Dynamics of Entanglement for Two-Electron Atoms

Osenda, Omar; Serra, Pablo; Kais, Sabre

doi:10.1142/s0219749908003463

Cited by 6 publications

(11 citation statements)

References 29 publications

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“…Where the expectation value 1 r 12 n has its maximum the corresponding linear entropy has its minimum. The inverse behavior showed by the entropy and the Coulombian repulsion has been observed previously [11,26].…”

Section: The Entropysupporting

confidence: 73%

“…(10) we added α as a basis index to indicate that in general the variational eigenfunction is α-dependent. The matrix elements of the kinetic energy, the Coulombic repulsion between the electrons and other mathematical details involving the functions |n 1 , n 2 ; l; α are given in references [26], [27].…”

Section: The Model and Basic Resultsmentioning

confidence: 99%

“…Moreover, as has been stressed in Reference [2], a given numerical method could be useful to accurately calculate the spectrum of a quantum system, but hopelessly inaccurate to calculate the entanglement. In few body systems there is evidence that there is a strong correlation between the entanglement and the Coulombian repulsion between the components of the system [5,9,11,26]. Because of this correlation we will carefully investigate the behavior of the Coulombian repulsion between the electrons in our model.…”

Section: The Entropymentioning

confidence: 99%

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Entropy, fidelity, and double orthogonality for resonance states in two-electron quantum dots

et al. 2010

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Resonance states of a two-electron quantum dots are studied using a variational expansion with both real basis-set functions and complex scaling methods. The two-electron entanglement (linear entropy) is calculated as a function of the electron repulsion at both sides of the critical value, where the ground (bound) state becomes a resonance (unbound) state. The linear entropy and fidelity and double orthogonality functions are compared as methods for the determination of the real part of the energy of a resonance. The complex linear entropy of a resonance state is introduced using complex scaling formalism.

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Section: The Entropysupporting

confidence: 73%

Section: The Model and Basic Resultsmentioning

confidence: 99%

Section: The Entropymentioning

confidence: 99%

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Entropy, fidelity, and double orthogonality for resonance states in two-electron quantum dots

et al. 2010

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“…so we refer to the basis set size using both N and M. The matrix elements of the kinetic energy, the Coulombic repulsion between the electrons and other mathematical details involving the functions |n 1 , n 2 ; l; α are given in references [9], [15], [16]. The resonance states can be analyzed using the spectrum obtained with a basis of L 2 functions (see [10] and References therein).…”

Section: The Model and Basic Resultsmentioning

confidence: 99%

“…so we refer to the basis set size using both N and M. The matrix elements of the kinetic energy, the Coulombic repulsion between the electrons and other mathematical details involving the functions |n 1 , n 2 ; l; α are given in references [9], [15], [16]. The figure shows the same variational eigenvalues that (a) (black lines) and the energy calculated using the complex scaling method (green line) for a parameter θ = π/10.…”

Section: The Model and Basic Resultsmentioning

confidence: 99%

The scaling of the density of states in systems with resonance states

Pont¹,

Osenda²,

Serra³

2010

Phys. Scr.

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Resonance states of a two-electron quantum dot are studied using a variational expansion with both real basis-set functions and complex scaling methods. We present numerical evidence about the critical behavior of the density of states in the region where there are resonances. The critical behavior is signaled by a strong dependence of some features of the density of states with the basis-set size used to calculate it. The resonance energy and lifetime are obtained using the scaling properties of the density of states PACS numbers: 31.15.ac,03.67.Mn,73.22.-f

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Electron–vibration entanglement in the Born–Oppenheimer description of chemical reactions and spectroscopy

McKemmish

McKenzie

Hush

et al. 2015

Phys. Chem. Chem. Phys.

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Entanglement is sometimes regarded as the quintessential measure of the quantum nature of a system and its significance for the understanding of coupled electronic and vibrational motions in molecules has been conjectured. Previously, we considered the entanglement developed in a spatially localized diabatic basis representation of the electronic states, considering design rules for qubits in a low-temperature chemical quantum computer. We extend this to consider the entanglement developed during high-energy processes. We also consider the entanglement developed using adiabatic electronic basis, providing a novel way for interpreting effects of the breakdown of the Born-Oppenheimer (BO) approximation. We consider: (i) BO entanglement in the ground-state wavefunction relevant to equilibrium thermodynamics, (ii) BO entanglement associated with low-energy wavefunctions relevant to infrared and tunneling spectroscopies, (iii) BO entanglement in high-energy eigenfunctions relevant to chemical reaction processes, and (iv) BO entanglement developed during reactive wavepacket dynamics. A two-state single-mode diabatic model descriptive of a wide range of chemical phenomena is used for this purpose. The entanglement developed by BO breakdown correlates simply with the diameter of the cusp introduced by the BO approximation, and a hierarchy appears between the various BO-breakdown correction terms, with the first-derivative correction being more important than the second-derivative correction which is more important than the diagonal correction. This simplicity is in contrast to the complexity of BO-breakdown effects on thermodynamic, spectroscopic, and kinetic properties. Further, processes poorly treated at the BO level that appear adequately treated using the Born-Huang adiabatic approximation are found to have properties that can only be described using a non-adiabatic description. For the entanglement developed between diabatic electronic states and the nuclear motion, qualitatively differently behavior is found compared to traditional properties of the density matrix and hence entanglement provides new information about system properties. For chemical reactions, this type of entanglement simply builds up as the transition-state region is crossed. It is robust to small changes in parameter values and is therefore more attractive for making quantum qubits than is the related fragile ground-state entanglement, provided that coherent motion at the transition state can be sustained.

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Dynamics of Entanglement for Two-Electron Atoms

Cited by 6 publications

References 29 publications

Entropy, fidelity, and double orthogonality for resonance states in two-electron quantum dots

Entropy, fidelity, and double orthogonality for resonance states in two-electron quantum dots

The scaling of the density of states in systems with resonance states

Electron–vibration entanglement in the Born–Oppenheimer description of chemical reactions and spectroscopy

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