Decoherence, Anti-Decoherence, and Fisher Information

In this work, we study quantum decoherence as reflected by the dynamics of a system that accounts for the interaction between matter and a given field. The process is described by an important information geometry tool: Fisher’s information measure (FIM). We find that it appropriately describes this concept, detecting salient details of the quantum–classical changeover (qcc). A good description of the qcc report can thus be obtained; in particular, a clear insight into the role that the uncertainty principle (UP) plays in the pertinent proceedings is presented. Plotting FIM versus a system’s motion invariant related to the UP, one can also visualize how anti-decoherence takes place, as opposed to the decoherence process studied in dozens of papers. In Fisher terms, the qcc can be seen as an order (quantum)–disorder (classical, including chaos) transition.

On Certain Properties and Applications of the Perturbed Meixner–Pollaczek Weight

This paper deals with monic orthogonal polynomials orthogonal with a perturbation of classical Meixner–Pollaczek measure. These polynomials, called Perturbed Meixner–Pollaczek polynomials, are described by their weight function emanating from an exponential deformation of the classical Meixner–Pollaczek measure. In this contribution, we investigate certain properties such as moments of finite order, some new recursive relations, concise formulations, differential-recurrence relations, integral representation and some properties of the zeros (quasi-orthogonality, monotonicity and convexity of the extreme zeros) of the corresponding perturbed polynomials. Some auxiliary results for Meixner–Pollaczek polynomials are revisited. Some applications such as Fisher’s information, Toda-type relations associated with these polynomials, Gauss–Meixner–Pollaczek quadrature as well as their role in quantum oscillators are also reproduced.

Beta Generalized Exponentiated Frechet Distribution with Applications

In this article we introduce a new six - parameters model called the Beta Generalized Exponentiated-Frechet (BGEF) distribution which exhibits decreasing hazard rate. Many models such as Beta Frechet (BF), Beta ExponentiatedFrechet (BEF), Generalized Exponentiated-Frechet (GEF), ExponentiatedFrechet (EF), Frechet (F) are sub models. Some of its properties including rth moment, reliability and hazard rate are investigated. The method of maximum likelihood isproposed to estimate the model parameters. The observed Fisher’s information matrix is given. Moreover, we give the advantage of the (BGEF) distribution by an application using two real datasets

Analysis of quantum-mechanical states of the ring-shaped Mie-type diatomic molecular model via the Fisher's information

Recently, the information theory of quantum-mechanical systems has aroused the interest of many theoretical physicists. This is due to the fact that it provides a deeper insight into the internal structure of the system. Also, it is the strongest support of the modern quantum computation and information, which is a basic theory for numerous technological developments. This study reports the solution of Schrödinger equation with the ring-shaped Mie-type potential. The rotational-vibrational spectroscopic study of some few selected diatomic molecules are given. The probability distribution density of the system which gives the probability density for observing the electron in the state characterized by the quantum numbers (n, l, m) in the ring-shaped Mie-type potential is obtained. Finally, the analysis for this distribution via a complementary information measures of a probability distribution known as the Fisher's information have been presented.

Generalized Wavelet Fisher’s Information of1/fαSignals

This paper defines the generalized wavelet Fisher information of parameterq. This information measure is obtained by generalizing the time-domain definition of Fisher’s information of Furuichi to the wavelet domain and allows to quantify smoothness and correlation, among other signals characteristics. Closed-form expressions of generalized wavelet Fisher information for1/fαsignals are determined and a detailed discussion of their properties, characteristics and their relationship with waveletq-Fisher information are given. Information planes of1/fsignals Fisher information are obtained and, based on these, potential applications are highlighted. Finally, generalized wavelet Fisher information is applied to the problem of detecting and locating weak structural breaks in stationary1/fsignals, particularly for fractional Gaussian noise series. It is shown that by using a joint Fisher/F-Statistic procedure, significant improvements in time and accuracy are achieved in comparison with the sole application of theF-statistic.

On the comparison of fisher information of some probability distributions

In 1998 Gupta, R. C., Gupta, P. L. and Gupta, R. D. have introduced the exponentiated exponential distribution (or the generalized exponential distribution) as a generalization of the standard exponential distribution. The mathematical properties of this distribution have been studied in detail by Gupta and Kundu (2001). The aim of this paper is to establish some relations concerning the Fisher’s information of the generalized exponential distribution and the similar information corresponding in the case of the weighted version.