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Title: Dissociative recombination by frame transformation to Siegert pseudostates: A comparison with a numerically solvable model

Authors:
; ; ; ; ; ;
Publication Date:
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1419821
Grant/Contract Number:
AC02-05CH11231; SC0010545
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review A
Additional Journal Information:
Journal Volume: 97; Journal Issue: 2; Related Information: CHORUS Timestamp: 2018-02-07 09:58:12; Journal ID: ISSN 2469-9926
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English

Citation Formats

Hvizdoš, Dávid, Váňa, Martin, Houfek, Karel, Greene, Chris H., Rescigno, Thomas N., McCurdy, C. William, and Čurík, Roman. Dissociative recombination by frame transformation to Siegert pseudostates: A comparison with a numerically solvable model. United States: N. p., 2018. Web. doi:10.1103/PhysRevA.97.022704.
Hvizdoš, Dávid, Váňa, Martin, Houfek, Karel, Greene, Chris H., Rescigno, Thomas N., McCurdy, C. William, & Čurík, Roman. Dissociative recombination by frame transformation to Siegert pseudostates: A comparison with a numerically solvable model. United States. doi:10.1103/PhysRevA.97.022704.
Hvizdoš, Dávid, Váňa, Martin, Houfek, Karel, Greene, Chris H., Rescigno, Thomas N., McCurdy, C. William, and Čurík, Roman. 2018. "Dissociative recombination by frame transformation to Siegert pseudostates: A comparison with a numerically solvable model". United States. doi:10.1103/PhysRevA.97.022704.
@article{osti_1419821,
title = {Dissociative recombination by frame transformation to Siegert pseudostates: A comparison with a numerically solvable model},
author = {Hvizdoš, Dávid and Váňa, Martin and Houfek, Karel and Greene, Chris H. and Rescigno, Thomas N. and McCurdy, C. William and Čurík, Roman},
abstractNote = {},
doi = {10.1103/PhysRevA.97.022704},
journal = {Physical Review A},
number = 2,
volume = 97,
place = {United States},
year = 2018,
month = 2
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on February 7, 2019
Publisher's Accepted Manuscript

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  • Within the theory of Siegert pseudostates, it is possible to accurately calculate bound states and resonances. The energy continuum is replaced by a discrete set of states. Many questions of interest in scattering theory can be addressed within the framework of this formalism, thereby avoiding the need to treat the energy continuum. For practical calculations it is important to know whether a certain subset of Siegert pseudostates comprises a basis. This is a nontrivial issue, because of the unusual orthogonality and overcompleteness properties of Siegert pseudostates. Using analytical and numerical arguments, it is shown that the subset of bound statesmore » and outgoing Siegert pseudostates forms a basis. Time evolution in the context of Siegert pseudostates is also investigated. From the Mittag-Leffler expansion of the outgoing-wave Green's function, the time-dependent expansion of a wave packet in terms of Siegert pseudostates is derived. In this expression, all Siegert pseudostates - bound, antibound, outgoing, and incoming - are employed. Each of these evolves in time in a nonexponential fashion. Numerical tests underline the accuracy of the method.« less
  • The transmission of a nonsymmetric potential barrier is a two-channel quantum problem. In this aspect it is analogous to the two-channel radial problem. The analytical properties of the S matrix are similar for both generic quantum-mechanical systems. We here develop an explicit mapping between the two problems. It allows us to formulate barrier transmission in terms of the Siegert pseudostates similarly to the approach developed recently for the two-channel radial case. This results in an efficient method of treating barrier transmission including on equal footing both resonance effects and smooth background behavior.
  • We describe a simple model for electron-molecule collisions that has one nuclear and one electronic degree of freedom and that can be solved to arbitrarily high precision, without making the Born-Oppenheimer approximation, by employing a combination of the exterior complex scaling method and a finite-element implementation of the discrete variable representation. We compare exact cross sections for vibrational excitation and dissociative attachment with results obtained using the local complex potential approximation as commonly applied in the ''boomerang'' model, and suggest how this two-dimensional model can be used to test the underpinnings of contemporary nonlocal approximations to resonant collisions.
  • Progress in semiconductor technology introduces a new platform for quantum optics studies in solid state: a quantum dot strongly coupled to a cavity mode. We present a numerically solvable model for the combined electron, photon, and phonon dynamics. For a cavity mode prepared in a Fock state, the model reproduces the Jaynes-Cumming solution and interaction with a phonon bath leads to a higher value for the intensity-intensity correlation function: g{sup (2)} (0) . In contrast, for an initial thermal photon distribution, the phonon-bath interaction gives a counterintuitive reduction in g{sup (2)} (0) , resulting in the classical photon distribution evolvingmore » into a nonclassical one.« less