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Non-Perturbative Quantum Mechanics from Non-Perturbative Strings

Schiappa, Ricardo
Submitted to Journal of High Energy Physics. 2017
Description 55
Abstract This work develops a new method to calculate non-perturbative corrections in one-dimensional Quantum Mechanics, based on trans-series solutions to the refined holomorphic anomaly equations of topological string theory. The method can be applied to traditional spectral problems governed by the Schr"odinger equation, where it both reproduces and extends the results of well-established approaches, such as the exact WKB method. It can be also applied to spectral problems based on the quantization of mirror curves, where it leads to new results on the trans-series structure of the spectrum. Various examples are discussed, including the modified Mathieu equation, the double-well potential, and the quantum mirror curves of local P2 and local F0. In all these examples, it is verified in detail that the trans-series obtained with this new method correctly predict the large-order behavior of the corresponding perturbative sectors.
Keywords Quantum MechanicsTopological StringsWKBQuantizationHolomorphic AnomalyNonperturbative
arXiv: 1712.02603
Note 55 pages, 9 figures
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Article (1.6 MB) - public document Free access
Research group Physique mathématique
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CODESIDO SANCHEZ, Santiago, MARINO BEIRAS, Marcos, SCHIAPPA, Ricardo. Non-Perturbative Quantum Mechanics from Non-Perturbative Strings. Submitted to: Journal of High Energy Physics, 2017. https://archive-ouverte.unige.ch/unige:101100

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Deposited on : 2018-01-03

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