H. Nagoya, B. Grammaticos, A. Ramani, “Quantum Painlevé Equations: from Continuous to Discrete and Back”, Regul. Chaotic Dyn., 2008, Volume 13, Issue 5,Pages <nobr>417

This article is cited in 4 papers

Nonholonomic mechanics

Quantum Painlevé Equations: from Continuous to Discrete and Back

H. Nagoya^a, B. Grammaticos^b, A. Ramani^c

^a Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, 153-8914 Tokyo, Japan
^b IMNC, Université Paris VII & XI, CNRS, UMR 8165, Bât. 104, 91406 Orsay, France
^c Centre de Physique Théorique, Ecole Polytechnique, CNRS, 91128 Palaiseau, France

Abstract: We present a cascade of quantum Painlevé equations consisting in successive contiguity relations, whereupon starting form a continuous equations we obtain a discrete one, and continuous limits of the latter. We start from the quantum Painlevé V and in the process derive the quantum form of continuous PIII which was missing in previous studies.

Keywords: discrete systems, quantization, Painlev$\acute{e}$ equations.

MSC: 34M55, 37K55, 81S99

Received: 02.05.2008
Accepted: 10.07.2008

Language: English

DOI: 10.1134/S1560354708050031