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 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.
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01669800
Contributeur : Inspire Hep <>
Soumis le : jeudi 21 décembre 2017 - 00:55:51
Dernière modification le : mercredi 12 décembre 2018 - 07:11:45

Lien texte intégral

Identifiants

Citation

Jie Gu, Tin Sulejmanpasic. High order perturbation theory for difference equations and Borel summability of quantum mirror curves. JHEP, 2017, 12, pp.014. 〈10.1007/JHEP12(2017)014〉. 〈hal-01669800〉

Partager

Métriques

Consultations de la notice

64