Yangian Algebras and Classical Riemann Problems

We investigate different Hopf algebras associated to Yang's solution of quantum Yang-Baxter equation. It is shown that for the precise definition of the algebra one needs the commutation relations for the deformed algebra of formal currents and the specialization of the Riemann problem for the currents. Two different Riemann problems are considered. They lead to the central extended Yangian double associated with ${sl}_2$ and to the degeneration of scaling limit of elliptic affine algebra. Unless the defining relations for the generating functions of the both algebras coincide their properties and the theory of infinite-dimensional representations are quite different. We discuss also the Riemann problem for twisted algebras and for scaled elliptic algebra.Comment: 36 pages, 3 figures under bezier.sty, corrected some typo

Hydrodynamic fluctuations in relativistic superfluids

The Hamiltonian formulation of superfluids based on noncanonical Poisson brackets is studied in detail. The assumption that the momentum density is proportional to the flow of the conserved energy is shown to lead to the covariant relativistic theory previously suggested by Khalatnikov, Lebedev and Carter, and some potentials in this theory are given explicitly. We discuss hydrodynamic fluctuations in the presence of dissipative effects and we derive the corresponding set of hydrodynamic correlation functions. Kubo relations for the transport coefficients are obtained.Comment: 13 pages, no figures, two references adde

Simulation of Beam-Beam Effects and Tevatron Experience

Effects of electromagnetic interactions of colliding bunches in the Tevatron had a variety of manifestations in beam dynamics presenting vast opportunities for development of simulation models and tools. In this paper the computer code for simulation of weak-strong beam-beam effects in hadron colliders is described. We report the collider operational experience relevant to beam-beam interactions, explain major effects limiting the collider performance and compare results of observations and measurements with simulations.Comment: 23 pages, 17 figure