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pro vyhledávání: '"Olshanetsky, M. A."'
Autor:
Olshanetsky, M.
We define the families of Kuramoto models (KM) related to bounded symmetric domains. The families include the Lohe unitary model and the spherical models as special cases. Our approach is based on the construction proposed by Watanabe and Strogats WS
Externí odkaz:
http://arxiv.org/abs/2411.06829
In this short review we compare constructions of 2d integrable models by means of two gauge field theories. The first one is the 4d Chern-Simons (4d-CS) theory proposed by Costello and Yamazaki. The second one is the 2d generalization of the Hitchin
Externí odkaz:
http://arxiv.org/abs/2202.10106
Autor:
Olshanetsky, M.
In this article we consider two particular examples of general construction proposed in arXiv:2012.15529. We consider the integrable extensions of the classical elliptic Calogero-Moser model of N particles with spin and the integrable Euler-Arnold to
Externí odkaz:
http://arxiv.org/abs/2103.10099
Publikováno v:
J. Phys. A: Math. Theor. 53 (2020) 185202
We study a general ansatz for an odd supersymmetric version of the Kronecker elliptic function, which satisfies the genus one Fay identity. The obtained result is used for construction of the odd supersymmetric analogue for the classical and quantum
Externí odkaz:
http://arxiv.org/abs/1910.05712
Publikováno v:
Journal of Mathematical Physics 61 (2020) 103504
We introduce an odd supersymmetric version of the Kronecker elliptic function. It satisfies the genus one Fay identity and supersymmetric version of the heat equation. As an application we construct an odd supersymmetric extensions of the elliptic $R
Externí odkaz:
http://arxiv.org/abs/1910.01814
Publikováno v:
Journal of Mathematical Physics, 59:10 (2018), 103509
We define the quasi-compact Higgs $G^{\mathbb C}$-bundles over singular curves introduced in our previous paper for the Lie group SL($N$). The quasi-compact structure means that the automorphism groups of the bundles are reduced to the maximal compac
Externí odkaz:
http://arxiv.org/abs/1712.08851
Publikováno v:
JETP Letters, Vol. 106, No. 3 (2017) 179-183
We consider the classical Calogero-Sutherland system with two types of interacting spin variables. It can be reduced to the standard Calogero-Sutherland system, when one of the spin variables vanishes. We describe the model in the Hitchin approach an
Externí odkaz:
http://arxiv.org/abs/1706.08793
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Publikováno v:
J. Phys. A: Math. Theor. 49:39 (2016) 395202
In this paper we suggest generalizations of elliptic integrable tops to matrix-valued variables. Our consideration is based on $R$-matrix description which provides Lax pairs in terms of quantum and classical $R$-matrices. First, we prove that for re
Externí odkaz:
http://arxiv.org/abs/1603.06101
Publikováno v:
Theoret. and Math. Phys. 188:2 (2016) 1121-1154
We construct twisted Calogero-Moser (CM) systems with spins as the Hitchin systems derived from the Higgs bundles over elliptic curves, where transitions operators are defined by an arbitrary finite order automorphisms of the underlying Lie algebras.
Externí odkaz:
http://arxiv.org/abs/1507.04265