Abstract
We provide a diagonal form of a reduced density matrix of S-symmetry resonance states of two electron systems determined under the framework of the complex scaling method. We have employed the variational Hylleraas type wavefunction to estimate the complex entropies in doubly excited resonance states of helium atom. Our results are in good agreement with the corresponding ones determined under the framework of the stabilization method (Lin and Ho in Few-Body Syst 56:157, 2015).
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Nielsen, N., Chuang, I.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Tichy, M.C., Mintert, F., Buchleitner, A.: Essential entanglement for atomic and molecular physics. J. Phys. B: At. Mol. Opt. Phys. 44, 192001 (2011)
Boguslawski, K., Tecmer, P.: Orbital entanglement in quantum chemistry. Int. J. Quantum Chem. 115, 1289 (2015)
Coe, J.P., Sudbery, A., D’Amico, I.: Entanglement and density-functional theory: testing approximations on Hooke’s atom. Phys. Rev. B 77, 205122 (2008)
Tennie, F., et al.: Pinning of fermionic occupation numbers: general concepts and one spatial dimension. Phys. Rev. A 93, 042126 (2016)
Harshman, N.L.: One-dimensional traps, two-body interactions, few-body symmetries: I. One, two, and three particles. Few-Body Syst. 57, 11 (2016)
Kościk, P.: Entanglement in S states of two-electron quantum dots with Coulomb impurities at the center. Phys. Lett. A 377, 2393 (2013)
Kościk, P.: Quantum entanglement of two harmonically trapped dipolar particles. Few-Body Syst. 56, 107 (2015)
Sowiński, T., Gajda, M., Rza̧żewski, K.: Pairing in a system of a few attractive fermions in a harmonic trap. EPL 109, 26005 (2015)
García-March, M.A., Dehkharghani, A.S., Zinner, N.T.: Entanglement of an impurity in a few-body one-dimensional ideal Bose system. J. Phys. B: At. Mol. Opt. Phys. 49, 075303 (2016)
Dehkharghani, A.S., Volosniev, A.G., Zinner, N.T.: Impenetrable mass-imbalanced particles in one-dimensional harmonic traps. J. Phys. B: At. Mol. Opt. Phys. 49, 085301 (2016)
Nagy, I., Glasser, M.L.: Information-theoretic aspects of friction in the quantum mechanics of an interacting two-electron harmonic atom. J. Math. Chem. 53, 1274 (2015)
Glasser, M.L., Nagy, I.: Exact evaluation of entropic quantities in a solvable two-particle model. Phys. Lett. A 377, 2317 (2013)
Yaüez, R.J., Plastino, A.R., Dehesa, J.S.: Quantum entanglement in a soluble two-electron model atom. Eur. Phys. J. D 56, 141 (2010)
Peng, H.T., Ho, Y.K.: Entanglement for excited states of ultracold bosonic atoms in one-dimensional harmonic traps with contact interaction. Mod. Phys. Lett. B 29, 1550189 (2015)
Xu, F., et al.: Quantum tunneling effect in entanglement dynamics. Int. J. Quantum Chem. 116, 7 (2016)
Pȩcak, D., Sowiński, T., Gajda, M.: Two-flavor mixture of a few fermions of different mass in a one-dimensional harmonic trap. New J. Phys. 18, 013030 (2016)
Dehesa, J., et al.: Quantum entanglement in helium. J. Phys. B: At. Mol. Opt. Phys. 45, 015504 (2012)
Kościk, P., Okopińska, A.: Entanglement entropies in the ground states of helium-like atoms. Few-Body Syst. 55, 1151 (2014)
López-Rosa, S., et al.: Quantum entanglement of helium-like systems with varying-Z: compact state-of-the-art CI wave functions. J. Phys. B: At. Mol. Opt. Phys. 48, 175002 (2015)
Esquivel, R.O., López-Rosa, S., Dehesa, J.S.: Correlation energy as a measure of non-locality: quantum entanglement of helium-like systems. EPL 111, 40009 (2015)
Lin, Y.C., Ho, Y.K.: Quantum entanglement for two electrons in the excited states of helium-like systems. Can. J. Phys. 93, 646 (2015)
