Előadó: Fehér László (Wigner FK, SZTE)
Az előadás témája: On the bi-Hamiltonian structure of spin Ruijsenaars-Schneider-Sutherland models
Az előadás időpontja: 2021. január 29., péntek, 14.00
Meeting ID: 960 4718 9540
Many classical integrable systems admit a bi-Hamiltonian formulation, which means that the equations of motion can be encoded using two different Poisson brackets and corresponding Hamiltonians. After recalling this notion, we present a bi-Hamiltonian structure for the finite dimensional dynamical systems derived by Braden and Hone in 1996 from the solitons of affine Toda field theory. These evolution equations have been related to the so called spin Ruijsenaars-Schneider model as well as to the hyperbolic spin Sutherland model that arises by reduction of free geodesic motion on a symmetric space.The integrable models just mentioned describe interacting point `particles' moving along a line and include also `spin' degrees of freedom akin to time dependent coupling parameters. The second half of the lecture is devoted to analogous models of particles moving on a circle. In this case a bi-Hamiltonian structure will be derived via reducing a bi-Hamiltonian structure associated with free geodesic motion on the unitary group U(n). The talk is based on the papers arXiv:1901.03558 and arXiv:1908.02467.