Abstract:
this is an introductory course to the lanczos method and density matrix renormalization group algorithms (dmrg), two among the leading numerical techniques applied in studies of low-dimensional quantum models. the idea of studying the models on clusters of a finite size in order to extract their physical properties is briefly discussed. the important role played by the model symmetries is also examined. special emphasis is given to the dmrg.

Abstract:
This is an introductory course to the Lanczos Method and Density Matrix Renormalization Group Algorithms (DMRG), two among the leading numerical techniques applied in studies of low-dimensional quantum models. The idea of studying the models on clusters of a finite size in order to extract their physical properties is briefly discussed. The important role played by the model symmetries is also examined. Special emphasis is given to the DMRG.

Abstract:
Spin incommensurability has been recently experimentally discovered in the hole-doped Ni-oxide chain compound $\rm Y_{2-x}Ca_x Ba Ni O_5$ (G. Xu {\it al.}, Science {\bf 289}, 419 (2000)). Here a two orbital model for this material is studied using computational techniques. Spin IC is observed in a wide range of densities and couplings. The phenomenon originates in antiferromagnetic correlations ``across holes'' dynamically generated to improve hole movement, as it occurs in the one-dimensional Hubbard model and in recent studies of the two-dimensional extended t-J model. The close proximity of ferromagnetic and phase-separated states in parameter space are also discussed.

Abstract:
The main properties of realistic models for manganites are studied using analytic mean-field approximations and computational numerical methods, focusing on the two-orbital model with electrons interacting through Jahn-Teller (JT) phonons and/or Coulombic repulsions. Analyzing the model including both interactions by the combination of the mean-field approximation and the exact diagonalization method, it is argued that the spin-charge-orbital structure in the insulating phase of the purely JT-phononic model is not qualitatively changed by the inclusion of the Coulomb interactions. As an important application of the present mean-field approximation, the CE-type AFM state, the charge-stacked structure along the z-axis, and the (3x^2-r^2)/(3y^2-r^2)-type orbital ordering are successfully reproduced based on the JT-phononic model for the half-doped manganite. Topological arguments and the relevance of the Heisenberg exchange among localized t_{\rm 2g} spins explains why the nearest-neighbor Coulomb interaction does not destroy the charge stacking structure. It is also verified that the phase-separation tendency is observed both in purely JT-phononic and purely Coulombic models in the vicinity of the hole undoped region, as long as realistic hopping matrices are used. This highlights the qualitative similarities of both approaches, and the relevance of mixed-phase tendencies in the context of manganites. In addition, the rich and complex phase diagram of the two-orbital Coulombic model in one dimension is presented. Our results provide robust evidence that Coulombic and JT-phononic approaches to manganites are not qualitatively different ways to carry out theoretical calculations, but they share a variety of common features.

Abstract:
In the present paper we develop an algorithm to solve the time dependent Ginzburg-Landau (TDGL) equations, by using the link variables technique, for circular geometries. In addition, we evaluate the Helmholtz and Gibbs free energy, the magnetization, and the number of vortices. This algorithm is applied to a circular sector. We evaluate the superconduting-normal magnetic field transition, the magnetization, and the superconducting density. Furthermore, we study the nucleation of giant and multi-vortex states for that geometry.

Abstract:
Recent results on Dalitz analysis of three-pseudoscalar decays are discussed in the context of probing charm hadronic-decay mechanisms: the role of FSI effects, which create phase shifts between the interfering resonant channels, can be studied in the different decay modes and the annihilation contribution measured in the charm sector through the $D^+_s \to \pi^+\pi^-\pi^+$ decay.

Abstract:
Finite-Size-Scaling and Conformal Invariance are used in order to find the phase diagram and critical exponents of a quantum spin chain with spin $S=3/2$. The model has a tetracritical point besides critical lines. The conformal anomaly and anomalous dimensions of some primary operators are calculated at the tetracritical point.

Abstract:
A review of the charmed meson and baryon lifetimes is presented. Our knowledge of charmed particle lifetimes has greatly improved over the past two years, a crucial r\^ole having been played by the E687 experiment at Fermilab, which has almost quadrupled the samples of $D$ mesons. The lifetime ratios $\tau(D^+)/\tau(D^0)$ and $\tau(D_s^+)/\tau(D^0)$ are now known with an accuracy of 1.7\% and 3.7\% respectively. In the baryon sector the statistics is still limited, but the experimental results on $\Lambda_c^+$, $\Xi_c^0$ and $\Xi_c^+$ exhibit a clear pattern of lifetime hierarchy, as expected from simple theoretical arguments. The first measurement of $\tau(\Omega_c^0)$ from E687 is also presented to complete the charmed baryon lifetime picture. The more accurate experimental scenario can provide information on non-perturbative QCD effects and the hadronic matrix elements.

Abstract:
The potentiality of interpreting the D-meson decay-dynamics has revealed itself to be strongly dependent on our understanding of the light-meson sector. The statistics collected by FOCUS is already at a level that manifests parametrization problems for scalar particles. In this paper the first application of the K-matrix approach in the charm sector is illustrated and preliminary results on the D+ and Ds decays to three pions are shown.

Abstract:
Dalitz analysis is a powerful tool for physics studies within and beyond the Standard Model. In the last decade it has helped to investigate the Heavy Flavor hadronic decay dynamics and is now being applied to extract angles of the CKM Unitarity triangle. To perform such sophisticate analyses we need to model the strong interaction effects. The FOCUS experiment has performed pilot studies in the charm sector through the K-matrix formalism. What has been learnt from charm will be beneficial for future accurate beauty measurements. Experience and results from FOCUS are presented and discussed.