r-matrices for relativistic deformations of integrable systems

We include the relativistic lattice KP hierarchy, introduced by Gibbons and Kupershmidt, into the $r$-matrix framework. An $r$-matrix account of the nonrelativistic lattice KP hierarchy is also provided for the reader's convenience. All relativistic constructions are regular one-parameter perturbations of the nonrelativistic ones. We derive in a simple way the linear Hamiltonian structure of the relativistic lattice KP, and find for the first time its quadratic Hamiltonian structure. Amasingly, the latter turns out to coincide with its nonrelativistic counterpart (a phenomenon, known previously only for the simplest case of the relativistic Toda lattice)

Direct photons in d+Au collisions at s_(NN)**(1/2)=200GeV with STAR

Results are presented of an ongoing analysis of direct photon production in s_(NN)=200GeV deuteron-gold collisions with the STAR experiment at RHIC. A significant excess of direct photons is observed near mid-rapidity 0<y<1 and found to be consistent with next-to-leading order pQCD calculations including the contribution from fragmentation photons.Comment: 4 pages, 4 figures, HotQuarks 200

Systems of Hess-Appel'rot type

We construct higher-dimensional generalizations of the classical Hess-Appel'rot rigid body system. We give a Lax pair with a spectral parameter leading to an algebro-geometric integration of this new class of systems, which is closely related to the integration of the Lagrange bitop performed by us recently and uses Mumford relation for theta divisors of double unramified coverings. Based on the basic properties satisfied by such a class of systems related to bi-Poisson structure, quasi-homogeneity, and conditions on the Kowalevski exponents, we suggest an axiomatic approach leading to what we call the "class of systems of Hess-Appel'rot type".Comment: 40 pages. Comm. Math. Phys. (to appear

Medium-modified DGLAP evolution of fragmentation functions from large to small x

The unified description of fragmentation function evolution from large to small x which was developed for the vacuum in previous publications is now generalized to the medium, and is studied for the case in which the complete contribution from the largest class of soft gluon logarithms, the double logarithms, are accounted for and with the fixed order part calculated to leading order. In this approach it proves possible to choose the remaining degrees of freedom related to the medium such that the distribution of produced hadrons is suppressed at large momenta while the production of soft radiation-induced charged hadrons at small momenta is enhanced, in agreement with experiment. Just as for the vacuum, our approach does not require further assumptions concerning fragmentation and is more complete than previous computations of evolution in the medium

Isospectral Flow and Liouville-Arnold Integration in Loop Algebras

A number of examples of Hamiltonian systems that are integrable by classical means are cast within the framework of isospectral flows in loop algebras. These include: the Neumann oscillator, the cubically nonlinear Schr\"odinger systems and the sine-Gordon equation. Each system has an associated invariant spectral curve and may be integrated via the Liouville-Arnold technique. The linearizing map is the Abel map to the associated Jacobi variety, which is deduced through separation of variables in hyperellipsoidal coordinates. More generally, a family of moment maps is derived, identifying certain finite dimensional symplectic manifolds with rational coadjoint orbits of loop algebras. Integrable Hamiltonians are obtained by restriction of elements of the ring of spectral invariants to the image of these moment maps. The isospectral property follows from the Adler-Kostant-Symes theorem, and gives rise to invariant spectral curves. {\it Spectral Darboux coordinates} are introduced on rational coadjoint orbits, generalizing the hyperellipsoidal coordinates to higher rank cases. Applying the Liouville-Arnold integration technique, the Liouville generating function is expressed in completely separated form as an abelian integral, implying the Abel map linearization in the general case.Comment: 42 pages, 2 Figures, 1 Table. Lectures presented at the VIIIth Scheveningen Conference, held at Wassenaar, the Netherlands, Aug. 16-21, 199

