This paper presents an approach to the Hamiltonian structure of isomonodromic systems of matrix ODE’s on a torus from their spectral curve. An isomonodromic analogue of the so called SU(2) Calogero-Gaudin system is used for a case study of this approach. A clue of this approach is a mapping from the Lax equation to a dynamical system of a finite number of points on the spectral curve. The coord...

In the article arXiv:0903.5277 [quant-ph], we have presented a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential V (x) = αx−2. In such a way, we have described all possible s.a. operators (s.a. Hamiltonians) associated with the formal differential expression Ȟ = −dx + αx−2 for the Calogero Hamiltonian. Here, we discuss a new...

We show that the construction of super-Calogero model with OSp(2|2) supersymmetry is not unique. In particular, we find a new co-ordinate representation of the generators of the OSp(2|2) superalgebra that appears as the dynamical supersymmetry of the rational super-Calogero model. Both the quadratic and the cubic Casimir operators of the OSp(2|2) are necessarily zero in this new representation,...

We consider the isomonodromic formulation of Calogero-Painlev\'e multi-particle systems and proceed to their canonical quantization. then quantum Hamiltonian reduction on a special representation radial variables, in analogy with classical case also theory Calogero equations. This quantized version is compared generalization result Nagoya integral representations certain solutions Painlev\'e pr...

This is the second part of a series of papers dealing with an extensive class of analytic difference operators admitting reflectionless eigenfunctions. In the first part, the pertinent difference operators and their reflectionless eigenfunctions are constructed from given “spectral data”, in analogy with the IST for reflectionless Schrödinger and Jacobi operators. In the present paper, we intro...