scholarly journals Information Entropy and Information Distances in Atoms, Nuclei and Bosonic Systems

2019 ◽  
Vol 14 ◽  
pp. 191
Author(s):  
K. Ch. Chatzisavvas ◽  
Ch. C. Moustakidis ◽  
C. P. Panos
Keyword(s):  
Information Entropy ◽  
Atomic Clusters ◽  
Wave Functions ◽  
Body Density ◽  
Bose Gases ◽  
Hartree Fock ◽  
Density Distributions ◽  
The One ◽  
Jensen Shannon Divergence ◽  
Short Range Correlations

The universal property for the information entropy S = a + h In Ζ is verified for atoms using a systematic study with Roothaan-Hartree-Fock (RHF) wave functions with atomic number Ζ — 2 — 54. The above relation was proposed previously for atoms, nuclei, atomic clusters and correlated atoms in a trap. Kullback-Leibler relative entropy Κ and Jensen-Shannon divergence J are employed to compare RHF with Thomas-Fermi (TF) density of atoms as well as another phenomenological density obtained by Sagar et al. Two-body density distributions in position- and momentum-space are used to calculate and compare the corresponding information entropies for correlated and uncorrelated nuclei and bosonic systems (correlated atoms in a trap). It is seen that short-range correlations (SRC) increase the values of S. One-body information entropy entropy S\ is compared with two-body information entropy and a conjecture is made for TV-body information entropy SN- The entropy Κ and the divergence J are also used to evaluate the information distance between correlated and uncorrelated densities both at the one- and the two-body levels for nuclei and trapped Bose gases.

scholarly journals APPLICATIONS OF DENSITY MATRICES IN A TRAPPED BOSE GAS

2006 ◽  
Vol 20 (15) ◽  
pp. 2189-2221 ◽  
Author(s):  
K. CH. CHATZISAVVAS ◽  
S. E. MASSEN ◽  
CH. C. MOUSTAKIDIS ◽  
C. P. PANOS
Keyword(s):  
Quantum Information ◽  
Bose Gas ◽  
Einstein Condensation ◽  
Density Distributions ◽  
Occupation Numbers ◽  
The One ◽  
Bose Einstein ◽  
Jensen Shannon Divergence ◽  
Analytical Expressions ◽  
Short Range Correlations

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.

Particle-hole pair and beelectron states in ZnO/(Zn,Mg)O quantum wells and Dirac materials.

2015 ◽  
Vol 10 (1) ◽  
pp. 2583-2604
Author(s):  
Lyubov E. Lokot
Keyword(s):  
Quantum Well ◽  
Charge Density ◽  
Heavy Hole ◽  
Wave Functions ◽  
One Dimensional ◽  
Exchange Correlation ◽  
Hartree Fock ◽  
Exchange Correlation Potential ◽  
Correlation Potential ◽  
The One

In this paper a theoretical studies of the space separation of electron and hole wave functions in the quantum well ZnO/Mg(0.27)Zn(0.73)O are presented. For this aim the self-consistent solution of the Schrödinger equations for electrons and holes and the Poisson equations at the presence of spatially varying quantum well potential due to the piezoelectric effect and local exchange-correlation potential is found. The one-dimensional Poisson equation contains the Hartree potential which includes the one-dimensional charge density for electrons and holes along the polarization field distribution. The three-dimensional Poisson equation contains besides the one-dimensional charge density for electrons and holes the exchange-correlation potential which is built on convolutions of a plane-wave part of wave functions in addition. The shifts of the Hartree valence band spectrums and the conduction band spectrum with respect to the flat band spectrums as well as the Hartree-Fock band spectrums with respect to the Hartree ones are found. An overlap integrals of the wave functions of holes and electron with taking into account besides the piezoelectric effects the exchange-correlation effects in addition is greater than an overlap integral of Hartree ones. The Hartree particles distribute greater on edges of quantum well than Hartree-Fock particles. It is found that an effective mass of heavy hole of Mg(0.27)Zn(0.73)O under biaxial strain is greater than an effective-mass of heavy hole of ZnO. It is calculated that an electron mass is less than a hole mass. It is found that the Bohr radius is grater than the localization range particle-hole pair, and the excitons may be spontaneously created.Schrödinger equation for pair of two massless Dirac particles when magnetic field is applied in Landau gauge is solved exactly. In this case the separation of center of mass and relative motion is obtained. Landau quantization $\epsilon=\pm\,B\sqrt{l}$ for pair of two Majorana fermions coupled via a Coulomb potential from massless chiral Dirac equation in cylindric coordinate is found. The root ambiguity in energy spectrum leads into Landau quantization for beelectron, when the states in which the one simultaneously exists are allowed. The tachyon solution with imaginary energy in Cooper problem ($\epsilon^{2}<0$) is found.

