The reduced density matrix has been solved in the Markov approach. We show that the bath induces correlations between the particles. The coherence induced by the bath is studied calculating: off-diagonal elements of the density matrix, spatiotemporal dispersion, purity, and quantum mutual information. We have found a characteristic timescale pointing out when this coherence is maximum. In addition a Wigner-like distribution in the phase-space (lattice) has been introduced as an indirect indicator of the quantumness of total correlations and coherence induced by the thermal bath. The negative volume of the Wigner function shows also a behavior which is in agreement with the timescale that we have found. A Gaussian distribution for the profile of particles is not obtained and interference pattern are observed as the result of bath induced coherence. As the temperature of bath vanishes the ballistic behavior of the tight-binding model is recovered. The geometric quantum discord has been calculated to characterize the nature of the correlations.
Theory of diffusion in finite random media with a dynamic boundary condition. Manuel O. Cáceres C... 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. ...
The Einstein-Langevin equations for a Robertson-Walker universe in which a small stochastic pertu... 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 Q expansion and find that the cosmological constant plays an essential role in the long time stability of the model.
First-passage-time statistics in disordered media. E. Hernández-García and Manuel O. Cáceres Depa... more First-passage-time statistics in disordered media. E. Hernández-García and Manuel O. Cáceres Departament de Física, Universitat de les Illes Balears, E-07071, Palma de Mallorca, Spain. Received 23 January 1990 A method ...
The simplest model for the evolution of the mean-value of a surface gravity wave propagating in a... more The simplest model for the evolution of the mean-value of a surface gravity wave propagating in a random bottom has been connected with the telegrapher’s equation. This analysis is based on the comparison of the mean-value solution of dispersive plane-wave modes propagating in a binary exponential-correlated disordered floor with the solution of the homogeneous telegrapher’s equation. Analytical results for the exact dispersion-relation are presented. In addition, the time-dependent analysis of mean-value monochromatic waves is also shown.
The time evolution of correlations for two indistinguishable free particles, in a one-dimensional... more The time evolution of correlations for two indistinguishable free particles, in a one-dimensional lattice interacting with a quantum bath, is studied in the Born-Markov approximation. The analytical solution for the density matrix is obtained, for bosons and fermions, in the second quantization formalism. The time evolution of the negativity of indistinguishable particles is analyzed for quantum mixed states. Quantum correlations heavily depend on the selected bipartition; in return, a small difference between the statistics of the particles is noted, due to the Pauli exclusion principle. In the presence of dissipation, the negativity (a nonclassical correlation) shows a time-oscillatory behavior for a particular geometrical bipartition. The total probability of finding one particle in each subsystem is also calculated and shows consistent behavior.
Ensayos sobre la Percepcion-Creación artística, 2010
Marco teórico del Proyecto de investigacion "Sobre los paradigmas dualistas en el proceso de la p... more Marco teórico del Proyecto de investigacion "Sobre los paradigmas dualistas en el proceso de la percepción-creación artística" UNA- Dto Artes Visuales. Drs Manuel O.Cáceres y A. Cáceres- R 0306/07 2007/2009
We study a linear Langevin dynamics driven by an additive non-Markovian symmetrical dichotomic no... more We study a linear Langevin dynamics driven by an additive non-Markovian symmetrical dichotomic noise. It is shown that when the statistics of the time intervals between noise transitions is characterized by two well differentiated timescales, the stationary distribution may develop multimodality (bi-and trimodality). The underlying effects that lead to a probability concentration in different points include intermittence and also a dynamical locking of realizations. Our results are supported by numerical simulations as well as by an exact treatment obtained from a Markovian embedding of the full dynamics, which leads to a third-order differential equation for the stationary distribution.
We described the first passage time distribution associated to the stochastic evolution from an u... more We described the first passage time distribution associated to the stochastic evolution from an unstable uniform state to a patterned one (attractor of the system), when the time evolution is given by an integro-differential equation describing a population model. In order to obtain analytical results we used the Stochastic Path Perturbation Approach introducing a minimum coupling approximation into the nonlinear dynamics, and a stochastic multiscale perturbation expansion. We show that the stochastic multiscale perturbation is a necessary tool to handle other problems like: nonlinear instabilities and multiplicative stochastic partial differential equations. A small noise parameter was introduced to define the random escape of the stochastic field. We carried out Monte Carlo simulations in a non-local Fisher like equation, to show the agreement with our theoretical predictions.
