A complex guided spectral transform Lanczos method for studying quantum resonance states

Yu, Hua-Gen

doi:10.1063/1.4905083

Title: A complex guided spectral transform Lanczos method for studying quantum resonance states

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Abstract

A complex guided spectral transform Lanczos (cGSTL) algorithm is proposed to compute both bound and resonance states including energies, widths and wavefunctions. The algorithm comprises of two layers of complex-symmetric Lanczos iterations. A short inner layer iteration produces a set of complex formally orthogonal Lanczos (cFOL) polynomials. They are used to span the guided spectral transform function determined by a retarded Green operator. An outer layer iteration is then carried out with the transform function to compute the eigen-pairs of the system. The guided spectral transform function is designed to have the same wavefunctions as the eigenstates of the original Hamiltonian in the spectral range of interest. Therefore the energies and/or widths of bound or resonance states can be easily computed with their wavefunctions or by using a root-searching method from the guided spectral transform surface. The new cGSTL algorithm is applied to bound and resonance states of HO₂, and compared to previous calculations.

Authors:

Yu, Hua-Gen ^[1]

Brookhaven National Lab. (BNL), Upton, NY (United States). Dept. of Chemistry

Publication Date:: Sun Dec 28 00:00:00 EST 2014

Research Org.:: Brookhaven National Lab. (BNL), Upton, NY (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1182481

Alternate Identifier(s):: OSTI ID: 1226656

Report Number(s):: BNL-107310-2014-JA
Journal ID: ISSN 0021-9606; JCPSA6; R&D Project: 04540; 04548; TRN: US1500504

Grant/Contract Number:: SC00112704

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Chemical Physics

Additional Journal Information:: Journal Volume: 141; Journal Issue: 24; Journal ID: ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)

Country of Publication:: United States

Language:: English

Subject:: 74 ATOMIC AND MOLECULAR PHYSICS; iterative diagonalization; complex symmetric matrix; spectral transform Lanczos

Citation Formats


                    Yu, Hua-Gen. A complex guided spectral transform Lanczos method for studying quantum resonance states.  United States: N. p., 2014. 
Web.  doi:10.1063/1.4905083.

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                    Yu, Hua-Gen. A complex guided spectral transform Lanczos method for studying quantum resonance states.  United States.  https://doi.org/10.1063/1.4905083

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                    Yu, Hua-Gen. Sun .  
"A complex guided spectral transform Lanczos method for studying quantum resonance states".  United States.  https://doi.org/10.1063/1.4905083.  https://www.osti.gov/servlets/purl/1182481.

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@article{osti_1182481,

  title        = {A complex guided spectral transform Lanczos method for studying quantum resonance states},

  author       = {Yu, Hua-Gen},

  abstractNote = {A complex guided spectral transform Lanczos (cGSTL) algorithm is proposed to compute both bound and resonance states including energies, widths and wavefunctions. The algorithm comprises of two layers of complex-symmetric Lanczos iterations. A short inner layer iteration produces a set of complex formally orthogonal Lanczos (cFOL) polynomials. They are used to span the guided spectral transform function determined by a retarded Green operator. An outer layer iteration is then carried out with the transform function to compute the eigen-pairs of the system. The guided spectral transform function is designed to have the same wavefunctions as the eigenstates of the original Hamiltonian in the spectral range of interest. Therefore the energies and/or widths of bound or resonance states can be easily computed with their wavefunctions or by using a root-searching method from the guided spectral transform surface. The new cGSTL algorithm is applied to bound and resonance states of HO₂, and compared to previous calculations.},

  doi          = {10.1063/1.4905083},

  journal      = {Journal of Chemical Physics},

  number       = 24,

  volume       = 141,

  place        = {United States},

  year         = {Sun Dec 28 00:00:00 EST 2014},

  month        = {Sun Dec 28 00:00:00 EST 2014}

}

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