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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6 Citations (Scopus)

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
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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title = "Spectral Equations for the Modular Oscillator",

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 - Kashaev, Rinat M.

AU - Sergeev, Sergey M.

PY - 2018/8/1

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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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DO - 10.1142/S0129055X18400093

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VL - 30

JO - Reviews in Mathematical Physics

JF - Reviews in Mathematical Physics

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ER -

Spectral Equations for the Modular Oscillator

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