Spectral Equations for the Modular Oscillator

Rinat M. Kashaev; Sergey M. Sergeev

doi:10.1142/S0129055X18400093

Spectral Equations for the Modular Oscillator

Rinat M. Kashaev, Sergey M. Sergeev

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Abstract

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 P1 × P1 and complex values of Planck's constant. We illustrate our analytical results by numerical calculations. In memory of Ludwig Faddeev.

Original language	English
Article number	1840009
Pages (from-to)	1-23
Number of pages	23
Journal	Reviews in Mathematical Physics
Volume	30
Issue number	7
DOIs	https://doi.org/10.1142/S0129055X18400093
Publication status	Published - 1 Aug 2018

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abstract = "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 P1 × P1 and complex values of Planck's constant. We illustrate our analytical results by numerical calculations. In memory of Ludwig Faddeev.",

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AU - Sergeev, Sergey M.

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N2 - 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 P1 × P1 and complex values of Planck's constant. We illustrate our analytical results by numerical calculations. In memory of Ludwig Faddeev.

AB - 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 P1 × P1 and complex values of Planck's constant. We illustrate our analytical results by numerical calculations. In memory of Ludwig Faddeev.

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JF - Reviews in Mathematical Physics

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Spectral Equations for the Modular Oscillator

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