Optimal Control Realizations of Lagrangian Systems with Symmetry

A new relation among a class of optimal control systems and Lagrangian systems with symmetry is discussed. It will be shown that a family of solutions of optimal control systems whose control equation are obtained by means of a group action are in correspondence with the solutions of a mechanical Lagrangian system with symmetry. This result also explains the equivalence of the class of Lagrangian systems with symmetry and optimal control problems discussed in \cite{Bl98}, \cite{Bl00}. The explicit realization of this correspondence is obtained by a judicious use of Clebsch variables and Lin constraints, a technique originally developed to provide simple realizations of Lagrangian systems with symmetry. It is noteworthy to point out that this correspondence exchanges the role of state and control variables for control systems with the configuration and Clebsch variables for the corresponding Lagrangian system. These results are illustrated with various simple applications

Universality Classes of Diagonal Quantum Spin Ladders

We find the classification of diagonal spin ladders depending on a characteristic integer $N_p$ in terms of ferrimagnetic, gapped and critical phases. We use the finite algorithm DMRG, non-linear sigma model and bosonization techniques to prove our results. We find stoichiometric contents in cuprate $CuO_2$ planes that allow for the existence of weakly interacting diagonal ladders.Comment: REVTEX4 file, 3 color figures, 1 tabl

Resonant Raman scattering off neutral quantum dots

Resonant inelastic (Raman) light scattering off neutral GaAs quantum dots which contain a mean number, N=42, of electron-hole pairs is computed. We find Raman amplitudes corresponding to strongly collective final states (charge-density excitations) of similar magnitude as the amplitudes related to weakly collective or single-particle excitations. As a function of the incident laser frequency or the magnetic field, they are rapidly varying amplitudes. It is argued that strong Raman peaks should come out in the spin-density channels, not related to valence-band mixing effects in the intermediate states.Comment: Accepted in Physical Review

Stripe Ansatzs from Exactly Solved Models

Using the Boltzmann weights of classical Statistical Mechanics vertex models we define a new class of Tensor Product Ansatzs for 2D quantum lattice systems, characterized by a strong anisotropy, which gives rise to stripe like structures. In the case of the six vertex model we compute exactly, in the thermodynamic limit, the norm of the ansatz and other observables. Employing this ansatz we study the phase diagram of a Hamiltonian given by the sum of XXZ Hamiltonians along the legs coupled by an Ising term. Finally, we suggest a connection between the six and eight-vertex Anisotropic Tensor Product Ansatzs, and their associated Hamiltonians, with the smectic stripe phases recently discussed in the literature.Comment: REVTEX4.b4 file, 10 pages, 2 ps Figures. Revised version to appear in PR

Unveiling the Active Nucleus of Centaurus A

We report new HST WFPC2 and NICMOS observations of the center of the nearest radio galaxy Centaurus A (NGC 5128) and discuss their implications for our understanding of the active nucleus and jet. We detect the active nucleus in the near-IR (K and H) and, for the first time, in the optical (I and V), deriving the spectral energy distribution of the nucleus from the radio to X-rays. The optical and part of the near-IR emission can be explained by the extrapolation of the X-ray power law reddened by A_V~14mag, a value consistent with other independent estimates. The 20pc-scale nuclear disk discovered by Schreier et al. (1998) is detected in the [FeII] 1.64mic line and presents a morphology similar to that observed in Pa alpha with a [FeII]/Pa alpha ratio typical of low ionization Seyfert galaxies and LINERs. NICMOS 3 Pa alpha observations in a 50"x50" circumnuclear region suggest enhanced star formation (~0.3Msun/yr) at the edges of the putative bar seen with ISO, perhaps due to shocks driven into the gas. The light profile, reconstructed from V, H and K observations, shows that Centaurus A has a core profile with a resolved break at ~4" and suggests a black--hole mass of ~10^9 Msun. A linear blue structure aligned with the radio/X-ray jet may indicate a channel of relatively low reddening in which dust has been swept away by the jet.Comment: 19 pages, 13 figures, Astrophysical Journal, in press. High quality figures available at http://www.arcetri.astro.it/~marconi/colpic.htm