An analysis of Helium resonant states in terms of entropy, information, complexity and entanglement measures

Restrepo, Juliana; Sanz-Vicario, José Luis

doi:10.1088/1742-6596/488/15/152004

Cited by 3 publications

(5 citation statements)

References 5 publications

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“…We observe that entanglement of (d − 1)-dimensional spherium tends to increase with energy. A similar behaviour has been observed in other models, such as the Crandall and the Hooke ones [5], as well as for the singlet states of the Helium atom employing highquality, state-of-the-art wavefunctions [12] (although for more general states of Helium the energy-entanglement connection seems to be much more complicated [28,29]). …”

Section: Entanglement In (D − 1)-spheriumsupporting

confidence: 81%

Quantum entanglement in (d−1)-spherium

Toranzo¹,

Plastino²,

Sánchez-Moreno³

et al. 2015

J. Phys. A: Math. Theor.

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There are very few systems of interacting particles (with continuous variables) for which the entanglement of the concomitant eigenfunctions can be computed in an exact, analytical way. Here we present analytical calculations of the amount of entanglement exhibited by s-states of spherium. This is a system of two particles (electrons) interacting via a Coulomb potential and confined to a (d − 1)-sphere (that is, to the surface of a d-dimensional ball). We investigate the dependence of entanglement on the radius R of the system, on the spatial dimensionality d, and on energy. We find that entanglement increases monotonically with R, decreases with d, and also tends to increase with the energy of the eigenstates. These trends are discussed and compared with those observed in other two-electron atomic-like models where entanglement has been investigated. 03.67.Mn

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Section: Entanglement In (D − 1)-spheriumsupporting

confidence: 81%

Quantum entanglement in (d−1)-spherium

Toranzo¹,

Plastino²,

Sánchez-Moreno³

et al. 2015

J. Phys. A: Math. Theor.

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“…It shows agreements on the resonance parameters are quite good. As for the entanglement entropy for such doubly excited resonance states in the helium atom, we are not aware of any published numerical results in the literature for comparison;  notwithstanding that an investigation on some doubly excited states in helium was reported at a meeting [38].…”

Section: Calculations and Resultsmentioning

confidence: 99%

“…notwithstanding that an investigation on some doubly excited states in helium was reported at a meeting [38].…”

Section: Calculations and Resultsmentioning

confidence: 99%

Quantification of Entanglement Entropies for Doubly Excited States in Helium

Lin

2015

Few-Body Syst

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In this work, we study the quantum entanglement for doubly excited resonance states in helium by using highly correlated Hylleraas type functions to represent such states of the two-electron system.The doubly-excited resonance states are determined by calculation of density of resonance states under the framework of the stabilization method. The spatial (electron-electron orbital) entanglement measures for the low-lying doubly excited 2s 2 , 2s3s, and 2p 2 1 S e states are carried out. Once a resonance state wave function is obtained, the linear entropy and von Neumann entropy for such a state are quantified using the Schmidt-Slater decomposition method. To check the consistence, linear entropy is also determined by solving analytically the needed four-electron (12-dimensional) integrals.

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“…(6) been carried out [50,51]. It would be of interest in the future to quantify von Neumann entropy for shape resonance states in the region when Z < Zcr using highly correlated wave functions and keeping the full Hamiltonian for these two-electron systems.…”

Section: Discussionmentioning

confidence: 99%

“…In passing, we are aware of an attempt to investigate such phenomenon using the S-wave model (keeping just the leading monopole term in the expansion of the electron-electron interacting potential operator) for such two-electron systems[49]. Quantification of von Neumann entropy and linear entropy for doubly excited Feshbach resonances in two-electron atoms has recently been carried out[50,51]. It would be of interest in the future to quantify von Neumann entropy for shape resonance states in the region when Z < Zcr using highly correlated wave functions and keeping the full Hamiltonian for these two-electron systems.…”

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confidence: 99%

Shannon information entropy in position space for two-electron atomic systems

Lin

2015

Chemical Physics Letters

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Entropic measures provide analytic tools to help us understand correlation in quantum systems. In our previous work, we calculated linear entropy and von Neumann entropy as entanglement measures for the ground state and lower lying excited states in helium-like systems. In this work, we adopt another entropic measure, Shannon entropy, to probe the nature of correlation effects. Besides the results of the Shannon entropy in coordinate space for the singlet ground states of helium-like systems including positronium negative ion, hydrogen negative ion, helium atom, and lithium positive ion, we also show results for systems with nucleus charge around the ionization threshold.

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An analysis of Helium resonant states in terms of entropy, information, complexity and entanglement measures

Cited by 3 publications

References 5 publications

Quantum entanglement in (d−1)-spherium

Quantum entanglement in (d−1)-spherium

Quantification of Entanglement Entropies for Doubly Excited States in Helium

Shannon information entropy in position space for two-electron atomic systems

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