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The European Physical Journal Plus

Shannon information entropy in the presence of magnetic and Aharanov–Bohm (AB) fields

Collins Okon Edet, A. N. Ikot

Published Apr 1, 2021• 49 citations
Publisher
DOI
10.1140/epjp/s13360-021-01438-4

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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.
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 paper, Fisher and Shannon information entropies in two-dimensional spaces were analysed for hydrogen diatomic molecules using a non-central exponential-type potential, both in the presence and absence of magnetic and Aharanov-Bohm (AB) flux fields. By solving the two-dimensional Schrödinger equation in the presence of charged Hamiltonian using the parametric Nikiforov-Uvarov (NU) method, we obtained numerical solutions for different potential depths for Fisher and Shannon information entropies. These results adhere to Bialynicki-Birula and Mycielski (BBM) and Fisher-based inequalities. The findings have significant applications in chemical physics, aiding in the analysis of molecular electronic properties, stability and reactivity under varying external influences. Additionally, the study contributes to quantum information by offering insights into the localisation and delocalisation phenomena, with direct applications to quantum computation, entanglement, and communication technologies.