Gaussian ensembles distributions from mixing quantum systems

In the context of the mixing dynamical systems we present a derivation of the Gaussian ensembles distributions from mixing quantum systems having a classical analog that is mixing. We find that mixing factorization property is satisfied for the mixing quantum systems expressed as a factorization of quantum mean values. For the case of the kicked rotator and in its fully chaotic regime, the factorization property links decoherence by dephasing with Gaussian ensembles in terms of the weak limit, interpreted as a decohered state. Moreover, a discussion about the connection between random matrix theory and quantum chaotic systems, based on some attempts made in previous works and from the viewpoint of the mixing quantum systems, is presented

Entropic measures of joint uncertainty: effects of lack of majorization

We compute R\'enyi entropies for the statistics of a noisy simultaneous observation of two complementary observables in two-dimensional quantum systems. The relative amount of uncertainty between two states depends on the uncertainty measure used. These results are not reproduced by a more standard duality relation. We show that these behaviors are consistent with the lack of majorization relation between the corresponding statistics.Comment: 10 pages, 3 figure

On a generalized entropic uncertainty relation in the case of the qubit

We revisit generalized entropic formulations of the uncertainty principle for an arbitrary pair of quantum observables in two-dimensional Hilbert space. R\'enyi entropy is used as uncertainty measure associated with the distribution probabilities corresponding to the outcomes of the observables. We derive a general expression for the tight lower bound of the sum of R\'enyi entropies for any couple of (positive) entropic indices (\alpha,\beta). Thus, we have overcome the H\"older conjugacy constraint imposed on the entropic indices by Riesz-Thorin theorem. In addition, we present an analytical expression for the tight bound inside the square [0 , 1/2] x [0 , 1/2] in the \alpha-\beta plane, and a semi-analytical expression on the line \beta = \alpha. It is seen that previous results are included as particular cases. Moreover, we present an analytical but suboptimal bound for any couple of indices. In all cases, we provide the minimizing states.Comment: 15 pages, 6 figure

Excited states of 4He droplets

We study low-lying excited states of 4He clusters up to a cluster size of 40 atoms in a variational framework. The ansatz wave function combines two- and three-body correlations, coming from a translationally invariant configuration interaction description, and Jastrow-type short-range correlation. We have previously used this scheme to determine the ground-state energies of 4He and 3He clusters. Here we present an extension of this ansatz wave function having a good quantum angular momentum L. The variational procedure is applied independently to the cases with L = 0,2,4, and upper bounds for the corresponding energies are thus obtained. Moreover, centroid energies for L excitations are calculated through the use of sum rules. A comparison with previous calculations is also made.Fil: Guardiola, R.. Facultad de Física / Dpto de Física Atómica y Nuclear; EspañaFil: Navarro, J.. Csic - Univ. de Valencia / Inst. de Física Corpuscular; EspañaFil: Portesi, Mariela Adelina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentin

Position-momentum uncertainty relations based on moments of arbitrary order

The position-momentum uncertainty-like inequality based on moments of arbitrary order for d-dimensional quantum systems, which is a generalization of the celebrated Heisenberg formulation of the uncertainty principle, is improved here by use of the Renyi-entropy-based uncertainty relation. The accuracy of the resulting lower bound is physico-computationally analyzed for the two main prototypes in d-dimensional physics: the hydrogenic and oscillator-like systems.Comment: 31 pages, 9 figure

A semiclassical condition for chaos based on Pesin theorem

A semiclassical method to determine if the classical limit of a quantum system is chaotic or not, based on Pesin theorem, is presented. The method is applied to a phenomenological Gamow--type model and it is concluded that its classical limit is chaotic

