Numerical Continuation of Resonances and Bound States in Coupled Channel Schrödinger Equations

Klosiewicz, Przemyslaw; Broeckhove, J.; Vanroose, Wim

doi:10.4208/cicp.121209.050111s

Cited by 1 publication

(2 citation statements)

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“…In [19] it is shown that this procedure does not introduce false solutions, that is, the zeros of F are precisely the poles of S, and that it eliminates any singularities at k = 0. This is an extension of a similar result for the one-dimensional, singlechannel systems case [17,21].…”

Section: A the Case Of N Channels Equal Thresholdsmentioning

confidence: 99%

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Numerical continuation of bound and resonant states of the two-channel Schrödinger equation

2012

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Resonant solutions of the quantum Schrödinger equation occur at complex energies where the S matrix becomes singular. Knowledge of such resonances is important in the study of the underlying physical system. Often the Schrödinger equation depends on some parameter and one is interested in following the path of the resonances in the complex energy plane as the parameter changes. This is particularly true in coupled-channel systems where the resonant behavior is highly influenced by the strength of the channel coupling, the energy separation of the channels, and other factors. In previous work it was shown that numerical continuation, a technique familiar in the study of dynamical systems, can be brought to bear on the problem of following the resonance path in one-dimensional problems [J. Broeckhove, P. Klosiewicz, and W. Vanroose, J. Comput. Appl. Math. 234, 1238 (2010).] and multichannel problems without energy separation between the channels [P. Kłosiewicz, J. Broeckhove, and W. Vanroose, Commun. Comput. Phys.11, 435 (2012).]. A regularization can be defined that eliminates coalescing poles and zeros that appear in the S matrix at the origin due to symmetries. Following the zeros of this regularized function then traces the resonance path. In this work we show that this approach can be extended to channels with energy separation, albeit limited to two channels. The issue here is that the energy separation introduces branch cuts in the complex energy domain that need to be eliminated with a so-called uniformization. We demonstrate that the resulting approach is suitable for investigating resonances in two-channel systems and provide an extensive example.

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Section: A the Case Of N Channels Equal Thresholdsmentioning

confidence: 99%

“…In [19] the method has been extended to many-channel problems where all channels have the same asymptotic energy threshold. Applications have demonstrated the viability of the approach in tracing the parameter dependence of the resonance in the system.…”

Section: Introductionmentioning

confidence: 99%