Do the low PN velocity dispersions around elliptical galaxies imply that these lack dark matter?

While kinematical modelling of the low PN velocity dispersions observed in the outer regions of elliptical galaxies suggest a lack of dark matter around these galaxies, we report on an analysis of a suite of $N$-body simulations (with gas) of major mergers of spiral galaxies embedded in dark matter halos, and find that the outer velocity dispersions are as low as observed for the PNe. The inconsistency between our dynamical modelling and previous kinematical modelling is caused by very radial stellar orbits and projection effects when viewing face-on oblate ellipticals. Our simulations (weakly) suggest the youth of PNe around ellipticals, and we propose that the universality of the PN luminosity function may be explained if the bright PNe in ellipticals are formed after the regular accretion of very low mass gas-rich galaxies.Comment: Contributed talk at meeting, "Planetary Nebulae as astronomical tools", Gdansk, Poland, June-July 2005, ed. R. Szczerba, G. Stasi\'nska, and S. K. G\'orny, AIP Conference Proceedings, Melville, New York, 2005. 4 or 5 pages, 6 figure

Quantum transmission in disordered insulators: random matrix theory and transverse localization

We consider quantum interferences of classically allowed or forbidden electronic trajectories in disordered dielectrics. Without assuming a directed path approximation, we represent a strongly disordered elastic scatterer by its transmission matrix ${\bf t}$. We recall how the eigenvalue distribution of ${\bf t.t}^{\dagger}$ can be obtained from a certain ansatz leading to a Coulomb gas analogy at a temperature $\beta^{-1}$ which depends on the system symmetries. We recall the consequences of this random matrix theory for quasi--$1d$ insulators and we extend our study to microscopic three dimensional models in the presence of transverse localization. For cubes of size $L$, we find two regimes for the spectra of ${\bf t.t}^{\dagger}$ as a function of the localization length $\xi$. For $L / \xi \approx 1 - 5$, the eigenvalue spacing distribution remains close to the Wigner surmise (eigenvalue repulsion). The usual orthogonal--unitary cross--over is observed for {\it large} magnetic field change $\Delta B \approx \Phi_0 /\xi^2$ where $\Phi_0$ denotes the flux quantum. This field reduces the conductance fluctuations and the average log--conductance (increase of $\xi$) and induces on a given sample large magneto--conductance fluctuations of typical magnitude similar to the sample to sample fluctuations (ergodic behaviour). When $\xi$ is of the order of theComment: Saclay-S93/025 Email: [email protected]

Localization in a quantum spin Hall system

Localization problem of electronic states in a two-dimensional quantum spin Hall system (QSH - a symplectic model with a non-trivial topological structure) is studied by the transfer matrix method. The phase diagram in the plane of energy and disorder strength is exposed, and demonstrates "levitation" and "pair-annihilation" of the domains of extended states analogous to that of the integer quantum Hall system. The critical exponent $\nu$ for the divergence of the localization length is estimated as $\nu \cong 1.6$ which is distinct from both exponents pertaining to the conventional symplectic and the unitary quantum Hall systems. This strongly suggests a different universality class related to the non-trivial topology of the QSH system.Comment: 5 pages, 4 figures, REVTe

Lost and found dark matter in elliptical galaxies

The kinematical properties of elliptical galaxies formed during the mergers of equal mass, stars+gas+dark matter spiral galaxies are compared to the observed low velocity dispersions found for planetary nebulae on the outskirts of ellipticals, which have been interpreted as pointing to a lack of dark matter in ellipticals (which poses a problem for the standard model of galaxy formation). We find that the velocity dispersion profiles of the stars in the simulated ellipticals match well the observed ones. The low outer stellar velocity dispersions are mainly caused by the radial orbits of the outermost stars, which, for a given binding energy must have low angular momentum to reach their large radial distances, usually driven out along tidal tails.Comment: Talk presented at 21st IAP meeting, Mass Profiles andShapes of Cosmological Structures. Ed. G. A. Mamon, F. Combes, C. Deffayet & B. Fort (Paris: EDP), 4 pages, 3 figures (4 plots

