×

zbMATH — the first resource for mathematics

Fisher-Shannon plane and statistical complexity of atoms. (English) Zbl 1217.81155
Summary: Using the Hartree-Fock non-relativistic wave functions in the position and momentum spaces, the statistical measure of complexity \(C\), due to López-Ruiz, Mancini, and Calbet for the neutral atoms as well as their monopositive and mononegative ions with atomic number \(Z=1-54\) are reported. In \(C\), given by the product of exponential power Shannon entropy and the average density, the latter is then replaced by the Fisher measure to obtain the Fisher-Shannon plane. Our numerical results suggest that in overall the Fisher-Shannon plane reproduces the trends given by \(C\), with significantly \(enhanced\) sensitivity in the position, momentum and the product spaces in all neutral atoms and ions considered.

MSC:
81V45 Atomic physics
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
68Q19 Descriptive complexity and finite models
94A17 Measures of information, entropy
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Kolmogorov, A.N., Probl. inf. transm., 1, 3, (1965)
[2] Chaitin, G., J. ACM, 13, 547, (1966)
[3] López-Ruiz, R.; Mancini, H.L.; Calbet, X., Phys. lett. A, 209, 321, (1995)
[4] Catalán, R.G.; Garay, J.; López-Ruiz, R., Phys. rev. E, 66, 011102, (2002)
[5] Landsberg, P.T., Phys. lett. A, 102, 171, (1984)
[6] Shiner, J.S.; Davison, M.; Landsberg, P.T., Phys. rev. E, 59, 1459, (1999)
[7] Chatzisavvas, K.Ch.; Moustakidis, Ch.C.; Panos, C.P., J. chem. phys., 123, 174111, (2005)
[8] Panos, C.P.; Chatzisavvas, K.Ch.; Moustakidis, Ch.C.; Kyrkou, E.G., Phys. lett. A, 363, 78, (2007)
[9] Bunge, C.F.; Barrientos, J.A.; Bunge, A.V., At. data nucl. data tables, 53, 113, (1993)
[10] Koga, T.; Kanayama, K.; Watanabe, S.; Thakkar, A.J., Int. J. quantum chem., 71, 491, (1999)
[11] Koga, T.; Kanayama, K.; Watanabe, S.; Imai, T.; Thakkar, A.J., Theor. chem. acc., 104, 411, (2000)
[12] Romera, E.; Dehesa, J.S., J. chem. phys., 120, 8906, (2004)
[13] Yamano, T., J. math. phys., 45, 1974, (2004)
[14] Shannon, C.E.; Shannon, C.E., Bell syst. tech., Bell syst. tech., 27, 623, (1948)
[15] Dembo, A.; Cover, T.A.; Thomas, J.A., IEEE trans. inf. theory, 37, 1501, (1991)
[16] Carbó, R.; Arnau, J.; Leyda, L., Int. J. quantum chem., 17, 1185, (1980)
[17] Borgoo, A.; Godefroid, M.; Indelicato, P.; De Proft, F.; Geerlings, P., J. chem. phys., 126, 044102, (2007)
[18] Angulo, J.C.; Antolín, J., J. chem. phys., 126, 044106, (2007)
[19] Onicescu, O., C. R. acad. sci. Paris A, 263, 25, (1966)
[20] Hall, M.J.W., Phys. rev. A, 59, 2602, (1999)
[21] Pennini, F.; Plastino, A., Phys. lett. A, 365, 262, (2007)
[22] Hyman, A.S.; Yaniger, S.I.; Liebman, J.L., Int. J. quantum chem., 19, 757, (1978)
[23] Fisher, R.A., Proc. Cambridge philos. soc., 22, 700, (1925)
[24] Sears, S.B.; Parr, R.G.; Dinur, U., Israel J. chem., 19, 165, (1980)
[25] Reginatto, M., Phys. rev. A, 58, 1775, (1998)
[26] Frieden, B.R., Science from Fisher information, (2004), Cambridge Univ. Press · Zbl 0881.60016
[27] Nalewajski, R., Chem. phys. lett., 372, 28, (2003)
[28] Nagy, Á., J. chem. phys., 119, 9401, (2003)
[29] Romera, E.; Sánchez-Moreno, P.; Dehesa, J.S., Chem. phys. lett., 414, 468, (2005)
[30] Nagy, Á., Chem. phys. lett., 425, 157, (2006)
[31] Nagy, A.; Sen, K.D., Phys. lett. A, 360, 291, (2006)
[32] Liu, S., J. chem. phys., 126, 191107, (2007)
[33] Sen, K.D.; Panos, C.P.; Chatzisavvas, K.Ch.; Moustakidis, Ch.C., Phys. lett. A, 364, 286, (2007)
[34] Romera, E.; Sánchez-Moreno, P.; Dehesa, J.S.; Dehesa, J.S.; López-Rosa, S.; Olmos, B.; Yáñez, R.J.; Romera, E.; Sánchez-Moreno, P.; Dehesa, J.S.; Sánchez-Moreno, P.; González-Férez, R.; Dehesa, J.S.; Dehesa, J.S.; González-Férez, R.; Sánchez-Moreno, P.; Dehesa, J.S.; López-Rosa, S.; Yáñez, R.J., Chem. phys. lett., J. math. phys., J. math. phys., New J. phys. A, J. phys. A, J. math. phys., 48, 043503, (2007)
[35] Hornyák, I.; Nagy, Á., Chem. phys. lett., 437, 132, (2007)
[36] Cover, T.M.; Thomas, J.A.; Dembo, A.; Cover, T.M.; Thomas, J.A., Elements of information theory, IEEE trans. inf. theory, 37, 1501, (1991), Wiley-Interscience New York · Zbl 0741.94001
[37] Pearson, J.M., Proc. amer. math. soc., 125, 3335, (1997)
[38] Kullback, S., Information theory and statistics, (1977), Dover Mineola · Zbl 0149.37901
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.