"VECTAL" REPRESENTATION OF THE WAVE FUNCTION AND ITS PHYSICAL MEANING

1967 ◽  
Vol 45 (11) ◽  
pp. 3667-3676
Author(s):  
C. S. Lin
Keyword(s):  
Wave Function ◽  
Wave Functions ◽  
Electron Wave Function ◽  
Electron Wave ◽  
Expectation Values ◽  
Expectation Value ◽  
Hartree Fock ◽  
The One ◽  
The Relationship ◽  
Determinantal Form

A new form of one-electron wave function, "vectal," is introduced. It is shown that an arbitrary CI geminal and a certain class of many-electron wave functions can be represented in a single-determinantal form in terms of the vectal. Eigenvalue equations for the vectal, similar to that of the Hartree–Fock theory, are derived and the vectal representation is shown to enable a formal interpretation of the CI theory in the Hartree–Fock manner. The eigenvalue, vectal energy, is interpreted as the negative of an ionization potential, in Koop-man's sense, of the system described by the CI wave function. It is also shown that the expectation value of any one-electron operator, [Formula: see text], where Ψ is the CI wave function, is expressible in terms of the expectation values of the same operator with respect to the vectals. The vectals are interpreted as the one-electron wave function in the CI space.A possible application of the vectal representation is briefly described, and the relationship between the vectal representation and the "scalar representation" is discussed.

Magneto-optical Properties of Small Atomic Clusters of Ga and In with As, V and Mn

2005 ◽  
Vol 906 ◽  
Author(s):  
Liudmila A. Pozhar ◽  
Alan T. Yeates ◽  
Frank Szmulowicz ◽  
William C. Mitchel
Keyword(s):  
Optical Properties ◽  
Energy Level ◽  
Optical Transition ◽  
Electronic Energy ◽  
Atomic Clusters ◽  
Fundamental Theory ◽  
Transition Energies ◽  
Hartree Fock ◽  
Density Distributions ◽  
Electronic Energy Level

AbstractThe Hartree-Fock (HF) method is used to synthesize virtually (i.e., fundamental theory-based, computationally) small stable atomic clusters of Ga and In with As and V, and an In-based cluster with As and Mn. The electronic energy level structures (ELSs), optical transition energies (OTEs), and charge/spin density distributions of these clusters have been analyzed. It has been shown that the spin of such clusters is collectivized, and that this collectivization is responsible for a dramatic drop in the clusters’ OTEs as compared to those of similar pyramidal clusters that do not contain “magnetic” atoms.

scholarly journals Short-range correlations and the one-body density matrix in finite nuclei

1995 ◽  
Vol 594 (2) ◽  
pp. 117-136 ◽  
Author(s):  
A. Polls ◽  
H. Müther ◽  
W.H. Dickhoff
Keyword(s):  
Density Matrix ◽  
Short Range ◽  
Body Density ◽  
The One ◽  
Finite Nuclei ◽  
Short Range Correlations

scholarly journals Towards a formal definition of static and dynamic electronic correlations

2017 ◽  
Vol 19 (20) ◽  
pp. 12655-12664 ◽  
Author(s):  
Carlos L. Benavides-Riveros ◽  
Nektarios N. Lathiotakis ◽  
Miguel A. L. Marques
Keyword(s):  
Electron Correlation ◽  
Density Functional ◽  
Recent Progress ◽  
Electronic Correlation ◽  
Body Density ◽  
Hartree Fock ◽  
Static Electron ◽  
Pure States ◽  
The One ◽  
Definition Of

Some of the most spectacular failures of density-functional and Hartree–Fock theories are related to an incorrect description of the so-called static electron correlation. Motivated by recent progress in the N-representability problem of the one-body density matrix for pure states, we propose a way to quantify the static contribution to the electronic correlation.

