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Non-normal Lanczos methods for quantum scattering
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10.1063/1.2940733
/content/aip/journal/jcp/129/3/10.1063/1.2940733
http://aip.metastore.ingenta.com/content/aip/journal/jcp/129/3/10.1063/1.2940733

Figures

Image of FIG. 1.
FIG. 1.

State to state reaction probabilities for the collinear reaction below .

Image of FIG. 2.
FIG. 2.

Log plot of (a) the components of the intermediate solution of the decomposition of Eq. (13) and (b) the residual error vs size of Krylov subspace, for , 1.25, and for the collinear reaction.

Image of FIG. 3.
FIG. 3.

Log plot of the residual error (solid line) after 6500 block Lanczos iterations (for energies below ) for the collinear reaction. The dotted line corresponds to the last element of intermediate solution.

Image of FIG. 4.
FIG. 4.

Plot of the number Lanczos vectors (twice the number of block Lanczos iterations) required to converge the solution of the system of equations with a residual error of less than . The results are for 4000 energies below . The dots show those eigenvalues (real part) of the colllinear Hamiltonian that have also converged with a residual error less than .

Image of FIG. 5.
FIG. 5.

Diabatic and adiabatic potential energy curves for the nonadiabatic tunneling Hamiltonian.

Image of FIG. 6.
FIG. 6.

Log plot of the eigenvector of the Lanczos tridiagonal matrix corresponding to the lowest eigenvalue of the nonadiabatic tunneling quartic CAP Hamiltonian for (a) , (b) , (c) , and (d) . The dotted lines correspond to associated spurious Ritz values.

Image of FIG. 7.
FIG. 7.

Log plot of the eigenvector of the Arnoldi Hessenberg matrix corresponding to the lowest eigenvalue of the nonadiabatic tunneling CAP Hamiltonian with .

Image of FIG. 8.
FIG. 8.

Log plot of the eigenvector of the Lanczos tridiagonal matrix corresponding to the lowest eigenvalue of the nonadiabatic tunneling Woods–Saxon CAP Hamiltonian, .

Image of FIG. 9.
FIG. 9.

Log plot of the eigenvectors of the Lanczos tridiagonal matrix corresponding to (a) and (b) for the colllinear Hamiltonian. The dotted lines correspond to spurious Ritz values.

Image of FIG. 10.
FIG. 10.

Log plot of the eigenvector of the Arnoldi Hessenberg matrix corresponding to (a) and (b) for the colllinear Hamiltonian.

Image of FIG. 11.
FIG. 11.

Log plot of reflection (solid line) and transmission (dot line) probabilities for the nonadiabatic tunneling Hamiltonian. Thirteen reflection resonances are evident at which we have a reflection probability of 100%.

Image of FIG. 12.
FIG. 12.

Log plot of (a) the residual error for , 1.25, and and (b) the residual error after 20 000 block Lanczos iterations for the collinear reaction.

Tables

Generic image for table
Table I.

State to state reaction probabilities for the collinear reaction.

Generic image for table
Table II.

Condition number for the nonadiabatic tunneling Hamiltonian augmented with a quartic CAP for different CAP strengths.

Generic image for table
Table III.

Residual and relative errors for the lowest eigenvalues obtained by the Lanczos algorithm for the nonadiabatic tunneling quartic CAP Hamiltonian with different CAP strengths. The eigenvalues obtained by diagonalizing the Hamiltonian with IMSL are considered as exact. Only the real part of the eigenvalues and Ritz values are reported.

Generic image for table
Table IV.

Relative errors for the lowest eigenvalues obtained by the Arnoldi algorithm for the nonadiabatic tunneling quartic CAP Hamiltonian with different CAP strengths. The eigenvalues obtained by diagonalizing the Hamiltonian with IMSL are considered as exact. Only the real part of the eigenvalues and Ritz values are reported.

Generic image for table
Table V.

Relative errors for eigenvalues and obtained by the Arnoldi and Lanczos algorithms for the ClHCl system augmented with a Woods–Saxon CAP. The eigenvalues obtained by diagonalizing the Hamiltonian with IMSL are considered as exact. Only the real part of the eigenvalues and Ritz values are reported.

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/content/aip/journal/jcp/129/3/10.1063/1.2940733
2008-07-21
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Non-normal Lanczos methods for quantum scattering
http://aip.metastore.ingenta.com/content/aip/journal/jcp/129/3/10.1063/1.2940733
10.1063/1.2940733
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