Binding Energy in Two and Three-Body Relativistic Dynamics

Two-body and three-body systems of scalar bosons are considered in the framework of covariant constraint dynamics. The reduced equation obtained after eliminating redundant degrees of freedom can be viewed as an eigenvalue equation for an observable which is intimately related with the relative motion. We display the connection of this observable with binding energy.Comment: 12 pages, LaTeX. Talk presented at the Workshop "Critical Stability of Few-Body Quantum Systems", Les Houches Oct. 8-12, 200

Covariant Model for Relativistic Three-Body Systems

The system is described by three mass-shell constraints. After a nonlinear transformation of the momenta, the analytic form taken by admissible interactions (allowing compatibility) is characterized in terms of the new variables. These variables mix two-body clusters, which results in automatically incorporating three-body forces. Two superfluous degrees of freedom are eliminated, which yields a reduced equation for a wave function depending on three-dimensional arguments. When at least two masses are equal, this picture has a reasonable nonrelativistic limit. At first post-Galilean order and provided the interaction is not too much energy-dependent, the relativistic correction is tractable like a conventional perturbation problem. A covariant version of harmonic oscillator is given as a toy model.Comment: Latex without style files: 5 pages. Talk given at "Quark Confinement and the Hadron Spectrum VI", Villasimius, Cagliari, Sardinia, Italy. 21-25 September 200

Urn model of separation of sand

We introduce an urn model which describes spatial separation of sand. In this dynamical model, in a certain range of parameters spontaneous symmetry breaking takes place and equipartitioning of sand into two compartments is broken. The steady-state equation for an order parameter, a critical line, and the tricritical point on the phase diagram are found exactly. Master equation and the first-passage problem for the model are solved numerically and the results are used to locate first-order transitions. Exponential divergence of a certain characteristic time shows that the model can also exhibit very strong metastability. In certain cases characteristic time diverges as N^{z}, where N is the number of balls and z=1/2 (critical line), 2/3 (tricritical point), or 1/3 (limits of stability).Comment: 10 pages, eps figures include

A Simplification of Combinatorial Link Floer Homology

We define a new combinatorial complex computing the hat version of link Floer homology over Z/2Z, which turns out to be significantly smaller than the Manolescu-Ozsvath-Sarkar one.Comment: 20 pages with figures, final version printed in JKTR, v.3 of Oberwolfach Proceeding