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M. P. Pato

Publications and source records attributed to M. P. Pato.

At least 19 recordsLinked to original sources
arXiv2020

Entanglement of pseudo-Hermitian random states

In a recent paper (arXiv:1905.07348v1), Dyson scheme to deal with density matrix of non-Hermitian Hamiltonians has been used to investigate the entanglement of states of a PT-symmetric bosonic system. They found that von Neumann entropy can show a different behavior in the broken and unbroken regime. We show that their results can be recast in terms of an abstract model of pseudo-Hermitian random matrices. It is found however that, although the formalism is practically the same, the entanglement is not of Fock states but of Bell states.

quant-ph↗
arXiv2012

Distribution of Schmidt-like eigenvalues for Gaussian Ensembles of the Random Matrix Theory

We analyze the form of the probability distribution function P_{n}^{(β)}(w) of the Schmidt-like random variable w = x_1^2/(\sum_{j=1}^n x^{2}_j/n), where x_j are the eigenvalues of a given n \times n β-Gaussian random matrix, βbeing the Dyson symmetry index. This variable, by definition, can be considered as a measure of how any individual eigenvalue deviates from the arithmetic mean value of all eigenvalues of a given random matrix, and its distribution is calculated with respect to the ensemble of such β-Gaussian random matrices. We show that in the asymptotic limit n \to \infty and for arbitrary βthe distribution P_{n}^{(β)}(w) converges to the Marčenko-Pastur form, i.e., is defined as P_{n}^{(β)}(w) \sim \sqrt{(4 - w)/w} for w \in [0,4] and equals zero outside of the support. Furthermore, for Gaussian unitary (β= 2) ensembles we present exact explicit expressions for P_{n}^{(β=2)}(w) which are valid for arbitrary n and analyze their behavior.

cond-mat.dis-nn↗
arXiv2011

Random matrices ensembles and the extensivity of the Sq entropy

We consider the joint density distribution of the elements of certain random matrix models which are example of globally correlated and asymptotically scale-invariant distributions. It is shown that in their cases, the nonadditive entropy $S_q$ is extensive only when the limit $q\rightarrow 1$ is taken. On the other hand, when restriction in the occupation of the phase space is imposed extensiveness is obtained for values of the entropic parameter different of one.

cond-mat.stat-mech↗
arXiv2011

Hyperbolic disordered ensembles of random matrices

Using the simple procedure, recently introduced, of dividing Gaussian matrices by a positive random variable, a family of random matrices is generated characterized by a behavior ruled by the generalized hyperbolic distribution. The spectral density evolves from the semi-circle law to a Gaussian-like behavior while concomitantly the local fluctuations show a transition from the Wigner-Dyson to the Poisson statistics. Long range statistics such as number variance exhibit large fluctuations typical of non-ergodic ensembles.

cond-mat.dis-nn↗
arXiv2010

Decomposition of spectral density in individual eigenvalue contributions

The eigenvalue densities of two random matrix ensembles, the Wigner Gaussian matrices and the Wishart covariant matrices, are decomposed in the contributions of each individual eigenvalue distribution. It is shown that the fluctuations of all eigenvalues, for medium matrix sizes, are described with a good precision by nearly normal distributions.

math-ph↗
arXiv2008

Deformations of the Tracy-Widom distribution

In random matrix theory (RMT), the Tracy-Widom (TW) distribution describes the behavior of the largest eigenvalue. We consider here two models in which TW undergoes transformations. In the first one disorder is introduced in the Gaussian ensembles by superimposing an external source of randomness. A competition between TW and a normal (Gaussian) distribution results, depending on the spreading of the disorder. The second model consists in removing at random a fraction of (correlated) eigenvalues of a random matrix. The usual formalism of Fredholm determinants extends naturally. A continuous transition from TW to the Weilbull distribution, characteristc of extreme values of an uncorrelated sequence, is obtained.

cond-mat.stat-mech↗
arXiv2008

Perturbative Treatment of Symmetry Breaking Within Random Matrix Theory

We discuss the applicability, within the Random Matrix Theory, of perturbative treatment of symmetry breaking to the experimental data on the flip symmetry breaking in quartz crystal. We found that the values of the parameter that measures this breaking are different for the spacing distribution as compared to those for the spectral rigidity. We consider both twofold and threefold symmetries. The latter was found to account better for the spectral rigidity than the former. Both cases, however, underestimate the experimental spectral rigidity at large L. This discrepancy can be resolved if an appropriate number of eigenfrequecies is considered to be missing in the sample. Our findings are relevant to isospin violation study in nuclei.

