High order perturbation theory for difference equations and Borel summability of quantum mirror curves
Abstract We adapt the Bender-Wu algorithm to solve perturbatively but very efficiently the eigenvalue problem of "relativistic" quantum mechanical problems whose Hamiltonians are difference operators of the exponential-polynomial type. We implement the algorithm in the function BWDifferenc...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-12-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP12(2017)014 |
| _version_ | 1828859605489287168 |
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| author | Jie Gu Tin Sulejmanpasic |
| author_facet | Jie Gu Tin Sulejmanpasic |
| author_sort | Jie Gu |
| collection | DOAJ |
| description | Abstract We adapt the Bender-Wu algorithm to solve perturbatively but very efficiently the eigenvalue problem of "relativistic" quantum mechanical problems whose Hamiltonians are difference operators of the exponential-polynomial type. We implement the algorithm in the function BWDifference in the updated Mathematica package BenderWu. With the help of BWDifference, we survey quantum mirror curves of toric fano Calabi-Yau threefolds, and find strong evidence that not only are the perturbative eigenenergies of the associated 1d quantum mechanical problems Borel summable, but also that the Borel sums are exact. |
| first_indexed | 2024-12-13T02:23:09Z |
| format | Article |
| id | doaj.art-91d82e137f4c4986b9ca822476dc6eb7 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-13T02:23:09Z |
| publishDate | 2017-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-91d82e137f4c4986b9ca822476dc6eb72022-12-22T00:02:44ZengSpringerOpenJournal of High Energy Physics1029-84792017-12-0120171213610.1007/JHEP12(2017)014High order perturbation theory for difference equations and Borel summability of quantum mirror curvesJie Gu0Tin Sulejmanpasic1Laboratoire de Physique Théorique, Ecole Normale Supérieure & PSL Research UniversityInstitut de Physique Théorique Philippe Meyer, Ecole Normale Supérieure & PSL Research UniversityAbstract We adapt the Bender-Wu algorithm to solve perturbatively but very efficiently the eigenvalue problem of "relativistic" quantum mechanical problems whose Hamiltonians are difference operators of the exponential-polynomial type. We implement the algorithm in the function BWDifference in the updated Mathematica package BenderWu. With the help of BWDifference, we survey quantum mirror curves of toric fano Calabi-Yau threefolds, and find strong evidence that not only are the perturbative eigenenergies of the associated 1d quantum mechanical problems Borel summable, but also that the Borel sums are exact.http://link.springer.com/article/10.1007/JHEP12(2017)014Nonperturbative EffectsResummationSolitons Monopoles and InstantonsTopological Strings |
| spellingShingle | Jie Gu Tin Sulejmanpasic High order perturbation theory for difference equations and Borel summability of quantum mirror curves Journal of High Energy Physics Nonperturbative Effects Resummation Solitons Monopoles and Instantons Topological Strings |
| title | High order perturbation theory for difference equations and Borel summability of quantum mirror curves |
| title_full | High order perturbation theory for difference equations and Borel summability of quantum mirror curves |
| title_fullStr | High order perturbation theory for difference equations and Borel summability of quantum mirror curves |
| title_full_unstemmed | High order perturbation theory for difference equations and Borel summability of quantum mirror curves |
| title_short | High order perturbation theory for difference equations and Borel summability of quantum mirror curves |
| title_sort | high order perturbation theory for difference equations and borel summability of quantum mirror curves |
| topic | Nonperturbative Effects Resummation Solitons Monopoles and Instantons Topological Strings |
| url | http://link.springer.com/article/10.1007/JHEP12(2017)014 |
| work_keys_str_mv | AT jiegu highorderperturbationtheoryfordifferenceequationsandborelsummabilityofquantummirrorcurves AT tinsulejmanpasic highorderperturbationtheoryfordifferenceequationsandborelsummabilityofquantummirrorcurves |