Analysis of Information Entropies for He-Like Ions
Abstract
Doi: 10.28991/ESJ-2022-06-04-08
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References
Shannon, C. E. (1948). A Mathematical Theory of Communication. Bell System Technical Journal, 27(3), 379–423. doi:10.1002/j.1538-7305.1948.tb01338.x.
Rényi, A. (1961, January). On measures of entropy and information. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Contributions to the Theory of Statistics, 4, 547-562, University of California Press, Oakland, United States.
Tsallis, C. (1988). Possible generalization of Boltzmann-Gibbs statistics. Journal of Statistical Physics, 52(1–2), 479–487. doi:10.1007/BF01016429.
Hô, M., Sagar, R. P., Pérez-Jordá, J. M., Smith, V. H., & Esquivel, R. O. (1994). A numerical study of molecular information entropies. Chemical Physics Letters, 219(1–2), 15–20. doi:10.1016/0009-2614(94)00029-8.
Saha, S., & Jose, J. (2020). Shannon entropy as a predictor of avoided crossing in confined atoms. International Journal of Quantum Chemistry, 120(22), e26374. doi:10.1002/qua.26374.
Martínez-Flores, C. (2021). The information theory of the helium atom in screened Coulomb potentials. International Journal of Quantum Chemistry, 121(6), e26529. doi:10.1002/qua.26529.
Nasser, I., Zeama, M., & Abdel-Hady, A. (2019). The nonadditive entropy for the ground state of helium-like ions using Hellmann potential. Molecular Physics, 118(3), 1612105. doi:10.1080/00268976.2019.1612105.
Nasser, I., Zeama, M., & Abdel-Hady, A. (2020). Rényi, Fisher, Shannon, and their electron correlation tools for two-electron series. Physica Scripta, 95(9), 095401. doi:10.1088/1402-4896/abaa09.
Lin, Y. C., Lin, C. Y., & Ho, Y. K. (2013). Spatial entanglement in two-electron atomic systems. Physical Review A - Atomic, Molecular, and Optical Physics, 87(2), 022316. doi:10.1103/PhysRevA.87.022316.
Lin, Y. C., & Ho, Y. K. (2014). Quantum entanglement for two electrons in the excited states of helium-like systems. Canadian Journal of Physics, 93(6), 646–653. doi:10.1139/cjp-2014-0437.
Sen, K. D. (2005). Characteristic features of Shannon information entropy of confined atoms. Journal of Chemical Physics, 123(7), 074110. doi:10.1063/1.2008212.
Nahum, A., Ruhman, J., & Huse, D. A. (2018). Dynamics of entanglement and transport in one-dimensional systems with quenched randomness. Physical Review B, 98(3), 035118. doi:10.1103/PhysRevB.98.035118.
Barghathi, H., Herdman, C. M., & Del Maestro, A. (2018). Rényi Generalization of the Accessible Entanglement Entropy. Physical Review Letters, 121(15), 150501. doi:10.1103/PhysRevLett.121.150501.
Herdman, C. M., Roy, P. N., Melko, R. G., & Maestro, A. Del. (2017). Entanglement area law in superfluid 4 He. Nature Physics, 13(6), 556–558. doi:10.1038/nphys4075.
Kaufman, A. M., Tai, M. E., Lukin, A., Rispoli, M., Schittko, R., Preiss, P. M., & Greiner, M. (2016). Quantum thermalization through entanglement in an isolated many-body system. Science, 353(6301), 794–800. doi:10.1126/science.aaf6725.
Rouse, I., & Willitsch, S. (2017). Superstatistical Energy Distributions of an Ion in an Ultracold Buffer Gas. Physical Review Letters, 118(14), 143401. doi:10.1103/PhysRevLett.118.143401.
Dechant, A., Kessler, D. A., & Barkai, E. (2015). Deviations from Boltzmann-Gibbs statistics in confined optical lattices. Physical Review Letters, 115(17), 173006. doi:10.1103/PhysRevLett.115.173006.
Najafizade, S. A., Hassanabadi, H., & Zarrinkamar, S. (2016). Nonrelativistic Shannon information entropy for Kratzer potential. Chinese Physics B, 25(4), 40301. doi:10.1088/1674-1056/25/4/040301.
Amadi, P. O., Ikot, A. N., Ngiangia, A. T., Okorie, U. S., Rampho, G. J., & Abdullah, H. Y. (2020). Shannon entropy and Fisher information for screened Kratzer potential. International Journal of Quantum Chemistry, 120(14), e26246. doi:10.1002/qua.26246.