nucl-th↗
arXiv2007

Symmetry Breaking Study with Random Matrix Ensembles

A random matrix model to describe the coupling of $m$-fold symmetry is constructed. The particular threefold case is used to analyze data on eigenfrequencies of elastomechanical vibration of an anisotropic quartz block. It is suggested that such experimental/theoretical study may supply a powerful means to discern intrinsic symmetry of physical systems.

physics.data-an↗
arXiv2007

Disordered ensembles of random matrices

It is shown that the families of generalized matrix ensembles recently considered which give rise to an orthogonal invariant stable Lévy ensemble can be generated by the simple procedure of dividing Gaussian matrices by a random variable. The nonergodicity of this kind of disordered ensembles is investigated. It is shown that the same procedure applied to random graphs gives rise to a family that interpolates between the Erdös-Renyi and the scale free models.

cond-mat.stat-mech↗
arXiv2007

Symmetry Breaking Study with Deformed Ensembles

A random matrix model to describe the coupling of m-fold symmetry in constructed. The particular threefold case is used to analyze data on eigenfrequencies of elastomechanical vibration of an anisotropic quartz block. It is suggested that such experimental/theoretical study may supply powerful means to discern intrinsic symmetries in physical systems.

physics.data-an↗
arXiv2006

Randomly incomplete spectra and intermediate statistics

By randomly removing a fraction of levels from a given spectrum a model is constructed that describes a crossover from this spectrum to a Poisson spectrum. The formalism is applied to the transitions towards Poisson from random matrix theory (RMT) spectra and picket fence spectra. It is shown that the Fredholm determinant formalism of RMT extends naturally to describe incomplete RMT spectra.

cond-mat.stat-mech↗
arXiv2005

Level density for deformations of the Gaussian orthogonal ensemble

Formulas are derived for the average level density of deformed, or transition, Gaussian orthogonal random matrix ensembles. After some general considerations about Gaussian ensembles we derive formulas for the average level density for (i) the transition from the Gaussian orthogonal ensemble (GOE) to the Poisson ensemble and (ii) the transition from the GOE to $m$ GOEs.

nucl-th↗
arXiv2004

Family of generalized random matrix ensembles

Using the Generalized Maximium Entropy Principle based on the nonextensive q entropy a new family of random matrix ensembles is generated. This family unifies previous extensions of Random Matrix Theory and gives rise to an orthogonal invariant stable Levy ensemble with new statistical properties. Some of them are analytically derived.

math-ph↗
arXiv2004

Missing levels in correlated spectra

Complete spectroscopy (measurements of a complete sequence of consecutive levels) is often considered as a prerequisite to extract fluctuation properties of spectra. It is shown how this goal can be achieved even if only a fraction of levels are observed. The case of levels behaving as eigenvalues of random matrices, of current interest in nuclear physics, is worked out in detail.

nucl-th↗
arXiv2004

Addendum: Attenuation of the intensity within a superdeformed band

We investigate a random matrix model [Phys. Rev. C {\bf 65} 024302 (2002] for the decay-out of a superdeformed band as a function of the parameters: $Γ^\downarrow/Γ_S$, $Γ_N/D$, $Γ_S/D$ and $Δ/D$. Here $Γ^\downarrow$ is the spreading width for the mixing of an SD state $|0>$ with a normally deformed (ND) doorway state $|d>$, $Γ_S$ and $Γ_N$ are the electromagnetic widths of the the SD and ND states respectively, $D$ is the mean level spacing of the compound ND states and $Δ$ is the energy difference between $|0>$ and $|d>$. The maximum possible effect of an order-chaos transition is inferred from analytical and numerical calculations of the decay intensity in the limiting cases for which the ND states obey Poisson and GOE statistics. Our results show that the sharp attenuation of the decay intensity cannot be explained solely by an order-chaos transition.

nucl-th↗
arXiv2004

Energy averages over regular and chaotic states in the decay out of superdeformed bands

We describe the decay out of a superdeformed band using the methods of reaction theory. Assuming that decay-out occurs due to equal coupling (on average) to a sea of equivalent chaotic normally deformed (ND) states, we calculate the average intraband decay intensity and show that it can be written as an ``optical'' background term plus a fluctuation term, in total analogy with average nuclear cross sections. We also calculate the variance in closed form. We investigate how these objects are modified when the decay to the ND states occurs via an ND doorway and the ND states' statistical properties are changed from chaotic to regular. We show that the average decay intensity depends on two dimensionless variables in the first case while in the second case, four variables enter the picture.

nucl-th↗