Bath-induced correlations in an infinite dimension Hilbert space has been shown. Quantum correlat... more Bath-induced correlations in an infinite dimension Hilbert space has been shown. Quantum correlations between two free spinless dissipative distinguishable particles (initially uncorrelated) are studied analytically using the quantum master equation. We show that for temperature $T>0$ the time-evolution of the reduced density matrix cannot be written as the direct product of two independent particles. We found a time-scale that characterizes the time when the bath-induced correlation is maximum before being wipe out by dissipation (purity, spatial, and mirror correlations are studied). We introduce a Wigner function associated to the Wannier lattice where the dissipative quantum walks move. Thus we discuss the peculiarities of the scenario of enlarging the lattice to the semi-integers in order to fulfilll all the fundamental properties of the Wigner function. We have supported the quantum character of the correlations by analyzing the negativity of the Wigner function.
The first passage time (FPT) problem is studied for superstatistical models assuming that the mes... more The first passage time (FPT) problem is studied for superstatistical models assuming that the mesoscopic system dynamics is described by a Fokker-Planck equation. We show that all moments of the random intensive parameter associated to the superstatistical approach can be put in one-to-one correspondence with the moments of the FPT. For systems subjected to an additional uncorrelated external force, the same statistical information is obtained from the dependence of the FPT-moments on the external force. These results provide an alternative technique for checking the validity of superstatistical models. As an example, we characterize the mean FPT for a forced Brownian particle.
A theory is presented for the transient process of decay from the state of marginal stability occ... more A theory is presented for the transient process of decay from the state of marginal stability occurring in a subcritical pitchfork bifurcation. We introduce an approximation for the stochastic paths that allows the calculation of a generating function for the statistics of the escape time. The timedependent moments and transient fluctuations are calculated from the distribution of passage times by a scaling transformation that is associated with initial non-Gaussian statistics. Our results are in agreement with numerical simulations reported also here.
The attenuation in the propagation of a plane wave in conducting media has been studied. We analy... more The attenuation in the propagation of a plane wave in conducting media has been studied. We analyzed a wave motion suffering dissipation by the Joule effect in its propagation in a medium with global disorder. We solved the stochastic telegrapher's equation in the Fourier-Laplace representation allowing us to find the space penetration length of a plane wave in a complex conducting medium. Considering fluctuations in the loss of energy, we found a critical value k c for Fourier's modes, thus if |k| < k c the waves are localized. We showed that the penetration length is inversely proportional to k c. Thus, the penetration length L = k −1 c becomes an important piece of information for describing wave propagation with Markovian and non-Markovian fluctuations in the rate of the absorption of energy τ −1. In addition, intermittent fluctuations in this rate have also been studied.
We investigated a diffusion-like equation with a bounded speed of signal propagation (the so call... more We investigated a diffusion-like equation with a bounded speed of signal propagation (the so called telegrapher’s equation) in a random media. We discuss some properties of the mean-value solution in a well-defined perturbation theory. The frequency-dependent effective-velocity of propagation is studied in the long and short time regime. We show that due to the wave-like character of telegrapher’s equation the effective-velocity is a complex dispersive function in time. Exact results and asymptotic perturbative long-time behaviors (for an exponential space-correlated binary disorder) are presented, showing their agreement and corroborating the goodness of the effective medium approximation in continuous system.
The 1D random Boltzmann-Lorentz equation has been connected with a set of stochastic hyperbolic e... more The 1D random Boltzmann-Lorentz equation has been connected with a set of stochastic hyperbolic equations. Therefore, the study of the Boltzmann-Lorentz gas with disordered scattering centers has been transformed into the analysis of a set of stochastic telegrapher's equations. For global binary disorder (Markovian and non-Markovian) exact analytical results for the second moment, the velocity autocorrelation function, and the selfdiffusion coefficient are presented. We have demonstrated that time-fluctuations in the lost of energy in the telegrapher's equation, can delay the entrance to the diffusive regime, this issue has been characterized by a timescale t c which is a function of disorder parameters. Indeed, producing a longer ballistic dynamics in the transport process. In addition, fluctuations of the space probability distribution have been studied, showing that the mean value of a stochastic telegrapher's Fourier mode is a good statistical object to characterize the solution of the random Boltzmann-Lorentz gas. In a different context, the stochastic telegrapher's equation has also been related to the run-and-tumble model in Biophysics. Then a discussion devoted to the potential applications when swimmers' speed and tumbling rate have time fluctuations has been pointed out.
