Rényi information of atoms

Abstract Position and momentum space Renyi information of order α has been studied within a Hartree–Fock framework for 103 neutral atoms, 54 singly charged cations and 43 anions in their ground state. The values of α ⩽ 1 ( α ⩾ 1 ) stress the shell structure for position-space (momentum-space) Renyi information. The relationship between the complexity and Renyi information is also studied.

[1]  INFORMATION ENTROPY AS A MEASURE OF THE QUALITY OF AN APPROXIMATE ELECTRONIC WAVE FUNCTION , 1998 .

[2]  Yáñez,et al.  Position and momentum information entropies of the D-dimensional harmonic oscillator and hydrogen atom. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[3]  Roman F. Nalewajski,et al.  Information principles in the theory of electronic structure , 2003 .

[4]  A. Hyman,et al.  Interrelations among x-ray scattering, electron densities, and ionization potentials , 1978 .

[5]  Ágnes Nagy,et al.  Fisher information in density functional theory , 2003 .

[6]  Rory A. Fisher,et al.  Theory of Statistical Estimation , 1925, Mathematical Proceedings of the Cambridge Philosophical Society.

[7]  Michael J. W. Hall,et al.  Universal geometric approach to uncertainty, entropy, and information , 1999 .

[8]  Á. Nagy,et al.  Phase-space Fisher information , 2007 .

[9]  Jesús S. Dehesa,et al.  The Fisher information of single-particle systems with a central potential , 2005 .

[10]  R. Renner,et al.  Information-theoretic security proof for quantum-key-distribution protocols , 2005, quant-ph/0502064.

[11]  C. Moustakidis,et al.  Dependence of Information Entropy of Uniform Fermi Systems on Correlations and Thermal Effects , 2004, HNPS Proceedings.

[12]  B. Roy Frieden,et al.  Fisher information as the basis for the Schrödinger wave equation , 1989 .

[13]  J. S. Dehesa,et al.  The Fisher-Shannon information plane, an electron correlation tool. , 2004, The Journal of chemical physics.

[14]  F. Illuminati,et al.  Extremal entanglement and mixedness in continuous variable systems , 2004, quant-ph/0402124.

[15]  J. S. Dehesa,et al.  Electron momentum densities of atoms , 1998 .

[16]  V. H. Smith,et al.  Atomic information entropies beyond the Hartree-Fock limit , 1994 .

[17]  R. Parr,et al.  On the Quantum‐Mechanical Kinetic Energy as a Measure of the Information in a Distribution , 1980 .

[18]  R. P. Sagar,et al.  Shannon-information entropy sum as a correlation measure in atomic systems , 2003 .

[19]  Á. Nagy,et al.  Atomic Fisher information versus atomic number , 2006 .

[20]  P. Geerlings,et al.  Quantum similarity study of atomic density functions: insights from information theory and the role of relativistic effects. , 2007, The Journal of chemical physics.

[21]  A numerical study of molecular information entropies , 1994 .

[22]  J. C. Angulo,et al.  Atomic quantum similarity indices in position and momentum spaces. , 2007, The Journal of chemical physics.

[23]  Seth Lloyd,et al.  Additivity properties of a Gaussian channel , 2004, quant-ph/0403075.

[24]  Flavia Pennini,et al.  Localization estimation and global vs. local information measures , 2007 .

[25]  F. Dunning,et al.  Pulse-induced focusing of Rydberg wave packets , 2003 .

[26]  Shridhar R. Gadre Information entropy and Thomas-Fermi theory , 1984 .

[27]  Á. Nagy Fisher information in a two-electron entangled artificial atom , 2006 .

[28]  Szilvia Nagy,et al.  Elementary formula for entanglement entropies of fermionic systems , 2005 .

[29]  R. Renner,et al.  An information-theoretic security proof for QKD protocols , 2005, quant-ph/0502064.

[30]  Marcel Reginatto,et al.  Derivation of the equations of nonrelativistic quantum mechanics using the principle of minimum Fisher information , 1998 .

[31]  B. Frieden,et al.  Physics from Fisher Information: A Unification , 1998 .

[32]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[33]  Takashi Imai,et al.  Analytical Hartree–Fock wave functions for the atoms Cs to Lr , 2000 .

[34]  R. P. Sagar,et al.  Information uncertainty-type inequalities in atomic systems , 2003 .

[35]  Tripathi,et al.  Electron correlation in momentum space: The beryllium-atom isoelectronic sequence. , 1992, Physical Review A. Atomic, Molecular, and Optical Physics.

[36]  K. Sen Characteristic features of Shannon information entropy of confined atoms. , 2005, The Journal of chemical physics.

[37]  Sears,et al.  Some novel characteristics of atomic information entropies. , 1985, Physical review. A, General physics.

[38]  Á. Nagy,et al.  Local wave-vector, Shannon and Fisher information , 2008 .

[39]  Fahrettin Gogtas,et al.  Time-dependent quantum study of the kinetics of the O(3P) + CN(X2+) → CO(X1+) + N(2D) reaction , 2006 .

[40]  M. Lewenstein,et al.  Entropic uncertainty relations and entanglement , 2004, quant-ph/0403219.

[41]  P. Geerlings,et al.  Complexity of Dirac–Fock atom increases with atomic number , 2007 .

[42]  Á. Nagy Fisher information and steric effect , 2007 .

[43]  R. P. Sagar,et al.  Local correlation measures in atomic systems. , 2005, The Journal of chemical physics.

[44]  Ricardo López-Ruiz,et al.  A Statistical Measure of Complexity , 1995, ArXiv.

[45]  J. S. Dehesa,et al.  Structure of the electron momentum density of atomic systems , 1997 .

[46]  A. Sergienko,et al.  Direct Measurement of Nonlinear Properties of Bipartite Quantum States , 2005, Open systems & information dynamics.

[47]  E. Romera Stam's principle D-dimensional uncertainty-like relationships and some atomic properties , 2002 .

[48]  Ágnes Nagy,et al.  The Fisher–Shannon information plane for atoms , 2008 .

[49]  Shubin Liu,et al.  On the relationship between densities of Shannon entropy and Fisher information for atoms and molecules. , 2007, The Journal of chemical physics.

[50]  Ramon Carbo,et al.  How similar is a molecule to another? An electron density measure of similarity between two molecular structures , 1980 .

[51]  A. Thakkar,et al.  Analytical Hartree–Fock wave functions subject to cusp and asymptotic constraints: He to Xe, Li+ to Cs+, H− to I− , 1999 .