arXiv subjects

S. E. Massen

Publications and source records attributed to S. E. Massen.

At least 19 recordsLinked to original sources

arXiv2013

Quantum Tunneling and Information Entropy in a Double Square Well Potential: Ammonia Molecule

Quantum tunneling is the quantum-mechanical effect where a particle tunnels through a classically forbidden region. Double Square Well Potential (DSWP) is a system where this phenomenon is feasible. Numerous phenomena can be illustrated by considering motion in a pair of wells that are separated by a barrier of finite height and width. The energy level splitting, resulting from barrier penetration, is the reason of the so-called inversion spectrum, which is an example of quantum tunneling. Out of several molecules ($NH_3$, $PH_3$, $AsH_3$, $NH_2CN$) where this inversion phenomenon occurs, ammonia molecule $NH_3$ provides a nice physical realization of a vibrational system with a DSWP. The main goal of the present work is to examine the implications of quantum tunneling on information entropy measures (Shannon's and Fisher's) and statistical complexity.

quant-ph↗

arXiv2013

Natural orbitals representation and Fermi sea depletion in finite nuclei and nuclear matter

The natural orbitals and natural occupation numbers of various N = Z, sp and sd shell nuclei are calculated by applying a correlated one-body density matrix. The correlated density matrix has been evaluated by considering central correlations of Jastrow type and an approximation named factor cluster expansion. The correlation effects on the natural orbitals, natural occupation numbers and the Fermi sea depletion are discussed and analysed. In addition, an approximate expression for the correlated one-body density matrix of the nuclear matter has been used for the evaluation of the relative momentum distribution and the Fermi sea depletion. We found that the value of the Fermi sea depletion is higher in closed shell nuclei compared to open shell ones and it is lower compared to the case of nuclear matter. This statement could be confirmed by relevant experimental studies.

nucl-th↗

arXiv2011

Augmentation of nucleon-nucleus scattering by information entropy

Quantum information entropy is calculated from the nucleon nucleus forward scattering amplitudes. Using a representative set of nuclei, from $^4$He to $^{208}$Pb, and energies, $T_{lab} < 1$\,[GeV], we establish a linear dependence of quantum information entropy as functions of logarithm nuclear mass $A$ and logarithm projectile energy $T_{lab}$.

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

Calculations of $^{8}$He+p Elastic Cross Sections Using Microscopic Optical Potential

An approach to calculate microscopic optical potential (OP) with the real part obtained by a folding procedure and with the imaginary part inherent in the high-energy approximation (HEA) is applied to study the $^8$He+p elastic scattering data at energies of tens of MeV/nucleon (MeV/N). The neutron and proton density distributions obtained in different models for $^{8}$He are utilized in the calculations of the differential cross sections. The role of the spin-orbit potential is studied. Comparison of the calculations with the available experimental data on the elastic scattering differential cross sections at beam energies of 15.7, 26.25, 32, 66 and 73 MeV/N is performed. The problem of the ambiguities of the depths of each component of the optical potential is considered by means of the imposed physical criterion related to the known behavior of the volume integrals as functions of the incident energy. It is shown also that the role of the surface absorption is rather important, in particular for the lowest incident energies (e.g., 15.7 and 26.25 MeV/nucleon).

nucl-th↗

arXiv2007

Nuclear symmetry energy effects on neutron stars properties

We construct a class of nuclear equations of state based on a schematic potential model, that originates from the work of Prakash et. al. \cite{Prakash-88}, which reproduce the results of most microscopic calculations. The equations of state are used as input for solving the Tolman-Oppenheimer-Volkov equations for corresponding neutron stars. The potential part contribution of the symmetry energy to the total energy is parameterized in a generalized form both for low and high values of the baryon density. Special attention is devoted to the construction of the symmetry energy in order to reproduce the results of most microscopic calculations of dense nuclear matter. The obtained nuclear equations of state are applied for the systematic study of the global properties of a neutron star (masses, radii and composition). The calculated masses and radii of the neutron stars are plotted as a function of the potential part parameters of the symmetry energy. A linear relation between these parameters, the radius and the maximum mass of the neutron star is obtained. In addition, a linear relation between the radius and the derivative of the symmetry energy near the saturation density is found. We also address on the problem of the existence of correlation between the pressure near the saturation density and the radius.

