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arXiv:2212.09208 · Physica Scripta

Quantum information entropy of a particle trapped by the Aharonov–Bohm-type effect

F. C. E. Lima, A. R. P. Moreira, C. A. S. Almeida, Collins Okon Edet, Norshamsuri Ali

Published May 5, 2023• 17 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1402-4896/acd309

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World Journal of Applied Science & Technology•Aug 29, 2024•0 citations
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.
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.
We investigate quantum information by a theoretical measurement approach of an Aharanov-Bohm (AB) ring with Yukawa interaction in curved space with disclination. We obtained the so-called Shannon entropy through the eigenfunctions of the system. The quantum states considered come from Schrödinger theory with the AB field in the background of curved space. With this entropy, we can explore the quantum information at the position space and reciprocal space. Furthermore, we discussed how the magnetic field, the AB flux, and the topological defect influence the quantum states and the information entropy.
Abstract In this work, we solve the Schrödinger equation of a particle restricted to move on a cone surface of finite height under the influence of an Aharonov–Bohm magnetic field. The energy eigenvalues and their respective wave functions are obtained analytically as a function of the radial distance from the apex and the apex angle. We compute the Shannon entropy in configuration and momentum space for the ground and the first excited states as a function of the slant height and the apex angle. In the absence of magnetic flux the states (n,m) and (n,−m) have identical Shannon entropies, but for non-zero fluxes the Shannon entropies of these states are different, their values depending on the state, the apex angle and the value of the magnetic flux.
The Shannon information entropy for scandium fluoride (ScF) and hydrogen (H2) molecules in the presence of magnetic and Aharanov–Bohm (AB) fields with modified Kratzer plus screened Coulomb potential in the position and momentum coordinate is investigated. The wavefunction and probability density are obtained by solving the two-dimensional (2D) Schrödinger wave equation using the Nikiforov–Uvarov functional analysis method and then applied to calculate the Shannon entropy. The graphical behaviour of the 2D wavefunction and probability density is showcased. Our results depict the effects of the external fields on Shannon entropy for ScF and (H2), the negative values of the position Shannon entropies obtained imply higher localisation of the particles and molecules indicating more stability of the system. Another interesting part of this work is that Bialynicki–Birula–Mycielski inequality is tested and proven bounded for both diatomic molecules. A few to mention, this research will enhance the apprehension of the dynamics of quantum molecules and systems subjected to external fields, quantum information signal processing and communication.
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.