On the imaginary part of coupling resonance points
We prove for rank one perturbations that the imaginary part of a coupling resonance point is inversely proportional by a factor of \(-2\) to the rate of change of the scattering phase, as a function of the coupling variable, evaluated at the real part of the resonance point. This equality is analogo...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2019-01-01
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| Series: | Opuscula Mathematica |
| Subjects: | |
| Online Access: | https://www.opuscula.agh.edu.pl/vol39/5/art/opuscula_math_3935.pdf |
| _version_ | 1818032748860801024 |
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| author | Nurulla Azamov Tom Daniels |
| author_facet | Nurulla Azamov Tom Daniels |
| author_sort | Nurulla Azamov |
| collection | DOAJ |
| description | We prove for rank one perturbations that the imaginary part of a coupling resonance point is inversely proportional by a factor of \(-2\) to the rate of change of the scattering phase, as a function of the coupling variable, evaluated at the real part of the resonance point. This equality is analogous to the Breit-Wigner formula from quantum scattering theory. For more general relatively trace class perturbations, we also give a formula for the spectral shift function in terms of coupling resonance points, non-real and real. |
| first_indexed | 2024-12-10T06:12:18Z |
| format | Article |
| id | doaj.art-663dff889b5842348e51ff217ca3c28a |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-12-10T06:12:18Z |
| publishDate | 2019-01-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-663dff889b5842348e51ff217ca3c28a2022-12-22T01:59:32ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742019-01-01395611621https://doi.org/10.7494/OpMath.2019.39.5.6113935On the imaginary part of coupling resonance pointsNurulla Azamov0https://orcid.org/0000-0002-5700-4980Tom Daniels1https://orcid.org/0000-0002-3930-9692Flinders University, College of Science and Engineering, South Rd, Tonsley, SA 5042 AustraliaFlinders University, College of Science and Engineering, South Rd, Tonsley, SA 5042 AustraliaWe prove for rank one perturbations that the imaginary part of a coupling resonance point is inversely proportional by a factor of \(-2\) to the rate of change of the scattering phase, as a function of the coupling variable, evaluated at the real part of the resonance point. This equality is analogous to the Breit-Wigner formula from quantum scattering theory. For more general relatively trace class perturbations, we also give a formula for the spectral shift function in terms of coupling resonance points, non-real and real.https://www.opuscula.agh.edu.pl/vol39/5/art/opuscula_math_3935.pdfscattering matrixscattering phaseresonance pointbreit-wigner formula |
| spellingShingle | Nurulla Azamov Tom Daniels On the imaginary part of coupling resonance points Opuscula Mathematica scattering matrix scattering phase resonance point breit-wigner formula |
| title | On the imaginary part of coupling resonance points |
| title_full | On the imaginary part of coupling resonance points |
| title_fullStr | On the imaginary part of coupling resonance points |
| title_full_unstemmed | On the imaginary part of coupling resonance points |
| title_short | On the imaginary part of coupling resonance points |
| title_sort | on the imaginary part of coupling resonance points |
| topic | scattering matrix scattering phase resonance point breit-wigner formula |
| url | https://www.opuscula.agh.edu.pl/vol39/5/art/opuscula_math_3935.pdf |
| work_keys_str_mv | AT nurullaazamov ontheimaginarypartofcouplingresonancepoints AT tomdaniels ontheimaginarypartofcouplingresonancepoints |