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Canadian Journal of Physics

Quantum information of a relativistic particle with position-dependent mass under the Aharonov–Casher effect

A. R. P. Moreira, P. O. Amadi, A. N. Ikot, R. Horchani, Norshamsuri Ali

Published Dec 5, 2024• 0 citations
Publisher

Abstract

In this work, the influence of the Aharonov–Casher (AC) effect is investigated for a relativistic particle with position-dependent mass through Shannon quantum information. Shannon’s formalism is appropriate because its results suggest explanations for the measurement uncertainties of a quantum system. To calculate Shannon’s entropy, it is necessary to obtain the description of quantum eigenstates. Using the eigenstates obtained, we analyzed the system quantum information in position and momentum space. Considering the results of Shannon’s entropy, it is possible to understand the influence of the AC effect and the position-dependent mass on the quantum information. It was possible to notice that the informational content decreases in the position space when we increase the value of the parameter that controls the mass profile. This result is strong, as it indicates a decrease in uncertainties related to particle position measurements. The opposite happens when we increase the quantum phase ΦAC.

DOI
10.1139/cjp-2024-0034

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In this work, the influence of the Aharonov–Casher (AC) effect is investigated for a relativistic particle with position-dependent mass through Shannon quantum information. Shannon’s formalism is appropriate because its results suggest explanations for the measurement uncertainties of a quantum system. To calculate Shannon’s entropy, it is necessary to obtain the description of quantum eigenstates. Using the eigenstates obtained, we analyzed the system quantum information in position and momentum space. Considering the results of Shannon’s entropy, it is possible to understand the influence of the AC effect and the position-dependent mass on the quantum information. It was possible to notice that the informational content decreases in the position space when we increase the value of the parameter that controls the mass profile. This result is strong, as it indicates a decrease in uncertainties related to particle position measurements. The opposite happens when we increase the quantum phase ΦAC.
Using Schrödinger’s formalism, we investigate the quantum eigenstates of the heavy mesons trapped by a point-like defect and by Cornell’s potential. One implements this defect to the model considering a spherical metric profile coupled to it. Furthermore, the Nikiforov–Uvarov method is applied to theory to study the quantum eigenstates of the heavy mesons. To calculate the quantum information entropy (QIE), one considers the wave functions that describe the charmonium and bottomonium states. To explore the QIE, we use the well-known Shannon’s entropy formulated at the position and reciprocal space. The analysis of the QIE gives us relevant information about how the quantum information change with the variation of the point-like defect. Consequently, considering the Bialynicki-Birula and Mycielski (BBM) relation, we show how this defect influences the quarkonium position and momentum uncertainty measures.
Abstract In this research article, we use the Shannon’s formalism to investigate the quantum information entropy of a particle trapped by the Aharonov–Bohm-type field. For quantum information study, it is necessary to investigate the eigenstates of the quantum system, i.e. the wave functions and energies of the quantum states. We assumed that the particle is in principle, confined in a cylindrical box in the presence of Aharonov–Bohm-type effect due to dislocation defect. Analysis of the quantum information entropy, reveals that the dislocation influences the eigenstates and, consequently, the quantum information of the system.
The Shannon information entropy for the Schrödinger equation with a nonuniform solitonic mass is evaluated for a hyperbolic-type potential. The number of nodes of the wave functions in the transformed space z are broken when recovered to original space x . The position S x and momentum S p information entropies for six low-lying states are calculated. We notice that the S x decreases with the increasing mass barrier width a and becomes negative beyond a particular width a , while the S p first increases with a and then decreases with it. The negative S x exists for the probability densities that are highly localized. We find that the probability density ρ ( x ) for n = 1, 3, 5 are greater than 1 at position x = 0. Some interesting features of the information entropy densities ρ s ( x ) and ρ s ( p ) are demonstrated. The Bialynicki–Birula–Mycielski (BBM) inequality is also tested for these states and found to hold.
In this research article, the influence of magnetic and Aharonov-Bohm flux fields on Shannon entropy with improved Kratzer potential for Scandium fluoride (ScF) and hydrogen (H2) molecules are studied analytically and numerically for three low-lying states. The wave function and probability density which controls the chemical and physical properties of atomic and molecular systems have been obtained by solving the Schrodinger wave equation coupled with charged particle Hamiltonian via the Nikiforov-Uvarov functional analysis method. The total normalized wave function was expressed in terms of the hypergeometric function of Jacobi polynomials and then utilized to evaluate the Shannon entropy for two diatomic molecules in position and momentum spaces. The wave function and electronic densities were graphically analyzed. Our numerical results of Shannon entropies sum as applied to ScF and H2 were verified to obey the Shannon-entropy-based uncertainty relation. Observations from our results also reveal negative values of Shannon entropies in the position coordinates depicting high localization of particles and stability. In Addition, the effects of the external fields on the quantum systems were observed to influence the quantum information-theoretic measure by small decrements in the Shannon entropy values when compared to the case of the absence of the external fields, indicating a further improvement in the localization of particles and system's stability. This work has applications in atomic and molecular dynamic, molecular drug design, nanostructure processes, information technology, amongst others.
Position and momentum information measures are evaluated for the ground state of the \emph{relativistic} hydrogen-like atoms. Consequences of the fact that the radial momentum operator is not self-adjoint are explicitly studied, exhibiting fundamental shortcomings of the conventional uncertainty measures in terms of the radial position and momentum variances. The Shannon and Rényi entropies, the Fisher information measure, as well as several related information measures, are considered as viable alternatives. Detailed results on the onset of relativistic effects for low nuclear charges, and on the extreme relativistic limit, are presented. The relativistic position density decays exponentially at large rrr, but is singular at the origin. Correspondingly, the momentum density decays as an inverse power of ppp. Both features yield divergent Rényi entropies away from a finite vicinity of the Shannon entropy. While the position space information measures can be evaluated analytically for both the nonrelativistic and the relativistic hydrogen atom, this is not the case for the relativistic momentum space. Some of the results allow interesting insight into the significance of recently evaluated Dirac-Fock vs. Hartree-Fock complexity measures for many-electron neutral atoms.
The Shannon information entropy for the Schrodinger equation with a nonuniform solitonic mass is evaluated for a hyperbolic-type potential. The number of nodes of the wave functions in the transformed space z are broken when recovered to original space x. The position Sx and momentum S p information entropies for six low-lying states are calculated. We notice that the Sx decreases with the increasing mass barrier width a and becomes negative beyond a particular width a,while the Sp first increases with a and then decreases with it. The negative Sx exists for the probability densities that are highly localized. We find that the probability density ρ(x) for n = 1, 3, 5 are greater than 1 at position x = 0. Some interesting features of the information entropy densities ρs(x) and ρs(p) are demonstrated. The Bialynicki–Birula–Mycielski(BBM)inequality is also tested for these states and found to hold.