Ch. C. Moustakidis

Information entropy, information distances, and complexity in atoms

Shannon information entropies in position and momentum spaces and their sum are calculated as functions of Z(2 < or = Z < or = 54) in atoms. Roothaan-Hartree-Fock electron wave functions are used. The universal property S = a + b ln Z is verified. In addition, we calculate the Kullback-Leibler relative entropy, the Jensen-Shannon divergence, Onicescus information energy, and a complexity measure recently proposed. Shell effects at closed-shell atoms are observed. The complexity measure shows local minima at the closed-shell atoms indicating that for the above atoms complexity decreases with respect to neighboring atoms. It is seen that complexity fluctuates around an average value, indicating that the atom cannot grow in complexity as Z increases. Onicescus information energy is correlated with the ionization potential. Kullback distance and Jensen-Shannon distance are employed to compare Roothaan-Hartree-Fock density distributions with other densities of previous works.

Net Fisher information measure versus ionization potential and dipole polarizability in atoms

Abstract The net Fisher information measure I T , defined as the product of position and momentum Fisher information measures I r and I k and derived from the non-relativistic Hartree–Fock wave functions for atoms with Z = 1 – 102 , is found to correlate well with the inverse of the experimental ionization potential. Strong direct correlations of I T are also reported for the static dipole polarizability of atoms with Z = 1 – 88 . The complexity measure, defined as the ratio of the net Onicescu information measure E T and I T , exhibits clearly marked regions corresponding to the periodicity of the atomic shell structure. The reported correlations highlight the need for using the net information measures in addition to either the position or momentum space analogues. With reference to the correlation of the experimental properties considered here, the net Fisher information measure is found to be superior than the net Shannon information entropy.

Comparison of SDL and LMC measures of complexity: Atoms as a testbed

Abstract The simple measure of complexity Γ α , β of Shiner, Davison and Landsberg (SDL) and the statistical one C , according to Lopez-Ruiz, Mancini and Calbet (LMC), are compared in atoms as functions of the atomic number Z . Shell effects i.e. local minima at the closed shells atoms are observed, as well as certain qualitative trends of Γ α , β ( Z ) and C ( Z ) . If we impose the condition that Γ and C behave similarly as functions of Z , then we can conclude that complexity increases with Z and for atoms the strength of disorder is α ≃ 0 and order is β ≃ 4 .

Direct detection of dark matter rates for various wimps

Abstract The event rates for the direct detection of dark matter candidates, originating from the universal extra dimension scenario, are evaluated for a number of nuclear targets. Realistic form factors as well as spin ME and response functions are employed. Due to LR + RL helicities contribution, the proton amplitude is found to be dominant. Various other non-susy dark matter candidates are examined at the end.

Comparison of the information entropy in fermionic and bosonic systems

It is shown that a similar functional form S = a + bln N holds approximately for the information entropy S as function of the number of particles N for atoms, nuclei and atomic clusters (fermionic systems) and correlated boson-atoms in a trap (bosonic systems). It is also seen that rigorous inequalities previously found to hold between S and the kinetic energy T for fermionic systems, hold for bosonic systems as well. It is found that Landsberg’s order parameter is an increasing function of N for the above systems. It is conjectured that the above properties are universal i.e. they do not depend on the kind of constituent particles (fermions or correlated bosons) and the size of the system. Shannon’s information entropy for a continuous probability distribution p(x) is defined as

Dependence of information entropy of uniform Fermi systems on correlations and thermal effects

The influence of correlations of uniform Fermi systems (nuclear matter, electron gas, and liquid

Dark matter search by exclusive studies of X-rays following WIMPs nuclear interactions

^{3}\mathrm{He}

One-body density matrix and momentum distribution in s p and s d shell nuclei

) on Shannons information entropy,

Direct dark matter search by observing electrons produced in neutralino–nucleus collisions

S

Thermal effects on nuclear symmetry energy with a momentum-dependent effective interaction

, is studied.