Ergodic statistical models: Entropic dynamics and chaos

We present an extension of the ergodic, mixing and Bernoulli levels of the ergodic hierarchy in dynamical systems, the information geometric ergodic hierarchy, making use of statistical models on curved manifolds in the context of information geometry. We discuss the 2×2 Gaussian Orthogonal Ensembles (GOE) within a 2D correlated model. For values of the correlation coefficient vanishingly small, we find that GOE belong to the information geometric (IG) mixing level having a maximum negative value of scalar curvature. Moreover, we propose a measure of distinguishability for the family of distributions of the 2D correlated model that results to be an upper bound of the IG correlation.Instituto de Física La PlataConsejo Nacional de Investigaciones Científicas y Técnica

Entropic Analysis of the Quantum Oscillator with a Minimal Length

The well-known Heisenberg-Robertson uncertainty relation for a pair of noncommuting observables, is expressed in terms of the product of variances and the commutator among the operators, computed for the quantum state of a system. Different modified commutation relations have been considered in the last years with the purpose of taking into account the effect of quantum gravity. Indeed it can be seen that letting [X,P]=iℏ(1+β P^2) implies the existence of a minimal length proportional to sqrt(β). The Bialynicki-Birula-Mycielski entropic uncertainty relation in terms of Shannon entropies is also seen to be deformed in the presence of a minimal length, corresponding to a strictly positive deformation parameter β. Generalized entropies can be implemented. Indeed, results for the sum of position and (auxiliary) momentum Rényi entropies with conjugated indices have been provided recently for the ground and first excited state. We present numerical findings for conjugated pairs of entropic indices, for the lowest lying levels of the deformed harmonic oscillator system in 1D, taking into account the position distribution for the wavefunction and the actual momentum.Fil: Puertas Centeno, David. Universidad Rey Juan Carlos; EspañaFil: Portesi, Mariela Adelina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentin

Radiación coherente y teoría de la información

El cuerpo de esta Tesis consta principalmente de dos partes y está organizado en cuatro capítulos, cuyo contenido detallamos en este sumario. La primera parte está dedicada al modelo de Dicke —que describe un conjunto de átomos interactuando con radiación electromagnética en una cavidad— y a la forma de caracterizar su dinámica por medio de la Teoría de la Información (TI). En este contexto informacional hacemos uso del concepto de entropía, que mediante maximización sujeta a ligaduras permite determinar el operador densidad que caracteriza al sistema cuántico en todo momento de su evolución. En la segunda parte de la Tesis, presentamos dos aplicaciones de una reciente generalización de la forma entròpica convencional de Boltzmann-Shannon. Una de ellas es el análisis de una formulación cuantitativa del Principio de Incerteza de la Mecánica Cuántica, en el espíritu de la TI. La otra aplicación se refiere a un estudio del tamaño aparente de un sistema físico en el contexto de la Mecánica Estadística no extensiva surgida de la entropía generalizada.Tesis digitalizada en SEDICI gracias a la Biblioteca de Física de la Facultad de Ciencias Exactas (UNLP).Facultad de Ciencias Exacta

Radiación coherente y teoría de la información

El cuerpo de esta Tesis consta principalmente de dos partes y está organizado en cuatro capítulos, cuyo contenido detallamos en este sumario. La primera parte está dedicada al modelo de Dicke —que describe un conjunto de átomos interactuando con radiación electromagnética en una cavidad— y a la forma de caracterizar su dinámica por medio de la Teoría de la Información (TI). En este contexto informacional hacemos uso del concepto de entropía, que mediante maximización sujeta a ligaduras permite determinar el operador densidad que caracteriza al sistema cuántico en todo momento de su evolución. En la segunda parte de la Tesis, presentamos dos aplicaciones de una reciente generalización de la forma entròpica convencional de Boltzmann-Shannon. Una de ellas es el análisis de una formulación cuantitativa del Principio de Incerteza de la Mecánica Cuántica, en el espíritu de la TI. La otra aplicación se refiere a un estudio del tamaño aparente de un sistema físico en el contexto de la Mecánica Estadística no extensiva surgida de la entropía generalizada.Tesis digitalizada en SEDICI gracias a la Biblioteca de Física de la Facultad de Ciencias Exactas (UNLP).Facultad de Ciencias Exacta