Entanglement in helium atom confined in an impenetrable cavity

Kościk, Przemysław; Saha, Jayanta K.

doi:10.1140/epjd/e2015-60453-4

Cited by 13 publications

(9 citation statements)

References 45 publications

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“…Shannon entropy for hydrogen-like and helium-like atomic systems with infinite confinement were investigated by Sen [22]. Recently, the von Neumann entropy for helium with finite confinement [23] and with infinite confinement were calculated by Koscik and Saha [24].…”

Section: Introductionmentioning

confidence: 99%

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Shannon Information Entropy in Position Space for the Ground and Singly Excited States of Helium with Finite Confinements

2017

Atoms

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Abstract:We provide benchmark values for Shannon information entropies in position space for the ground state and ls2s 1 S e excited state of helium confined with finite confinement potentials by employing the highly correlated Hylleraas-type wave functions. For the excited state, a "tilt" (small oscillation) on the curve of Shannon entropy as a function of width size for the confinement potential is observed. Justified by the behavior of the electron density, the localization or delocalization of the helium wave functions confined with repulsive and attractive finite oscillator (FO) potentials are examined.

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Section: Introductionmentioning

confidence: 99%

“…In Ref. [23,24], the von Neumann and linear entropies of the ground state helium inside a spherical cavity with finite or infinite confinements were calculated, but Shannon information entropy for helium with finite confinement has not been reported in the literature, to the best of our knowledge. This work presents such an investigation.…”

Section: Introductionmentioning

confidence: 99%

Shannon Information Entropy in Position Space for the Ground and Singly Excited States of Helium with Finite Confinements

2017

Atoms

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“…Nonspherical confinement models are also assumed to deal with important quantum mechanical problems. Vast applicability of the outcomes from such studies in different branches of science and technology makes the subject a topic of immense interest in the recent times …”

Section: Introductionmentioning

confidence: 99%

“…Vast applicability of the outcomes from such studies in different branches of science and technology makes the subject a topic of immense interest in the recent times. [16][17][18] Hydrogen atom confined in impenetrable spherical cavity was first studied by Michels et al [19] to model the effects of pressure on its energy and polarizability. Subsequently, many workers [20][21][22][23][24][25][26] have addressed this problem from different angles to develop a comprehensive understanding about such confined systems.…”

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confidence: 99%

Ritz variational calculation for the singly excited states of compressed two‐electron atoms

Saha

Bhattacharyya²,

Mukherjee³

2016

Int J of Quantum Chemistry

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A detailed analysis on the effect of spherical impenetrable confinement on the structural properties of two-electron ions in S2 states has been performed. The energy values of 1sns [n5224] ( 3 S e ) states of helium-like ions (Z5125) are estimated within the framework of Ritz variational method using explicitly correlated Hylleraas-type basis sets. The correlated wave functions used here are consistent with the finite boundary conditions due to spherical confinement. A comparative study between the singlet and triplet states originating from a particular electronic configuration shows incidental degeneracy and the subsequent level-crossing phenomena. The thermodynamic pressure felt by the ion inside the sphere pushes the energy levels toward continuum. Critical pressures for the transition to strong confinement regime (where the singly excited two-electron energy levels cross the corresponding one-electron threshold) as well as for the complete destabilization are also estimated.correlation, pressure confinement, two-electron atom, variational method | I N T R O D U C T I O NStudies on the subject of confined atomic systems have started soon after the advent of quantum mechanics. In recent years, a paradigm shift in the facility for doing controlled experiment on confined atom and modern high-speed computational resources open up a new horizon for this subject. The modifications of the structural and spectral properties of the atom or the molecule depending on the number and degree of confining parameters is the interesting aspect of the problem. Comprehensive reviews [1][2][3] are now available on this topic. Theoretically, different types of confinement models can be realized for different physical situations, for example, atoms under plasma environment, [4,5] endohedrally confined atoms and molecules in fullerene cages, [6] impurities in quantum dots or nano crystals, [7,8] matter under extreme pressure in zeolite sieves, [9] or in the walls of nuclear reactors, [10] and so forth. Moreover, the confined atom models assume contemporary significance in understanding the cores of Jovian planets such as Jupiter and Saturn. [11] Nonspherical confinement models [12][13][14][15] are also assumed to deal with important quantum mechanical problems. Vast applicability of the outcomes from such studies in different branches of science and technology makes the subject a topic of immense interest in the recent times. [16][17][18] Hydrogen atom confined in impenetrable spherical cavity was first studied by Michels et al. [19] to model the effects of pressure on its energy and polarizability. Subsequently, many workers [20][21][22][23][24][25][26] have addressed this problem from different angles to develop a comprehensive understanding about such confined systems. Helium atom confined by such spherical cavity is a much complicated numerical problem as compared to the hydrogen-like ions for obvious reasons. For ions having two or more electrons, the effect of electron correlation plays an important role in the str...

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“…To have an inner look of the squeezing of the wave function due to the positive nature of the confining potential, we have estimated the expectation values of different operators which are useful to estimate structural and spectral properties of such systems. The oneand two-electron radial densities at different values of the strength of the confining potential are also studied in detail which are important in estimating the correlation function [30,34] and the information entropy of quantum systems [35,36]. The methodology adopted here can yield precise effect of angular correlation on the energy value of the system and we have studied this for varying strength of the environment.…”

Section: Introductionmentioning

confidence: 99%

Structural modifications of two-electron systems under isotropic harmonic confinement

Hazra¹,

Mondal

Bhattacharyya³

et al. 2021

Eur. Phys. J. D

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Atomic systems placed in external potentials manifest various characteristic features which provide useful knowledge about the surroundings. We have studied the structural properties of the ground state of different two-electron systems under isotropic harmonic confinement (IHC). In particular, we have considered negative hydrogen ion, neutral helium atom and positive singly ionized lithium ion to cover all types of charge states. In addition, we have also studied the system of two electrons inside IHC. The wave function is expanded in Hylleraas basis to incorporate the effect of electron correlation in an explicit manner and Ritz variational calculations are performed to obtain the energy eigenvalues and the relative wave functions. The energy levels become more positive with increasing strength of the confining potential. The results show that for ionic systems, the two-electron energy level crosses the respective one-electron threshold at a certain value of the potential beyond which the two-electron level becomes quasi-bound. In order to get deeper insight into such threshold ionization phenomenon, we have examined the contribution of the correlated energy Ecorr [sum of radial and angular correlation energy] and radial correlation energy E rad.corr to the total energy for different two-electron systems under IHC. The Hellmann-Feynman theorem and the virial theorem have been verified as a quantitative validation of the accuracy of our results. The one-and two-electron radial densities have also been analyzed to gain a physical insight into the structural changes of the two-electron systems under IHC. Moreover, the expectation values of different radial and angular variables are also reported which are important to estimate different geometrical and spectral properties.

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Entanglement in helium atom confined in an impenetrable cavity

Cited by 13 publications

References 45 publications

Shannon Information Entropy in Position Space for the Ground and Singly Excited States of Helium with Finite Confinements

Shannon Information Entropy in Position Space for the Ground and Singly Excited States of Helium with Finite Confinements

Ritz variational calculation for the singly excited states of compressed two‐electron atoms

Structural modifications of two-electron systems under isotropic harmonic confinement

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