Dehesa, J. S., Koga, T., Yáñez, R. J., Plastino, A. R., & Esquivel, R. O. (2011). Quantum entanglement in helium. Journal of Physics B: Atomic, Molecular and Optical Physics, 45(1), 015504. doi:10.1088/0953-4075/45/1/015504.
López-Rosa, S., Martín, A. L., Antolín, J., & Angulo, J. C. (2019). Electron-pair entropic and complexity measures in atomic systems. International Journal of Quantum Chemistry, 119(7), e25861. doi:10.1002/qua.25861.
Lin, C. H., & Ho, Y. K. (2015). Shannon information entropy in position space for two-electron atomic systems. Chemical Physics Letters, 633(5), 261–264. doi:10.1016/j.cplett.2015.05.029.
Nascimento, W. S., de Almeida, M. M., & Prudente, F. V. (2021). Coulomb correlation and information entropies in confined helium-like atoms. European Physical Journal D, 75(6). doi:10.1140/epjd/s10053-021-00177-6.
Al-Jibbouri, H. Compton Profile of 1s2-State for 2≤Z≤10. Indian Journal of Pure & Applied Physics, 59(11), 752–755. Available online: Available online: http://nopr.niscair.res.in/handle/123456789/58624 (accessed on January 2022).
Majumdar, S., & Roy, A. K. (2020). Shannon entropy in confined he-like ions within a density functional formalism. Quantum Reports, 2(1), 189–207. doi:10.3390/quantum2010012.
Ou, J. H., & Ho, Y. K. (2019). Benchmark calculations of Rényi, Tsallis entropies, and Onicescu information energy for ground state helium using correlated Hylleraas wave functions. International Journal of Quantum Chemistry, 119(14), e25928. doi:10.1002/qua.25928.
Ou, J. H., & Ho, Y. K. (2017). Shannon information entropy in position space for the ground and singly excited states of helium with finite confinements. Atoms, 5(2), 15. doi:10.3390/atoms5020015.
Toranzo, I. V., Puertas-Centeno, D., & Dehesa, J. S. (2016). Entropic properties of D-dimensional Rydberg systems. Physica A: Statistical Mechanics and Its Applications, 462(6), 1197–1206. doi:10.1016/j.physa.2016.06.144.
Estañón, C. R., Aquino, N., Puertas-Centeno, D., & Dehesa, J. S. (2020). Two-dimensional confined hydrogen: An entropy and complexity approach. International Journal of Quantum Chemistry, 120(11), e26192. doi:10.1002/qua.26192.
Liu, S.-B., Rong, C.-Y., Wu, Z.-M., & Lu, T. (2015). Rényi Entropy, Tsallis Entropy and Onicescu Information Energy in Density Functional Reactivity Theory. Acta Physico-Chimica Sinica, 31(11), 2057–2063. doi:10.3866/pku.whxb201509183.
Ou, J. H., & Ho, Y. K. (2019). Shannon, rényi, tsallis entropies and onicescu information energy for low-lying singly excited states of helium. Atoms, 7(3), 1–15. doi:10.3390/atoms7030070.
Romera, E., & Dehesa, J. S. (2004). The Fisher-Shannon information plane, an electron correlation tool. Journal of Chemical Physics, 120(19), 8906–8912. doi:10.1063/1.1697374.
Shi, Q., & Kais, S. (2004). Finite size scaling for the atomic Shannon-information entropy. Journal of Chemical Physics, 121(12), 5611–5617. doi:10.1063/1.1785773.
Shi, Q., & Kais, S. (2005). Discontinuity of Shannon information entropy for two-electron atoms. Chemical Physics, 309(2–3), 127–131. doi:10.1016/j.chemphys.2004.08.020.
Farid, M., Abdel-Hady, A., & Nasser, I. (2017). Comparative study of the scaling behavior of the Rényi entropy for He-like atoms. Journal of Physics: Conference Series, 869, 012011. doi:10.1088/1742-6596/869/1/012011.
Nasser, I., Zeama, M., & Abdel-Hady, A. (2017). The Rényi entropy, a comparative study for He-like atoms using the exponential-cosine screened Coulomb potential. Results in Physics, 7(2), 3892–3900. doi:10.1016/j.rinp.2017.10.013.
Nasser, I., Zeama, M., & Abdel-Hady, A. (2021). Calculation of information entropies for the 1s2 state of helium-like ions. International Journal of Quantum Chemistry, 121(5), e26499. doi:10.1002/qua.26499.
Zeama, M., & Nasser, I. (2019). Tsallis entropy calculation for non-Coulombic helium. Physica A: Statistical Mechanics and Its Applications, 528, 121468. doi:10.1016/j.physa.2019.121468.