From the exact solution of the stochastic telegrapher's equation, Fourier plane-wave-like modes a... more From the exact solution of the stochastic telegrapher's equation, Fourier plane-wave-like modes are introduced. Then the time evolution of the plane-wave modes are analyzed when the absorption of energy in the telegrapher's equation has strong time fluctuations. We demonstrate that fluctuations in the loss of energy introduce a localized gap with a size that depends on the correlation timescale of the fluctuations. We prove that for a large time correlation the gap is strongly reduced, which means that there is delocalization in the plane-wave modes with respect to the plane waves in the ordinary telegrapher's equation. This result is of relevance in the study of the transport of electromagnetic waves in a conducting medium, and sheds light on the functional role of the fluctuations in the loss of energy in the telegrapher's dynamics.
Journal of Physics A: Mathematical and Theoretical, 2017
Quantum correlations and coherence generated between two free spinless particles in the lattice, ... more Quantum correlations and coherence generated between two free spinless particles in the lattice, interacting with a common quantum phonon bath are studied. The reduced density matrix has been solved in the Markov approach. We show that the bath induces correlations between the particles. The coherence induced by the bath is studied calculating: off-diagonal elements of the density matrix, spatiotemporal dispersion, purity, and quantum mutual information. We have found a characteristic timescale pointing out when this coherence is maximum. In addition a Wigner-like distribution in the phase-space (lattice) has been introduced as an indirect indicator of the quantumness of total correlations and coherence induced by the thermal bath. The negative volume of the Wigner function shows also a behavior which is in agreement with the timescale that we have found. A Gaussian distribution for the profile of particles is not obtained and interference pattern are observed as the result of bath induced coherence. As the temperature of bath vanishes the ballistic behavior of the tight-binding model is recovered. The geometric quantum discord has been calculated to characterize the nature of the correlations.
Theory of diffusion in finite random media with a dynamic boundary condition. Manuel O. Cáceres C... 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. ...
The Einstein-Langevin equations for a Robertson-Walker universe in which a small stochastic pertu... 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 Q expansion and find that the cosmological constant plays an essential role in the long time stability of the model.
First-passage-time statistics in disordered media. E. Hernández-García and Manuel O. Cáceres Depa... more First-passage-time statistics in disordered media. E. Hernández-García and Manuel O. Cáceres Departament de Física, Universitat de les Illes Balears, E-07071, Palma de Mallorca, Spain. Received 23 January 1990 A method ...
The simplest model for the evolution of the mean-value of a surface gravity wave propagating in a... more The simplest model for the evolution of the mean-value of a surface gravity wave propagating in a random bottom has been connected with the telegrapher’s equation. This analysis is based on the comparison of the mean-value solution of dispersive plane-wave modes propagating in a binary exponential-correlated disordered floor with the solution of the homogeneous telegrapher’s equation. Analytical results for the exact dispersion-relation are presented. In addition, the time-dependent analysis of mean-value monochromatic waves is also shown.
The time evolution of correlations for two indistinguishable free particles, in a one-dimensional... more The time evolution of correlations for two indistinguishable free particles, in a one-dimensional lattice interacting with a quantum bath, is studied in the Born-Markov approximation. The analytical solution for the density matrix is obtained, for bosons and fermions, in the second quantization formalism. The time evolution of the negativity of indistinguishable particles is analyzed for quantum mixed states. Quantum correlations heavily depend on the selected bipartition; in return, a small difference between the statistics of the particles is noted, due to the Pauli exclusion principle. In the presence of dissipation, the negativity (a nonclassical correlation) shows a time-oscillatory behavior for a particular geometrical bipartition. The total probability of finding one particle in each subsystem is also calculated and shows consistent behavior.
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