2017/12/07 by Santiago Codesido, Codesido, Santiago, Marcos Marino +3 · 2 citations
Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.1712.02603
56 pages, 9 figures
arxiv created 2018/10/12 · arxiv updated 2018/10/15
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 Schrödinger 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 \mathbbF0. 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.