High order perturbation theory for difference equations and Borel summability of quantum mirror curves. We adapt the Bender-Wu algorithm C. M. Bender and T. T. Wu, “Anharmonic oscillator. 2: A study of perturbation theory in large order” in [Phys. Rev. D 7, 1620–1636 (1973; doi:1103/PhysRevD.7.1620)] 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.
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References in zbMATH (referenced in 5 articles , 1 standard article )
Showing results 1 to 5 of 5.
- Emery, Yoan; Mariño, Marcos; Ronzani, Massimiliano: Resonances and PT symmetry in quantum curves (2020)
- Codesido, Santiago; Mariño, Marcos; Schiappa, Ricardo: Non-perturbative quantum mechanics from non-perturbative strings (2019)
- Duan, Zhihao; Gu, Jie; Hatsuda, Yasuyuki; Sulejmanpasic, Tin: Instantons in the Hofstadter butterfly: difference equation, resurgence and quantum mirror curves (2019)
- Mariño, Marcos; Zakany, Szabolcs: Quantum curves as quantum distributions (2019)
- Gu, Jie; Sulejmanpasic, Tin: High order perturbation theory for difference equations and Borel summability of quantum mirror curves (2017)