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Open Quantum Systems Decoherence
Quantum Simulation
High order perturbation theory for difference equations and Borel summability of quantum mirror curves
arXiv
Authors: Jie Gu, Tin Sulejmanpasic
Year
2017
Paper ID
7684
Status
Preprint
Abstract Read
~2 min
Abstract Words
85
Citations
N/A
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.
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- We adapt the Bender-Wu algorithm to solve perturbatively but very efficiently the eigenvalue problem of "relativistic" quantum mechanical problems whose Hamiltonians are...
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