Hartree–Fock Alpha Cluster Density Distributions in Light A = 4n Nuclei Using Density Dependent Effective Interactions

1973 ◽  
Vol 51 (24) ◽  
pp. 2522-2549 ◽  
Author(s):  
K. R. Lassey ◽  
M. R. P. Manning ◽  
A. B. Volkov
Keyword(s):  
Delta Function ◽  
Skyrme Interaction ◽  
Effective Interactions ◽  
Density Dependent ◽  
Hartree Fock ◽  
Density Distributions ◽  
Cluster Density ◽  
The One ◽  
Alpha Cluster ◽  
Selection Of

Hartree–Fock calculations have been performed for the A = 4n nuclei 12C to 40Ca, employing a selection of density dependent effective interactions. This selection consists of two density and momentum dependent delta function interactions, similar to the Skyrme interaction, and two density and momentum dependent finite range interactions whose radial forms are given as a sum of two Gaussian functions. A basis of single-particle axially deformed harmonic oscillator functions is used. Special emphasis is given to the study of the occurrence of alpha-particle type clustering in the density distributions of light A = 4n nuclei and the influence of the strength of the one-body spin–orbit field.

Über die Berechnung der Korrelationsenergie der Atomelektronen

1960 ◽  
Vol 15 (10) ◽  
pp. 909-926 ◽  
Author(s):  
Levente Szász
Keyword(s):  
Wave Function ◽  
Numerical Calculation ◽  
Ground State ◽  
Correlation Functions ◽  
Correlation Energy ◽  
Wave Functions ◽  
Electron Wave ◽  
Hartree Fock ◽  
Experimental Values ◽  
The One

To calculate the correlation energy of an atom with N electrons we suggest the wave functionwhere à is the antisymmetrizer operator, φ1, φ2, ..., φN are one electron wave functions, and Wjk are correlation functions of the following form:where the constants c j km, n, l are variational parameters. The function (a) is a generalization of thewave function of Hylleraas for He. After a discussion of the properties of our function, an energy expression is derived. Numerical calculation is made for the ground state of the Be atom with the functionwhere φ1 and φ2 are ls wave functions, φ3 and φ4 are 2s wave functions, r1, r2, r3 and r4 are the radial coordinates of the four electrons, r12 and r34 are the distances between the corresponding electrons, and C1 and c2 are variational parameters. Using the one electron wave functions calculated by Roothaan and coll. with the Roothaan procedure, we got the energy value E= -14.624 a. u. while the Hartree-Fock and experimental values are EH,F= -14.570 a. u. and Eexp= -14.668 a. u. respectively. Thus the function (c) gives about one-half of the correlation energy of the Be atom.

scholarly journals IIMLP: integrated information-entropy-based method for LncRNA prediction

2021 ◽  
Vol 22 (S3) ◽  
Author(s):  
Junyi Li ◽  
Huinian Li ◽  
Xiao Ye ◽  
Li Zhang ◽  
Qingzhe Xu ◽  
...  
Keyword(s):  
Machine Learning ◽  
Dna Sequences ◽  
Information Entropy ◽  
Area Under The Curve ◽  
Prediction Method ◽  
Machine Learning Algorithms ◽  
Reading Frame ◽  
Non Coding Rna ◽  
The One ◽  
Long Non Coding Rna

Abstract Background The prediction of long non-coding RNA (lncRNA) has attracted great attention from researchers, as more and more evidence indicate that various complex human diseases are closely related to lncRNAs. In the era of bio-med big data, in addition to the prediction of lncRNAs by biological experimental methods, many computational methods based on machine learning have been proposed to make better use of the sequence resources of lncRNAs. Results We developed the lncRNA prediction method by integrating information-entropy-based features and machine learning algorithms. We calculate generalized topological entropy and generate 6 novel features for lncRNA sequences. By employing these 6 features and other features such as open reading frame, we apply supporting vector machine, XGBoost and random forest algorithms to distinguish human lncRNAs. We compare our method with the one which has more K-mer features and results show that our method has higher area under the curve up to 99.7905%. Conclusions We develop an accurate and efficient method which has novel information entropy features to analyze and classify lncRNAs. Our method is also extendable for research on the other functional elements in DNA sequences.

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