Quantum Painlevé-Calogero correspondence for Painlevé VI

A. Zabrodin, A. Zotov

Результат исследований: Вклад в журналСтатьярецензирование

23 Цитирования (Scopus)

Аннотация

This paper is a continuation of our previous paper where the Painlevé-Calogero correspondence has been extended to auxiliary linear problems associated with Painlevé equations. We have proved, for the first five equations from the Painlevé list, that one of the linear problems can be recast in the form of the non-stationary Schrödinger equation whose Hamiltonian is a natural quantization of the classical Calogero-like Hamiltonian for the corresponding Painlevé equation. In the present paper we establish the quantum Painlevé-Calogero correspondence for the most general case, the Painlevé VI equation. We also show how the desired special gauge and the needed choice of variables can be derived starting from the corresponding Schlesinger system with rational spectral parameter.

Язык оригиналаАнглийский
Номер статьи073508
ЖурналJournal of Mathematical Physics
Том53
Номер выпуска7
DOI
СостояниеОпубликовано - 12 июл. 2012
Опубликовано для внешнего пользованияДа

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