Universal Drinfeld-Sokolov Reduction and Matrices of Complex Size

We construct affinization of the algebra $gl_{\lambda}$ of ``complex size'' matrices, that contains the algebras $\hat{gl_n}$ for integral values of the parameter. The Drinfeld--Sokolov Hamiltonian reduction of the algebra $\hat{gl_{\lambda}}$ results in the quadratic Gelfand--Dickey structure on the Poisson--Lie group of all pseudodifferential operators of fractional order. This construction is extended to the simultaneous deformation of orthogonal and simplectic algebras that produces self-adjoint operators, and it has a counterpart for the Toda lattices with fractional number of particles.Comment: 29 pages, no figure

On algebraic models of dynamical systems

We describe a universal algebraic model which, being read appropriately, yields (periodic and infinite) discrete dynamical systems, as well as their ‘continuous limits’, which cover all differential scalar Lax systems. For this model we give: Two different constructions of an infinity of integrals; modified equations; deformations; infinitesimal automorphisms. The basic tools are supplied by symbolic calculus and the abstract Hamiltonian formalism.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43214/1/11005_2004_Article_BF00401731.pd

Space-time evolution of hadronization

Beside its intrinsic interest for the insights it can give into color confinement, knowledge of the space-time evolution of hadronization is very important for correctly interpreting jet-quenching data in heavy ion collisions and extracting the properties of the produced medium. On the experimental side, the cleanest environment to study the space-time evolution of hadronization is semi-inclusive Deeply Inelastic Scattering on nuclear targets. On the theoretical side, 2 frameworks are presently competing to explain the observed attenuation of hadron production: quark energy loss (with hadron formation outside the nucleus) and nuclear absorption (with hadronization starting inside the nucleus). I discuss recent observables and ideas which will help to distinguish these 2 mechanisms and to measure the time scales of the hadronization process.Comment: 6 pages, 4 figures. Based on talks given at "Hot Quarks 2006", Villasimius, Italy, May 15-20, 2006, and at the "XLIV internataional winter meeting on nuclear physics", Bormio, Italy, Jan 29 - Feb 5, 2006. To appear in Eur.Phys.J.

Unraveling the Mott-Peierls intrigue in vanadium dioxide

Vanadium dioxide is one of the most studied strongly correlated materials. Nonetheless, the intertwining between electronic correlation and lattice effects has precluded a comprehensive description of the rutile metal to monoclinic insulator transition, in turn triggering a longstanding "the chicken or the egg" debate about which comes first, the Mott localization or the Peierls distortion. Here, we suggest that this problem is in fact ill posed: The electronic correlations and the lattice vibrations conspire to stabilize the monoclinic insulator, and so they must be both considered to not miss relevant pieces of the VO2 physics. Specifically, we design a minimal model for VO2 that includes all the important physical ingredients: the electronic correlations, the multiorbital character, and the two components of the antiferrodistortive mode that condense in the monoclinic insulator. We solve this model by dynamical mean-field theory within the adiabatic Born-Oppenheimer approximation. Consistently with the first-order character of the metal-insulator transition, the Born-Oppenheimer potential has a rich landscape, with minima corresponding to the undistorted phase and to the four equivalent distorted ones, and which translates into an equally rich thermodynamics that we uncover by the Monte Carlo method. Remarkably, we find that a distorted metal phase intrudes between the low-temperature distorted insulator and high-temperature undistorted metal, which sheds new light on the debated experimental evidence of a monoclinic metallic phase

Ising spins coupled to a four-dimensional discrete Regge skeleton

Regge calculus is a powerful method to approximate a continuous manifold by a simplicial lattice, keeping the connectivities of the underlying lattice fixed and taking the edge lengths as degrees of freedom. The discrete Regge model employed in this work limits the choice of the link lengths to a finite number. To get more precise insight into the behavior of the four-dimensional discrete Regge model, we coupled spins to the fluctuating manifolds. We examined the phase transition of the spin system and the associated critical exponents. The results are obtained from finite-size scaling analyses of Monte Carlo simulations. We find consistency with the mean-field theory of the Ising model on a static four-dimensional lattice.Comment: 19 pages, 7 figure