arXiv subjects

K. Ch. Chatzisavvas

Publications and source records attributed to K. Ch. Chatzisavvas.

17 recordsLinked to original sources

arXiv2013

Fisher Information and Atomic Structure

We present a comparative study of several information and statistical complexity measures in order to examine a possible correlation with certain experimental properties of atomic structure. Comparisons are also carried out quantitatively using Pearson correlation coefficient. In particular, we show that Fisher information in momentum space is very sensitive to shell effects, and is directly associated with some of the most characteristic atomic properties, such as atomic radius, ionization energy, electronegativity, and atomic dipole polarizability. Finally we present a relation that emerges between Fisher information and the second moment of the probability distribution in momentum space i.e. an energy functional of interest in (e,2e) experiments.

quant-ph↗

arXiv2010

Statistical measure of complexity of hard-sphere gas: applications to nuclear matter

We apply the statistical measure of complexity, introduced by López-Ruiz, Mancini and Calbet to a hard-sphere dilute Fermi gas whose particles interact via a repulsive hard-core potential. We employ the momentum distribution of this system to calculate the information entropy, the disequilibrium and the statistical complexity. We examine possible connections between the particle correlations and energy of the system with those information and complexity measures. The hard-sphere model serves as a test bed for concepts about complexity.

quant-ph↗

arXiv2009

Statistical measure of complexity and correlated behavior of Fermi systems

We apply the statistical measure of complexity, introduced by López-Ruiz, Mancini and Calbet (LMC), to uniform Fermi systems. We investigate the connection between information and complexity measures with the strongly correlated behavior of various Fermi systems as nuclear matter, electron gas and liquid helium. We examine the possibility that LMC complexity can serve as an index quantifying correlations in the specific system and to which extent could be related with experimental quantities. Moreover, we concentrate on thermal effects on the complexity of ideal Fermi systems. We find that complexity behaves, both at low and high values of temperature, in a similar way as the specific heat.

cond-mat.stat-mech↗

arXiv2009

Improving quantum gate fidelities using optimized Euler angles

An explicit algorithm for calculating the optimized Euler angles for both qubit state transfer and gate engineering given two arbitary fixed Hamiltonians is presented. It is shown how the algorithm enables us to efficiently implement single qubit gates even if the control is severely restricted and the experimentally accessible Hamiltonians are far from orthogonal. It is further shown that using the optimized Euler angles can significantly improve the fidelity of quantum operations even for systems where the experimentally accessible Hamiltonians are nearly orthogonal. Unlike schemes such as composite pulses, the proposed scheme does not significantly increase the number of local operations or gate operation times.

quant-ph↗

arXiv2009

Complexity and neutron stars structure

We apply the statistical measure of complexity introduced by Lopez-Ruiz, Mancini and Calbet to neutron stars structure. Neutron stars is a classical example where the gravitational field and quantum behavior are combined and produce a macroscopic dense object. Actually, we continue the recent application of Sanudo and Pacheco to white dwarfs structure. We concentrate our study on the connection between complexity and neutron star properties, like maximum mass and the corresponding radius, applying a specific set of realistic equation of states. Moreover, the effect of the strength of the gravitational field on the neutron star structure and consequently on the complexity measure is also investigated. It is seen that neutron stars, consistent with astronomical observations so far, are ordered systems (low complexity), which cannot grow in complexity as their mass increases. This is a result of the interplay of gravity, the short-range nuclear force and the very short-range weak interaction.

astro-ph.SR↗

arXiv2009

Complexity classification of quantum many-body systems according to the Pair of Order-Disorder Indices (PODI)

The statistical measures of complexity defined by Lopez-Ruiz, Mancini, and Calbet (LMC) and Shiner, Davison and Landsberg (SDL) are calculated as functions of the number of particles for four quantum many-body systems, i.e. atoms, nuclei, atomic clusters, and correlated atoms in a trap (bosons). A pair of order and disorder strengths, evaluated for each system, can serve as a Pair of Order-Disorder Indices (PODI), characterizing quantitatively order versus disorder in any quantum system. According to the above classification, we assign to bosons the complexity character of disorder, to atoms the character of order, while nuclei and atomic clusters are (less) disordered and lie between them. This criterion can be used to estimate the relative contribution of order and disorder to complexity for other more complicated quantum systems as well and even classical ones, if one is able to describe them probabilistically. We also address the issue, whether those systems can grow in complexity as the number of particles increases. Our comparative study indicates that atoms are the only quantum system out of four, which is ordered, with the ability to self-organize. We conjecture that this is an information-theoretic reason that atoms are suitable as building blocks of larger structures of biological interest i.e. molecules and macromolecules. This is in the spirit of Wheeler's "it from bit" quote, the project to present everything about the Universe in terms of information theory.

quant-ph↗

arXiv2008

A simple method for the evaluation of the information content and complexity in atoms. A proposal for scalability

We present a very simple method for the calculation of Shannon, Fisher, Onicescu and Tsallis entropies in atoms, as well as SDL and LMC complexity measures, as functions of the atomic number Z. Fractional occupation probabilities of electrons in atomic orbitals are employed, instead of the more complicated continuous electron probability densities in position and momentum spaces, used so far in the literature. Our main conclusions are compatible with the results of more sophisticated approaches and correlate fairly with experimental data. We obtain for the Tsallis entropic index the value q=1.031, which shows that atoms are very close to extensivity. A practical way towards scalability of the quantification of complexity for systems with more components than the atom is indicated. We also discuss the issue if the complexity of the electronic structure of atoms increases with Z. A Pair of Order-Disorder Indices (PODI), which can be introduced for any quantum many-body system, is evaluated in atoms. We conclude that "atoms are ordered systems, which do not grow in complexity as Z increases".