Lin, C.H., Ho, Y.K.: Quantification of entanglement entropy in helium by the SchmidtSlater decomposition method. Few-Body Syst. 55, 1141 (2014)
Lin, Y.C., Lin, C.Y., Ho, Y.K.: Spatial entanglement in two-electron atomic systems. Phys. Rev. A 87, 022316 (2013)
Lin, C.H., Lin, C.Y., Ho, Y.K.: Quantification of linear entropy for quantum entanglement in He, H- and Ps-ions using highly-correlated Hylleraas functions. Few-Body Syst. 54, 2147 (2013)
Lin, C.H., Ho, Y.K.: Calculation of von Neumann entropy for hydrogen and positronium negative ions. Phys. Lett. A 378, 2861 (2014)
Cuartas, J.P.R., Sanz-Vicario, J.L.: Information and entanglement measures applied to the analysis of complexity in doubly excited states of helium. Phys. Rev. A 91, 052301 (2015)
Lin, C.H., Ho, Y.K.: Quantification of entanglement entropies for doubly excited states in helium. Few-Body Syst. 56, 157 (2015)
Lin, C.H., Ho, Y.K.: Quantum entanglement and Shannon information entropy for the doubly excited resonance state in positronium negative ion. Atoms 3, 422 (2015)
Hofer, T.S.: On the basis set convergence of electronelectron entanglement measures: helium-like systems. Front. Chem. 1, 24 (2013)
Lin, Y.C., Fang, T.K., Ho, Y.K.: Quantum entanglement for helium atom in the Debye plasmas. Phys. Plasm. 22, 032113 (2015)
Ho, Y.K., Lin, C.H.: Quantification of entanglement entropies for doubly excited resonance states in two-electron atomic systems. J. Phys. Conf. Ser. 635, 092025 (2015)
Lin, C.H., Ho, Y.K.: Shannon information entropy in position space for two-electron atomic systems. Chem. Phys. Lett. 633, 261 (2015)
Pont, F.M., Osenda, O., Toloza, J.H., Serra, P.: Entropy, fidelity, and double orthogonality for resonance states in two-electron quantum dots. Phys. Rev. A 81, 042518 (2010)
Moiseyev, N.: Non-Hermitian Quantum Mechanics. Cambridge University Press, Cambridge (2011)
Reinhardt, W.P.: Complex coordinates in the theory of atomic and molecular structure and dynamics. Ann. Rev. Phys. Chem. 33, 223 (1982)
Junker, B.R.: Recent computational developments in the use of complex scaling in resonance phenomena. Adv. Atom. Mol. Phys 18, 208 (1982)
Ho, Y.K.: The method of complex coordinate rotation and its applications to atomic collision processes. Phys. Rep. 99, 1 (1983)
Kuroś, A., Okopińska, A.: Entanglement properties of the two-electron quasi-one dimensional Gaussian quantum dot. Few-Body Syst. 56, 853 (2015)
Kościk, P.: On the bipartite correlations in quantum resonance states. Phys. Lett. A 380, 1256 (2016)
Berggren, T.: Expectation value of an operator in a resonant state. Phys. Lett. B 373, 1 (1996)
Van der Merwe, A.: Old and new questions in physics, cosmology, philosophy, and theoretical biology. Plenum Press, New York (1983)
Ho, Y.K.: Complex-coordinate calculations for doubly excited states of two-electron atoms. Phys. Rev. A 23, 2137 (1981)
Moiseyev, N.: Quantum theory of resonances: calculating energies, widths and cross-sections by complex scaling. Phys. Rep. 302, 211 (1998)
Burgers, A., Wintgen, D., Rest, J.M.: Highly doubly excited S states of the helium atom. J. Phys. B: At. Mol. Opt. Phys. 28, 3163 (1995)
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An erratum to this article is available at http://dx.doi.org/10.1007/s00601-017-1245-y.
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Kuroś, A., Kościk, P. & Saha, J.K. Doubly Excited Resonance States of Helium Atom: Complex Entropies . Few-Body Syst 57, 1147–1153 (2016). https://doi.org/10.1007/s00601-016-1151-8
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DOI: https://doi.org/10.1007/s00601-016-1151-8