Nonstationary multistate Coulomb and multistate exponential models for nonadiabatic transitions

Ostrovsky, V N

doi:10.1103/PhysRevA.68.012710

Title: Nonstationary multistate Coulomb and multistate exponential models for nonadiabatic transitions

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Abstract

The nonstationary Schroedinger equation is considered in a finite basis of states. The model Hamiltonian matrix corresponds to a single diabatic potential curve with a Coulombic {approx}1/t time dependence. An arbitrary number of other diabatic potential curves are flat, i.e., time independent and have arbitrary energies. Related states are coupled by constant interactions with the Coulomb state. The resulting nonstationary Schroedinger equation is solved by the method of contour integral. Probabilities of transitions to any other state are obtained as t{yields}{infinity} in a simple analytical form for the case when the Coulomb state is populated initially (at instant of time t{yields}+0). The formulas apply both to the cases when a horizontal diabatic potential curve is crossed by the Coulomb one and to a noncrossing situation. In the limit of weak coupling, the transition probabilities are interpreted in terms of a sequence of pairwise Landau-Zener-type transitions. Mapping of the Coulomb model onto an exactly solvable exponential multistate model is established. For the special two-state case, the well-known Nikitin model is recovered.

Authors:

Ostrovsky, V N ^[1]

V. A. Fock Institute of Physics, The University of St. Petersburg, 198904 St. Petersburg, Russia (Russian Federation)

Publication Date:: Tue Jul 01 00:00:00 EDT 2003

OSTI Identifier:: 20639909

Resource Type:: Journal Article

Journal Name:: Physical Review. A

Additional Journal Information:: Journal Volume: 68; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevA.68.012710; (c) 2003 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947

Country of Publication:: United States

Language:: English

Subject:: 74 ATOMIC AND MOLECULAR PHYSICS; ALGEBRA; BASIC INTERACTIONS; COUPLING; ENERGY LEVELS; EXACT SOLUTIONS; HAMILTONIANS; LIFETIME; POTENTIAL ENERGY; POTENTIALS; PROBABILITY; QUANTUM MECHANICS; SCHROEDINGER EQUATION; TIME DEPENDENCE

Citation Formats


                    Ostrovsky, V N. Nonstationary multistate Coulomb and multistate exponential models for nonadiabatic transitions.  United States: N. p., 2003. 
        Web.  doi:10.1103/PhysRevA.68.012710.

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                    Ostrovsky, V N. Nonstationary multistate Coulomb and multistate exponential models for nonadiabatic transitions.  United States.  https://doi.org/10.1103/PhysRevA.68.012710

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                    Ostrovsky, V N. 2003.  
        "Nonstationary multistate Coulomb and multistate exponential models for nonadiabatic transitions".  United States.  https://doi.org/10.1103/PhysRevA.68.012710.

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@article{osti_20639909,

  title        = {Nonstationary multistate Coulomb and multistate exponential models for nonadiabatic transitions},

  author       = {Ostrovsky, V N},

  abstractNote = {The nonstationary Schroedinger equation is considered in a finite basis of states. The model Hamiltonian matrix corresponds to a single diabatic potential curve with a Coulombic {approx}1/t time dependence. An arbitrary number of other diabatic potential curves are flat, i.e., time independent and have arbitrary energies. Related states are coupled by constant interactions with the Coulomb state. The resulting nonstationary Schroedinger equation is solved by the method of contour integral. Probabilities of transitions to any other state are obtained as t{yields}{infinity} in a simple analytical form for the case when the Coulomb state is populated initially (at instant of time t{yields}+0). The formulas apply both to the cases when a horizontal diabatic potential curve is crossed by the Coulomb one and to a noncrossing situation. In the limit of weak coupling, the transition probabilities are interpreted in terms of a sequence of pairwise Landau-Zener-type transitions. Mapping of the Coulomb model onto an exactly solvable exponential multistate model is established. For the special two-state case, the well-known Nikitin model is recovered.},

  doi          = {10.1103/PhysRevA.68.012710},

  url          = {https://www.osti.gov/biblio/20639909},
  journal      = {Physical Review. A},

  issn         = {1050-2947},

  number       = 1,

  volume       = 68,

  place        = {United States},

  year         = {Tue Jul 01 00:00:00 EDT 2003},

  month        = {Tue Jul 01 00:00:00 EDT 2003}

}

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