Spectral Equations for the Modular Oscillator

Rinat M. Kashaev, Sergey M. Sergeev

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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 languageEnglish
Article number1840009
Pages (from-to)1
Number of pages23
JournalReviews in Mathematical Physics
Issue number7
Publication statusPublished - 1 Aug 2018


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