Admissibility as a Touchstone

Consider the problem of estimating simultaneously the means θi of independent normal random variables xi with unit variance. Under the weighted quadratic loss L(θ,a)=∑iλi(θi−ai)2 with positive weights it is well known that: (1) An estimator which is admissible under one set of weights is admissible under all weights. (2) Estimating individual coordinates by proper Bayes estimators results in an admissible estimator. (3) Estimating individual coordinates by admissible estimators may result in an inadmissible estimator, when the number of coordinates is large enough. A dominating estimator must link observations in the sense that at least one θi is estimated using observations other than xi. We consider an infinite model with a countable number of coordinates. In the infinite model admissibility does depend on the weights used and by linking coordinates it is possible to dominate even estimators which are proper Bayes for individual coordinates. Specifically, we show that when θi are square summable, the estimator δi(x)≡1 is admissible for λi=e−ic,c\u3e1/2, but inadmissible for λi=1/i1+c,c\u3e0. In the latter case, a dominating estimator π=(π1,π2,⋯) is of the form πi(x)=1−εi(x), where εi links all the observations x1,x2,⋯. Infinite models frequently arise in estimation problems for Gaussian processes. For example, in estimating the drift function θ of the Wiener process W under the loss L(θ,a)=∫[θ(t)−a(t)]2dt, the transformation xi=∫ΦidW with Φi an appropriate complete orthonormal sequence gives rise to a model which is equivalent to an infinite model with λi = 1/i2

Interplay between Josephson effect and magnetic interactions in double quantum dots

We analyze the magnetic and transport properties of a double quantum dot coupled to superconducting leads. In addition to the possible phase transition to a $\pi$ state, already present in the single dot case, this system exhibits a richer magnetic behavior due to the competition between Kondo and inter-dot antiferromagnetic coupling. We obtain results for the Josephson current which may help to understand recent experiments on superconductor-metallofullerene dimer junctions. We show that in such a system the Josephson effect can be used to control its magnetic configuration.Comment: 5 pages, 4 figure

Local Current Distribution and "Hot Spots" in the Integer Quantum Hall Regime

In a recent experiment, the local current distribution of a two-dimensional electron gas in the quantum Hall regime was probed by measuring the variation of the conductance due to local gating. The main experimental finding was the existence of "hot spots", i.e. regions with high degree of sensitivity to local gating, whose density increases as one approaches the quantum Hall transition. However, the direct connection between these "hot spots" and regions of high current flow is not clear. Here, based on a recent model for the quantum Hall transition consisting of a mixture of perfect and quantum links, the relation between the "hot spots" and the current distribution in the sample has been investigated. The model reproduces the observed dependence of the number and sizes of "hot spots" on the filling factor. It is further demonstrated that these "hot spots" are not located in regions where most of the current flows, but rather, in places where the currents flow both when injected from the left or from the right. A quantitative measure, the harmonic mean of these currents is introduced and correlates very well with the "hot spots" positions

Practical approximation scheme for the pion dynamics in the three-nucleon system

We discuss a working approximation scheme to a recently developed formulation of the coupled piNNN-NNN problem. The approximation scheme is based on the physical assumption that, at low energies, the 2N-subsystem dynamics in the elastic channel is conveniently described by the usual 2N-potential approach, while the explicit pion dynamics describes small, correction-type effects. Using the standard separable-expansion method, we obtain a dynamical equation of the Alt-Grassberger-Sandhas (AGS) type. This is an important result, because the computational techniques used for solving the normal AGS equation can also be used to describe the pion dynamics in the 3N system once the matrix dimension is increased by one component. We have also shown that this approximation scheme treats the conventional 3N problem once the pion degrees of freedom are projected out. Then the 3N system is described with an extended AGS-type equation where the spin-off of the pion dynamics (beyond the 2N potential) is taken into account in additional contributions to the driving term. These new terms are shown to reproduce the diagrams leading to modern 3N-force models. We also recover two sets of irreducible diagrams that are commonly neglected in 3N-force discussions, and conclude that these sets should be further investigated, because a claimed cancellation is questionable.Comment: 18 pages, including 5 figures, RevTeX, Eps