Comment on ``Enhancement of the Tunneling Density of States in Tomonaga-Luttinger Liquids''

In a recent Physical Review Letter, Oreg and Finkel'stein (OF) have calculated the electron density of states (DOS) for tunneling into a repulsive Luttinger liquid close to the location of an impurity. The result of their calculation is a DOS which is enhanced with respect to the pure system, and moreover diverging for not too strong repulsion. In this Comment we intend to show that OF's calculation suffers from a subtle flaw which, being corrected, results into a DOS not only vanishing at zero frequency but in fact suppressed in comparison with the DOS of a pure Luttinger liquid.Comment: 1 page, Revte

Statistical properties of localisation--delocalisation transition in one dimension

We study a one-dimensional model of disordered electrons (also relevant for random spin chains), which exhibits a delocalisation transition at half-filling. Exact probability distribution functions for the Wigner time and transmission coefficient are calculated. We identify and distinguish those features of probability densities that are due to rare, trapping configurations of the random potential from those which are due to the proximity to the delocalisation transition.Comment: 4 pages, RevTeX, 1 fi

Bose-glass, superfluid, and rung-Mott phases of hard-core bosons in disordered two-leg ladders

By means of Monte Carlo techniques, we study the role of disorder on a system of hard-core bosons in a two-leg ladder with both intra-chain ($t$) and inter-chain ($t^\prime$) hoppings. We find that the phase diagram as a function of the boson density, disorder strength, and $t^\prime/t$ is far from being trivial. This contrasts the case of spin-less fermions where standard localization arguments apply and an Anderson-localized phase pervades the whole phase diagram. A compressible Bose-glass phase always intrudes between the Mott insulator with zero (or one) bosons per site and the superfluid that is stabilized for weak disorder. At half filling, there is a direct transition between a (gapped) rung-Mott insulator and a Bose glass, which is driven by exponentially rare regions where disorder is suppressed. Finally, by doping the rung-Mott insulator, a direct transition to the superfluid is possible only in the clean system, whereas the Mott phase is always surrounded by the a Bose glass when disorder is present. The phase diagram based on our numerical evidence is finally reported.Comment: 8 pages, 7 figure

Near Infrared Spectroscopy of High Redshift Active Galactic Nuclei. II. Disappearing Narrow Line Regions and the Role of Accretion

We present new near infrared spectroscopic measurements for 29 luminous high-z quasars and use the data to discuss the size and other properties of the NLRs in those sources. The high resolution spectra have been used to carefully model the Fe II blends and to provide reliable [O III], Fe II and Hb measurements. We find that about 2/3 of all high luminosity sources show strong [O III] lines while the remaining objects show no or very weak such line. While weak [O III] emitters are also found among lower luminosity AGN, we argue that the implications for very high luminosity objects are different. In particular, we suggest that the averaging of these two populations in other works gave rise to claims of a Baldwin relationship in [O III] which is not confirmed by our data. We also argue that earlier proposed relations of the type R_NLR \propto L_[O III]^{1/2}, where R_NLR is the NLR radius, are theoretically sound yet they must break down for R_NLR exceeding a few kpc. This suggests that the NLR properties in luminous sources are different from those observed in nearby AGN. In particular, we suggest that some sources lost their very large, dynamically unbound NLR while others are in a phase of violent star-forming events that produce a large quantity of high density gas in the central kpc. This gas is ionized and excited by the central radiation source and its spectroscopic properties may be different from those observed in nearby, lower luminosity NLRs. We also discuss the dependence of EW(Hb) and Fe II/Hb on L, M_BH, and accretion rate for a large sample of AGNs. The strongest dependence of the two quantities is on the accretion rate and the Fe II/Hb correlation is probably due to the EW(Hb) dependence on accretion rate. We show the most extreme values measured so far of Fe II/Hb and address its correlation with EW([O III]).Comment: 10 pages (emulateapj), 9 figures. Accepted by Ap

Electron tunneling into a quantum wire in the Fabry-Perot regime

We study a gated quantum wire contacted to source and drain electrodes in the Fabry-Perot regime. The wire is also coupled to a third terminal (tip), and we allow for an asymmetry of the tip tunneling amplitudes of right and left moving electrons. We analyze configurations where the tip acts as an electron injector or as a voltage-probe, and show that the transport properties of this three-terminal set-up exhibit very rich physical behavior. For a non-interacting wire we find that a tip in the voltage-probe configuration affects the source-drain transport in different ways, namely by suppressing the conductance, by modulating the Fabry-Perot oscillations, and by reducing their visibility. The combined effect of electron electron interaction and finite length of the wire, accounted for by the inhomogeneous Luttinger liquid model, leads to significantly modified predictions as compared to models based on infinite wires. We show that when the tip injects electrons asymmetrically the charge fractionalization induced by interaction cannot be inferred from the asymmetry of the currents flowing in source and drain. Nevertheless interaction effects are visible as oscillations in the non-linear tip-source and tip-drain conductances. Important differences with respect to a two-terminal set-up emerge, suggesting new strategies for the experimental investigation of Luttinger liquid behavior.Comment: 27 pages, 10 figure

Interplay of Orbital Degeneracy and Superconductivity in a Molecular Conductor

We study electron propagation in a molecular lattice model. Each molecular site involves doubly degenerate electronic states coupled to doubly degenerate molecular vibration, leading to a so--called E-e type of Jahn-Teller Hamiltonian. For weak electron-phonon coupling and in the anti-adiabatic limit we find that the orbital degeneracy induces an intersite pairing mechanism which is absent in the standard non-degenerate polaronic model. In this limit we analyse the model in the presence of an additional on-site repulsion and we determine, within BCS mean field theory, the region of stability of superconductivity. In one dimension, where powerful analytical techniques are available, we are able to calculate the phase diagram of the model both for weak and for strong electron-phonon coupling.Comment: 11 pages, REVTEX style, 3 compressed figures adde

Phases of two coupled Luttinger liquids

A model of two interacting one--dimensional fermion systems (``Luttinger liquids'') coupled by single--particle hopping is investigated. Bosonization allows a number of exact statements to be made. In particular, for forward scattering only, the model contains two massless boson sectors and an Ising type critical sector. For general interactions, there is a spin excitation gap and either s-- or d--type pairing fluctuations dominate. It is shown that the same behavior is also found for strong interactions. A possible scenario for the crossover to a Fermi liquid in a many chain system is discussed.Comment: revised version, some changes, 11 pages, no figures, RexTeX3.

One-Particle Excitation of the Two-Dimensional Hubbard Model

The real part of the self-energy of interacting two-dimensional electrons has been calculated in the t-matrix approximation. It is shown that the forward scattering results in an anomalous term leading to the vanishing renormalization factor of the one-particle Green function, which is a non-perturbative effect of the interaction U. The present result is a microscopic demonstration of the claim by Anderson based on the conventional many-body theory. The effect of the damping of the interacting electrons, which has been ignored in reaching above conclusion, has been briefly discussed.Comment: 7 pages, LaTeX, 1 figure, uses jpsj.sty, to be published in J. Phys. Soc. Jpn. 66 No. 3 (1997