Onate, C. A., Ikot, A. N., Onyeaju, M. C., Ebomwonyi, O., & Idiodi, J. O. A. (2018). Effect of dissociation energy on Shannon and Rényi entropies. Karbala International Journal of Modern Science, 4(1), 134–142. doi:10.1016/j.kijoms.2017.12.004.
Ema, I., De La Vega, J. M. G., Miguel, B., Dotterweich, J., Meißner, H., & Steinborn, E. O. (1999). Exponential-type basis functions: Single- and double-zeta B function basis sets for the ground states of neutral atoms from Z = 2 to Z = 36. Atomic Data and Nuclear Data Tables, 72(1), 57–99. doi:10.1006/adnd.1999.0809.
Atkins, P. W., & Friedman, R. S. (2011). Molecular quantum mechanics (4th Ed.). Oxford University Press, Oxford, United States.
Filter, E., & Steinborn, E. O. (1978). Extremely compact formulas for molecular two-center one-electron integrals and Coulomb integrals over Slater-type atomic orbitals. Physical Review A, 18(1), 1–11. doi:10.1103/PhysRevA.18.1.
Ertürk, M., & Sahin, E. (2020). Generalized B functions applied to atomic calculations. Chemical Physics, 529, 110549. doi:10.1016/j.chemphys.2019.110549.
Al-Jibbouri, H. (2019). Ground State of Radial-Radial Distribution Function for C+4 and O+6 Ions. Journal of Physics: Conference Series, 1294(5), 052052. doi:10.1088/1742-6596/1294/5/052052.
Al-Jibbouri, H., & Alhasan, A. (2019). Study the Inter-Particle Function for Some Electronic System. Journal of Physics: Conference Series, 1294(2), 022014. doi:10.1088/1742-6596/1294/2/022014.
Mitnik, D. M., & Miraglia, J. E. (2005). Simple correlated wavefunctions for the K-shell electrons of neutral atoms. Journal of Physics B: Atomic, Molecular and Optical Physics, 38(18), 3325–3338. doi:10.1088/0953-4075/38/18/004.
Fernández Rico, J., López, R., Ramírez, G., & Ema, I. (1998). Multiple one-center expansions of charge distributions associated with Slater orbitals. Journal of Molecular Structure: THEOCHEM, 433(1–3), 7–18. doi:10.1016/S0166-1280(98)00005-0.
Gadre, S. R., Sears, S. B., Chakravorty, S. J., & Bendale, R. D. (1985). Some novel characteristics of atomic information entropies. Physical Review A, 32(5), 2602–2606. doi:10.1103/PhysRevA.32.2602.
Maassen, H., & Uffink, J. B. M. (1988). Generalized entropic uncertainty relations. Physical Review Letters, 60(12), 1103–1106. doi:10.1103/physrevlett.60.1103.
Panos, C. P., Nikolaidis, N. S., Chatzisavvas, K. C., & Tsouros, C. C. (2009). A simple method for the evaluation of the information content and complexity in atoms. A proposal for scalability. Physics Letters, Section A: General, Atomic and Solid State Physics, 373(27–28), 2343–2350. doi:10.1016/j.physleta.2009.04.070.
Al-Jibbouri, H. (2021). Variational calculation of lithium-like ions from B+2 to N+4 using β-type roothaan–hartree–fock wavefunction. Ukrainian Journal of Physics, 66(8), 684–690. doi:10.15407/ujpe66.8.684.
Saha, A., Talukdar, B., & Chatterjee, S. (2017). On the correlation measure of two-electron systems. Physica A: Statistical Mechanics and Its Applications, 474, 370–379. doi:10.1016/j.physa.2017.02.003.
Sagar, R. P., & Guevara, N. L. (2005). Mutual information and correlation measures in atomic systems. The Journal of Chemical Physics, 123(4), 044108. doi:10.1063/1.1953327.
Rastegin, A. E. (2014). Uncertainty and certainty relations for Pauli observables in terms of Rényi entropies of order α ∈ (0; 1]. Communications in Theoretical Physics, 61(3), 293–298. doi:10.1088/0253-6102/61/3/04.
Delgado-Soler, L., Toral, R., Tomás, M. S., & Rubio-Martinez, J. (2009). RED: A set of molecular descriptors based on rényi entropy. Journal of Chemical Information and Modeling, 49(11), 2457–2468. doi:10.1021/ci900275w.
Toranzo, I. V., & Dehesa, J. S. (2016). Rényi, Shannon and Tsallis entropies of Rydberg hydrogenic systems. EPL (Europhysics Letters), 113(4), 48003. doi:10.1209/0295-5075/113/48003.
DOI: 10.28991/ESJ-2022-06-04-08
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