quant-ph↗

arXiv2007

Application of information and complexity theories to public opinion polls. The case of Greece (2004-2007)

A general methodology to study public opinion inspired from information and complexity theories is outlined. It is based on probabilistic data extracted from opinion polls. It gives a quantitative information-theoretic explanation of high job approval of Greek Prime Minister Mr. Constantinos Karamanlis (2004-2007), while the same time series of polls conducted by the company Metron Analysis showed that his party New Democracy (abbr. ND) was slightly higher than the opposition party of PASOK -party leader Mr. George Papandreou. It is seen that the same mathematical model applies to the case of the popularity of President Clinton between January 1998 and February 1999, according to a previous study, although the present work extends the investigation to concepts as complexity and Fisher information, quantifying the organization of public opinion data.

stat.AP↗

arXiv2006

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

The "simple" measure of complexity of Shiner, Davison and Landsberg (SDL) and the "statistical" one, 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 SDL and LMC measueres of complexity. If we impose the condition that SDL and LMC behave similarly as functions of Z, then we can conclude that complexity increases with Z and for atoms the strength of disorder is zero and order is four.

quant-ph↗

arXiv2006

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

The net Fisher information measure, defined as the product of position and momentum Fisher information measures 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 the net Fisher information 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 and net Fisher information, 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.

quant-ph↗

arXiv2006

Quantum Computation Beyond the "Standard Circuit Model"

Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g. concerning the number of computational steps) and it neglects physical systems which cannot follow the "standard circuit model" analysis. We propose a computational scheme which overcomes the notion of the transposition from classical circuits providing a computation scheme with the least possible number of Hamiltonians in order to minimize the physical resources needed to perform quantum computation and to succeed a minimization of the computational procedure (minimizing the number of computational steps needed to perform an arbitrary unitary transformation). It is a general scheme of construction, independent of the specific system used for the implementation of the quantum computer. The open problem of controllability in Lie groups is directly related and rises to prominence in an effort to perform universal quantum computation.

quant-ph↗

arXiv2006

Applications of density matrices in a trapped Bose gas

An overview of the Bose-Einstein condensation of correlated atoms in a trap is presented by examining the effect of interparticle correlations to one- and two-body properties of the above systems at zero temperature in the framework of the lowest order cluster expansion. Analytical expressions for the one- and two-body properties of the Bose gas are derived using Jastrow-type correlation function. In addition numerical calculations of the natural orbitals and natural occupation numbers are also carried out. Special effort is devoted for the calculation of various quantum information properties including Shannon entropy, Onicescu informational energy, Kullback-Leibler relative entropy and the recently proposed Jensen-Shannon divergence entropy. The above quantities are calculated for the trapped Bose gases by comparing the correlated and uncorrelated cases as a function of the strength of the short-range correlations. The Gross-Piatevskii equation is solved giving the density distributions in position and momentum space, which are employed to calculate quantum information properties of the Bose gas.

cond-mat.other↗

arXiv2005

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 (Z=2-54) in atoms. Roothaan-Hartree-Fock electron wave functions are used. The universal property S=a+b lnZ is verified. In addition, we calculate the Kullback-Leibler relative entropy, the Jensen-Shannon divergence, Onicescu's information energy and a complexity measure recently proposed. Shell effects at closed shells atoms are observed. The complexity measure shows local minima at the closed shells 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. Onicescu's 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.

quant-ph↗

arXiv2005

Quantum-Information Content of Fractional Occupation Probabilities in Nuclei

Three measures of the information content of a probability distribution are briefly reviewed. They are applied to fractional occupation probabilities in light nuclei, taking into account short-range correlations. The effect of short-range correlations is to increase the information entropy (or disorder) of nuclei, comparing with the independent particle model. It is also indicated that the information entropy can serve as a sensitive index of order and short-range correlations in nuclei. It is concluded that increasing $Z$, the information entropy increases i.e. the disorder of the nucleus increases for all measures of information considered in the present work.

quant-ph↗

arXiv2005

Quantum-Information Theoretic Properties of Nuclei and Trapped Bose Gases

Fermionic (atomic nuclei) and bosonic (correlated atoms in a trap) systems are studied from an information-theoretic point of view. Shannon and Onicescu information measures are calculated for the above systems comparing correlated and uncorrelated cases as functions of the strength of short range correlations. One-body and two-body density and momentum distributions are employed. Thus the effect of short-range correlations on the information content is evaluated. The magnitude of distinguishability of the correlated and uncorrelated densities is also discussed employing suitable measures of distance of states i.e. the well known Kullback-Leibler relative entropy and the recently proposed Jensen-Shannon divergence entropy. It is seen that the same information-theoretic properties hold for quantum many-body systems obeying different statistics (fermions and bosons).

quant-ph↗

arXiv2003

Information-Theoretic Comparison of Quantum Many-Body Systems

An information measure inspired by Onicescu's information energy and Uffink's information measure (recently discussed by Brukner and Zeilinger) are calculated as functions of the number of particles $N$ for fermionic systems (nuclei and atomic clusters) and correlated bosonic systems (atoms in a trap). Our results are compared with previous ones obtained for Shannon's information entropy, where a universal property was derived for atoms, nuclei, atomic clusters and correlated bosons. It is indicated that Onicescu's and Uffink's definitions are finer measures of information entropy than Shannon's.

quant-ph↗

arXiv2001

Quantum machine language and quantum computation with Josephson junctions

An implementation method of a gate in a quantum computer is studied in terms of a finite number of steps evolving in time according to a finite number of basic Hamiltonians, which are controlled by on-off switches. As a working example, the case of a particular implementation of the two qubit computer employing a simple system of two coupled Josephson junctions is considered. The binary values of the switches together with the time durations of the steps constitute the quantum machine language of the system.

quant-ph↗