BWDifference
swMATH ID:  23722 
Software Authors:  Gu, Jie; Sulejmanpasic, Tin 
Description:  High order perturbation theory for difference equations and Borel summability of quantum mirror curves. We adapt the BenderWu 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 exponentialpolynomial 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 CalabiYau 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. 
Homepage:  https://link.springer.com/article/10.1007%2FJHEP12%282017%29014 
Dependencies:  Mathematica; BenderWu 
Keywords:  nonperturbative effects; resummation; CalabiYau threefold; BenderWu algorithm; solitons monopoles and instantons; topological strings 
Related Software:  BenderWu; Mathematica 
Referenced in:  5 Publications 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

High order perturbation theory for difference equations and Borel summability of quantum mirror curves. Zbl 1383.81267 Gu, Jie; Sulejmanpasic, Tin 
2017

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top 5
Referenced by 10 Authors
3  Mariño, Marcos 
2  Gu, Jie 
2  Sulejmanpasic, tin 
1  Codesido, Santiago 
1  Duan, Zhihao 
1  Emery, Yoan 
1  Hatsuda, Yasuyuki 
1  Ronzani, Massimiliano 
1  Schiappa, Ricardo 
1  Zakany, Szabolcs 
Referenced in 2 Serials
4  Journal of High Energy Physics 
1  Annales Henri Poincaré 
Referenced in 5 Fields
5  Quantum theory (81XX) 
5  Relativity and gravitational theory (83XX) 
2  Algebraic geometry (14XX) 
2  Partial differential equations (35XX) 
1  Several complex variables and analytic spaces (32XX) 