nucl-th↗

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 and nucleon correlations in nuclei

The information entropies in coordinate and momentum spaces and their sum ($S_r$, $S_k$, $S$) are evaluated for many nuclei using "experimental" densities or/and momentum distributions. The results are compared with the harmonic oscillator model and with the short-range correlated distributions. It is found that $S_r$ depends strongly on $\ln A$ and does not depend very much on the model. The behaviour of $S_k$ is opposite. The various cases we consider can be classified according to either the quantity of the experimental data we use or by the values of $S$, i.e., the increase of the quality of the density and of the momentum distributions leads to an increase of the values of $S$. In all cases, apart from the linear relation $S=a+b\ln A$, the linear relation $S=a_V+b_V \ln V$ also holds. V is the mean volume of the nucleus. If $S$ is considered as an ensemble entropy, a relation between $A$ or $V$ and the ensemble volume can be found. Finally, comparing different electron scattering experiments for the same nucleus, it is found that the larger the momentum transfer ranges, the larger the information entropy is. It is concluded that $S$ could be used to compare different experiments for the same nucleus and to choose the most reliable one.

nucl-th↗

arXiv2004

The 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 $^3$He) on Shannon's information entropy, $S$, is studied. $S$ is the sum of the information entropies in position and momentum spaces. It is found that, for three different Fermi systems with different particle interactions, the correlated part of $S$ ($S_{cor}$) depends on the correlation parameter of the systems or on the discontinuity gap of the momentum distribution through two parameter expressions. The values of the parameters characterize the strength of the correlations. A two parameter expression also holds between $S_{cor}$ and the mean kinetic energy ($K$) of the Fermi system. The study of thermal effects on the uncorrelated electron gas leads to a relation between the thermal part of $S$ ($S_{thermal}$) and the fundamental quantities of temperature, thermodynamical entropy and the mean kinetic energy. It is found that, in the case of low temperature limit, the expression connecting $S_{thermal}$ with $K$ is the same to the one which connects $S_{cor}$ with $K$. There are only some small differences on the values of the parameters. Thus, regardless of the reason (correlations or thermal) that changes $K$, $S$ takes almost the same value.

cond-mat.str-el↗

arXiv2003

Testing $^{6,8}$He density distributions by calculations of total reaction cross-sections of $^{6,8}$He+$^{28}$Si

Calculations of the $^{6,8}$He + $^{28}$Si total reaction cross sections at intermediate energies are performed on the basis of the Glauber-Sitenko microscopic optical-limit model. The target-nucleus density distribution is taken from the electron-nucleus scattering data, and the $^{6,8}$He densities are used as they are derived in different models. The results of the calculations are compared with the existing experimental data. The effects of the density tails of the projectile nuclei as well as the role of shell admixtures and short-range correlations are analyzed.

nucl-th↗

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↗

arXiv2002

Application of information entropy to nuclei

Shannon's information entropies in position- and momentum- space and their sum $S$ are calculated for various $s$-$p$ and $s$-$d$ shell nuclei using a correlated one-body density matrix depending on the harmonic oscillator size $b_0$ and the short range correlation parameter $y$ which originates from a Jastrow correlation function. It is found that the information entropy sum for a nucleus depends only on the correlation parameter $y$ through the simple relation $S= s_{0A} + s_{1A} y^{-λ_{sA}}$, where $s_{0A}$, $s_{1A}$ and $λ_{sA}$ depend on the mass number $A$. A similar approximate expression is also valid for the root mean square radius of the nucleus as function of $y$ leading to an approximate expression which connects $S$ with the root mean square radius. Finally, we propose a method to determine the correlation parameter from the above property of $S$ as well as the linear dependence of $S$ on the logarithm of the number of nucleons.

quant-ph↗

arXiv2002

Jastrow-type calculations of one-nucleon removal reactions on open $s$-$d$ shell nuclei

