Various complexity measures in confined hydrogen atom

Majumdar, Sangita; Mukherjee, Neetik; Roy, Amlan K.

doi:10.1016/j.cplett.2017.09.036

Cited by 28 publications

(18 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This is because they satisfy a number of mathematical requirements as already pointed out. However, other proposals of complexity‐like measures that do not generally satisfy the full set of criteria of an intrinsic statistical complexity show a similar behavior for all states, not being able to fully capture the internal structure of the system.…”

Section: Complexity Measuresmentioning

confidence: 97%

Two‐dimensional confined hydrogen: An entropy and complexity approach

Estañón

Aquino

Puertas‐Centeno

et al. 2020

Int J of Quantum Chemistry

View full text Add to dashboard Cite

The position and momentum spreading of the electron distribution of the two-dimensional confined hydrogenic atom, which is a basic prototype of the general multidimensional confined quantum systems, is numerically studied in terms of the confinement radius for the 1s, 2s, 2p, and 3d quantum states by means of the main entropy and complexity information-theoretical measures. First, the Shannon entropy and the Fisher information, as well as the associated uncertainty relations, are computed and discussed. Then, the Fisher-Shannon, lopezruiz-mancini-alvet, and LMC-Rényi complexity measures are examined and mutually compared. We have found that these entropy and complexity quantities reflect the rich properties of the electron confinement extent in the two conjugated spaces. K E Y W O R D SFisher information of the two-dimensional confined hydrogen atom, Fisher-Shannon complexity measure of the two-dimensional confined hydrogen atom, LMC-Rényi complexity measure of the two-dimensional confined hydrogen atom, Shannon entropy of the two-dimensional confined hydrogen atom, two-dimensional confined hydrogen atom | INTRODUCTIONThe fundamental and practical relevance of the spherically confined quantum systems has been manifested from the early days of quantum physics [1,2] up until now. [3][4][5][6][7] They have been used as prototypes to explain numerous phenomena and systems not only in the three-dimensional world but also for nonrelativistic and relativistic D-dimensional (D ≥ 2) chemistry and physics. [8][9][10][11][12][13][14] For example, pioneered by Gerhard Ertl, the 2007 Nobel Laureate in Chemistry, and his collaborators, surface chemistry has been extensively studied and has become a key branch in chemistry. [11][12][13] In physics of materials, two-dimensional systems have been used to gain insight into the properties of semiconductors (see, eg, refs. [15, 16]), and they start to play a fundamental role in bringing strong and new forms of control to the atomic-scale limit over the dynamics of matter in the extreme confinement of electromagnetic energy by phonon polaritonics. [10] Moreover, the properties of the real fluids can be studied by means of crystalline fluids (ie, with a symmetry) with nonstandard dimensions (see, eg, ref. [17]).The idea of two-and multidimensional spherical confinement of atoms has been used not only to simulate the effect of high pressure on the static dipole polarizability in hydrogen [18] but also to model a great deal of nanotechnological objects such as quantum dots; quantum wells and quantum wires; [19,20] atoms and molecules embedded in nanocavities, for example, in fullerenes, zeolites cages, and helium droplets; [4,6,7,[21][22][23] dilute bosonic and fermionic systems in magnetic traps of extremely low temperatures; [24][25][26] and a variety of quantum-information elements. [27,28] This has provoked a fast development of a density functional theory of independent particles moving in multidimensional central potentials with various analytical forms (see, eg, refs. [5-7, 29-...

show abstract

Section: Complexity Measuresmentioning

confidence: 97%

Two‐dimensional confined hydrogen: An entropy and complexity approach

Estañón

Aquino

Puertas‐Centeno

et al. 2020

Int J of Quantum Chemistry

View full text Add to dashboard Cite

show abstract

“…However, in confined environment LMC complexity has been investigated only for ground state of some model systems, like, CHO, confined h-atom, particle in spherical box and confined Helium atom [36,37]. Very recently, the present authors have pursued similar calculations for confined hydrogen atom [38] and found that, parameter b plays a key role in interpreting the property of a system. In this endeavor, our objective is to explore four different types of complexity emerging out of two order (I, E) and two disorder (S, R) parameters, in conjugate spaces, as functions of confinement radius (r c ).…”

Section: Introductionmentioning

confidence: 96%

Some complexity measures in confined isotropic harmonic oscillator

Mukherjee

Roy

2019

J Math Chem

Self Cite

View full text Add to dashboard Cite

Various well-known statistical measures like López-Ruiz, Mancini, Calbet (LMC) and Fisher-Shannon complexity have been explored for confined isotropic harmonic oscillator (CHO) in composite position (r) and momentum (p) spaces. To get a deeper insight about CHO, a more generalized form of these quantities with Rényi entropy (R) is invoked here. The importance of scaling parameter in the exponential part is also investigated. R is estimated considering order of entropic moments α, β as ( 2 3 , 3) in r and p spaces respectively. Explicit results of these measures with respect to variation of confinement radius r c is provided systematically for first eight energy states, namely, 1s, 1p, 1d, 2s, 1f, 2p, 1g and 2d. Detailed analysis of these complexity measures provides many hitherto unreported interesting features.

show abstract

“…This sum has been applied, along with other information measures, to study confined quantum systems . Confined quantum systems are of interest since they can be used to model systems at extreme pressures, including astrophysical and nanotechnological ones .…”

Section: Introductionmentioning

confidence: 99%

Shannon‐information entropy sum in the confined hydrogenic atom

Salazar

Laguna

Prasad

et al. 2020

Int J of Quantum Chemistry

View full text Add to dashboard Cite

The appearance of critical points in the Shannon entropy sum as a function of confinement radius, in ground and excited state confined hydrogenic systems, is discussed. We illustrate that the Coulomb potential in tandem with the hard sphere confinement are responsible for these points. The positions of these points are observed to vary with the intensity of the potential. The effects of the Coulomb potential on the system are further probed, by examining the differences between the densities of the confined atom and those of the particle confined in a spherical box, for the same confinement radius. These differences are quantified by using Kullback-Leibler and cumulative residual Kullback-Leibler distance measures from information theory. These measures detect that the effects of the Coulomb potential are squeezed out of the system as the confinement radius decreases. That is, the confined atom densities resemble the particle in a box ones, for smaller confinement radii. Furthermore, the critical points in the entropy sum lie in the same regions where there are changes in the distance measures, as the atom behaves more particle in a spherical box-like. The analysis is further complemented by examination of the derivative of the entropy sum with respect to confinement radius. This study illustrates the inhomogeneity in the magnitudes of the derivatives of the entropy sum components and their dependence on the Coulomb potential. A link between the derivative and the entropic force is also illustrated and discussed. Similar behaviors are observed when the virial ratio is compared to the entropic power one, as a function of confinement radius. K E Y W O R D S confined hydrogen atom, Kullback-Leibler distance measures, quantum uncertainties, Shannon entropy sum

show abstract

Various complexity measures in confined hydrogen atom

Cited by 28 publications

References 37 publications

Two‐dimensional confined hydrogen: An entropy and complexity approach

Two‐dimensional confined hydrogen: An entropy and complexity approach

Some complexity measures in confined isotropic harmonic oscillator

Shannon‐information entropy sum in the confined hydrogenic atom

Contact Info

Product

Resources

About