Single-Block Renormalization Group: Quantum Mechanical Problems

We reformulate the density matrix renormalization group method (DMRG) in terms of a single block, instead of the standard left and right blocks used in the construction of the superblock. This version of the DMRG, which we call the puncture renormalization group (PRG), makes easy and natural the extension of the DMRG to higher dimensional lattices. To test numerically this proposal, we study several quantum mechanical models in one, two and three dimensions. In 1D the performance of the standard DMRG is much better than its PRG version, however for 2D models the PRG is more efficient than the DMRG in a variety of circumstances. In 3D the PRG performs also quite well.Comment: RevTex4b4, 13 pages, two-column, 8 fig

The properties of the stellar populations in ULIRGs I: sample, data and spectral synthesis modelling

We present deep long-slit optical spectra for a sample of 36 Ultraluminous Infrared Galaxies (ULIRGs), taken with the William Herschel Telescope (WHT) on La Palma with the aim of investigating the star formation histories and testing evolutionary scenarios for such objects. Here we present the sample, the analysis techniques and a general overview of the properties of the stellar populations. Spectral synthesis modelling has been used in order to estimate the ages of the stellar populations found in the diffuse light sampled by the spectra in both the nuclear and extended regions of the target galaxies. We find that adequate fits can be obtained using combinations of young stellar populations (YSPs,t_YSP<=2 Gyr), with ages divided into two groups: very young stellar populations (VYSPs, t_VYSP <=100 Myr) and intermediate-young stellar populations (IYSPs, 0.1 < t_IYSP <= 2 Gyr). Our results show that YSPs are present at all locations of the galaxies covered by our slit positions, with the exception of the northern nuclear region of the ULIRG IRAS 23327+2913. Furthermore, VYSPs are presents in at least 85% of the 133 extraction apertures used for this study. Old stellar populations (OSPs, t_{OSP} > 2 Gyr) do not make a major contribution to the optical light in the majority of the apertures extracted. In fact they are essential for fitting the spectra in only 5% (7) of the extracted apertures. The estimated total masses for the YSPs (VYSPs+IYSPs) are in the range 0.18 x 10^{10} <= M_YSP <= 50 x 10^{10} Msun. We have also estimated the bolometric luminosities associated with the stellar populations detected at optical wavelengths, finding that they fall in the range 0.07 x 10^{12} < L_bol < 2.2 x 10^{12} Lsun. In addition, we find that reddening is significant at all locations in the galaxies.Comment: accepted for publication in MNRA

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

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

Starburst radio galaxies: general properties, evolutionary histories and triggering

In this paper we discuss the results of a programme of spectral synthesis modelling of a sample of starburst radio galaxies in the context of scenarios for the triggering of the activity and the evolution of the host galaxies. The starburst radio galaxies -- comprising ~15 - 25% of all powerful extragalactic radio sources -- frequently show disturbed morphologies at optical wavelengths, and unusual radio structures, although their stellar masses are typical of radio galaxies as a class. In terms of the characteristic ages of their young stellar populations (YSP), the objects can be divided into two groups: those with YSP ages t_ysp < 0.1 Gyr, in which the radio source has been triggered quasi-simultaneously with the main starburst episode, and those with older YSP in which the radio source has been triggered or re-triggered a significant period after the starburst episode. Combining the information on the YSP with that on the optical morphologies of the host galaxies, we deduce that the majority of the starburst radio galaxies have been triggered in galaxy mergers in which at least one of the galaxies is gas rich. However, the triggering (or re-triggering) of the radio jets can occur immediately before, around, or a significant period after the final coalescence of the merging nuclei, reflecting the complex gas infall histories of the merger events. Overall, our results provide further evidence that powerful radio jet activity can be triggered via a variety of mechanisms, including different evolutionary stages of major galaxy mergers; clearly radio-loud AGN activity is not solely associated with a particular stage of a unique type of gas accretion event.Comment: 16 pages, 3 Figures, accepted for publication in MNRA

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

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