Single-particle overlap functions and spectroscopic factors are calculated on the basis of Jastrow-type one-body density matrices of open-shell nuclei constructed by using a factor cluster expansion. The calculations use the relationship between the overlap functions corresponding to bound states of the $(A-1)$-particle system and the one-body density matrix for the ground state of the $A$-particle system. In this work we extend our previous analyses of reactions on closed-shell nuclei by using the resulting overlap functions for the description of the cross sections of $(p,d)$ reactions on the open $s$-$d$ shell nuclei $^{24}$Mg, $^{28}$Si and $^{32}$S and of $^{32}$S$(e,e^{\prime}p)$ reaction. The relative role of both shell structure and short-range correlations incorporated in the correlation approach on the spectroscopic factors and the reaction cross sections is pointed out.

nucl-th↗

arXiv2002

Universal property of the information entropy in fermionic and bosonic systems

It is shown that a similar functional form $S=a+b\ln N$ 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 $Ω$ 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.

quant-ph↗

arXiv2001

Bose-Einstein condensation of correlated atoms in a trap

The Bose-Einstein condensation of correlated atoms in a trap is studied by examining the effect of inter-particle correlations to one-body properties of atomic systems at zero temperature using a simplified formula for the correlated two body density distribution. Analytical expressions for the density distribution and rms radius of the atomic systems are derived using four different expressions of Jastrow type correlation function. In one case, in addition, the one-body density matrix, momentum distribution and kinetic energy are calculated analytically, while the natural orbitals and natural occupation numbers are also predicted in this case. Simple approximate expressions for the mean square radius and kinetic energy are also given.

cond-mat.soft↗

arXiv2001

A link of information entropy and kinetic energy for quantum many-body systems

A direct connection of information entropy $S$ and kinetic energy $T$ is obtained for nuclei and atomic clusters, which establishes $T$ as a measure of the information in a distribution. It is conjectured that this is a universal property for fermionic many-body systems. We also check rigorous inequalities previously found to hold between S and T for atoms and verify that they hold for nuclei and atomic clusters as well. These inequalities give a relationship of Shannon's information entropy in position-space with an experimental quantity i.e. the rms radius of nuclei and clusters.

nucl-th↗

arXiv2000

Evaluation of cluster expansions and correlated one-body properties of nuclei

Three different cluster expansions for the evaluation of correlated one-body properties of s-p and s-d shell nuclei are compared. Harmonic oscillator wave functions and Jastrow type correlations are used, while analytical expressions are obtained for the charge form factor, density distribution, and momentum distribution by truncating the expansions and using a standard Jastrow correlation function f. The harmonic oscillator parameter b and the correlation parameter βhave been determined by a least-squares fit to the experimental charge form factors in each case. The information entropy of nuclei in position-space (S_r) and momentum-space (S_k) according to the three methods are also calculated. It is found that the larger the entropy sum S=S_r+S_k (the information content of the system) the smaller the values of χ^2. This indicates that S is a criterion of the quality of a given nuclear model, according to the maximum entropy principle. Only two exceptions to this rule, out of many cases examined, were found. Finally an analytic expression for the so-called "healing" or "wound" integrals is derived with the function f considered, for any state of the relative two-nucleon motion and their values in certain cases are computed and compared.

nucl-th↗

arXiv2000

Universal trend of the information entropy of a fermion in a mean field

We calculate the information entropy of single-particle states in position-space $S_{r}$ and momentum-space $S_{k}$ for a nucleon in a nucleus, a $Λ$ particle in a hypernucleus and an electron in an atomic cluster. It is seen that $S_{r}$ and $S_{k}$ obey the same approximate functional form as functions of the number of particles, $S_{r}$ ({\rm or} $S_{k}) = a+bN^{1/3}$ in all of the above many-body systems in position- and momentum- space separately. The net information content $S_{r}+S_{k}$ is a slowly varying function of $N$ of the same form as above. The entropy sum $S_{r}+S_{k}$ is invariant to uniform scaling of coordinates and a characteristic of the single-particle states of a specific system. The order of single-particle states according to $S_r +S_k$ is the same as their classification according to energy keeping the quantum number $n$ constant. The spin-orbit splitting is reproduced correctly. It is also seen that $S_{r}+S_{k}$ enhances with excitation of a fermion in a quantum-mechanical system. Finally, we establish a relationship of $S_r +S_k$ with the energy of the corresponding single-particle state i.e. $S_r +S_k = k \ln (μE +ν)$. This relation holds for all the systems under consideration.

nucl-th↗