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Spectral Equations for the Modular Oscillator

Kashaev, M, Rinat; Sergeev, Sergey


Motivated by applications for non-perturbative topological strings in toric Calabi– Yau manifolds, we discuss the spectral problem for a pair of commuting modular conjugate (in the sense of Faddeev) Harper type operators, corresponding to a special case of the quantized mirror curve of local P 1 × P 1 and complex values of Planck’s constant. We illustrate our analytical results by numerical calculations.

CollectionsANU Research Publications
Date published: 2018
Type: Journal article
Source: Reviews in Mathematical Physics
DOI: 10.1142/S0129055X18400093


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