Quantum Painleve-Calogero correspondence
- National Research University Higher School of Economics, 20 Myasnitskaya Ulitsa, Moscow 101000 (Russian Federation)
- ITEP, Bol. Cheremushkinskaya str. 25, 117259 Moscow (Russian Federation)
The Painleve-Calogero correspondence is extended to auxiliary linear problems associated with Painleve equations. The linear problems are represented in a new form which has a suggestive interpretation as a 'quantized' version of the Painleve-Calogero correspondence. Namely, the linear problem responsible for the time evolution is brought into the form of non-stationary Schroedinger equation in imaginary time, {partial_derivative}{sub t}{psi}=((1/2) {partial_derivative}{sub x}{sup 2}+V(x,t)){psi}, whose Hamiltonian is a natural quantization of the classical Calogero-like Hamiltonian H=(1/2) p{sup 2}+V(x,t) for the corresponding Painleve equation. In present paper, we present explicit constructions for the first five equations from the Painleve list.
- OSTI ID:
- 22093647
- Journal Information:
- Journal of Mathematical Physics, Vol. 53, Issue 7; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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