Two-pion exchange potential and the πN\pi N amplitude

We discuss the two-pion exchange potential which emerges from a box diagram with one nucleon (the spectator) restricted to its mass shell, and the other nucleon line replaced by a subtracted, covariant $\pi N$ scattering amplitude which includes $\Delta$, Roper, and $D_{13}$ isobars, as well as contact terms and off-shell (non-pole) dressed nucleon terms. The $\pi N$ amplitude satisfies chiral symmetry constraints and fits $\pi N$ data below $\sim$ 700 MeV pion energy. We find that this TPE potential can be well approximated by the exchange of an effective sigma and delta meson, with parameters close to the ones used in one-boson-exchange models that fit $NN$ data below the pion production threshold.Comment: 9 pages (RevTex) and 7 postscript figures, in one uuencoded gzipped tar fil

Interacting Fermion Systems from Two Dimensional QCD

We consider two dimensional U(N) QCD on the cylinder with a timelike Wilson line in an arbitrary representation. We show that the theory is equivalent to N fermions with internal degrees of freedom which interact among themselves with a generalized Sutherland-type interaction. By evaluating the expectation value of the Wilson line in the original theory we explicitly find the spectrum and degeneracies of these particle systems.Comment: 11 pages, UVA-93-11, CERN-TH-6994/9

Two-dimensional gauge theories of the symmetric group S(n) and branched n-coverings of Riemann surfaces in the large-n limit

Branched n-coverings of Riemann surfaces are described by a 2d lattice gauge theory of the symmetric group S(n) defined on a cell discretization of the surface. We study the theory in the large-n limit, and we find a rich phase diagram with first and second order transition lines. The various phases are characterized by different connectivity properties of the covering surface. We point out some interesting connections with the theory of random walks on group manifolds and with random graph theory.Comment: Talk presented at the "Light-cone physics: particles and strings", Trento, Italy, September 200

The stability of the spectator, Dirac, and Salpeter equations for mesons

Mesons are made of quark-antiquark pairs held together by the strong force. The one channel spectator, Dirac, and Salpeter equations can each be used to model this pairing. We look at cases where the relativistic kernel of these equations corresponds to a time-like vector exchange, a scalar exchange, or a linear combination of the two. Since the model used in this paper describes mesons which cannot decay physically, the equations must describe stable states. We find that this requirement is not always satisfied, and give a complete discussion of the conditions under which the various equations give unphysical, unstable solutions

Enhancement of kinetic energy fluctuations due to expansion

Global equilibrium fragmentation inside a freeze out constraining volume is a working hypothesis widely used in nuclear fragmentation statistical models. In the framework of classical Lennard Jones molecular dynamics, we study how the relaxation of the fixed volume constraint affects the posterior evolution of microscopic correlations, and how a non-confined fragmentation scenario is established. A study of the dynamical evolution of the relative kinetic energy fluctuations was also performed. We found that asymptotic measurements of such observable can be related to the number of decaying channels available to the system at fragmentation time.Comment: 6 pages, 4 figure

Emergence of hierarchical networks and polysynchronous behaviour in simple adaptive systems

We describe the dynamics of a simple adaptive network. The network architecture evolves to a number of disconnected components on which the dynamics is characterized by the possibility of differently synchronized nodes within the same network (polysynchronous states). These systems may have implications for the evolutionary emergence of polysynchrony and hierarchical networks in physical or biological systems modeled by adaptive networks.Comment: 4 pages, 4 figure

Matrix string states in pure 2d Yang Mills theories

We quantize pure 2d Yang-Mills theory on a torus in the gauge where the field strength is diagonal. Because of the topological obstructions to a global smooth diagonalization, we find string-like states in the spectrum similar to the ones introduced by various authors in Matrix string theory. We write explicitly the partition function, which generalizes the one already known in the literature, and we discuss the role of these states in preserving modular invariance. Some speculations are presented about the interpretation of 2d Yang-Mills theory as a Matrix string theory.Comment: Latex file of 38 pages plus 6 eps figures. A note and few references added, figures improve

Direct evaluation of the isotope effect within the framework of density functional theory for superconductors

Within recent developments of density functional theory, its numerical implementation and of the superconducting density functional theory is nowadays possible to predict the superconducting critical temperature, Tc, with sufficient accuracy to anticipate the experimental verification. In this paper we present an analytical derivation of the isotope coefficient within the superconducting density functional theory. We calculate the partial derivative of Tc with respect to atomic masses. We verified the final expression by means of numerical calculations of isotope coefficient in monatomic superconductors (Pb) as well as polyatomic superconductors (CaC6). The results confirm the validity of the analytical derivation with respect to the finite difference methods, with considerable improvement in terms of computational time and calculation accuracy. Once the critical temperature is calculated (at the reference mass(es)), various isotope exponents can be simply obtained in the same run. In addition, we provide the expression of interesting quantities like partial derivatives of the deformation potential, phonon frequencies and eigenvectors with respect to atomic masses, which can be useful for other derivations and applications

The four-fermion interaction in D=2,3,4: a nonperturbative treatment

A new nonperturbative approach is used to investigate the Gross-Neveu model of four fermion interaction in the space-time dimensions 2, 3 and 4, the number $N$ of inner degrees of freedom being a fixed integer. The spontaneous symmetry breaking is shown to exist in $D=2,3$ and the running coupling constant is calculated. The four dimensional theory seems to be trivial.Comment: a minor correction: one more acknowledgement is added. Latex 2.09 file, 15 pages, no figures, accepted for publication to Int.J.Mod.Phys.