From cusps to cores: a stochastic model

The cold dark matter model of structure formation faces apparent problems on galactic scales. Several threads point to excessive halo concentration, including central densities that rise too steeply with decreasing radius. Yet, random fluctuations in the gaseous component can 'heat' the centres of haloes, decreasing their densities. We present a theoretical model deriving this effect from first principles: stochastic variations in the gas density are converted into potential fluctuations that act on the dark matter; the associated force correlation function is calculated and the corresponding stochastic equation solved. Assuming a power law spectrum of fluctuations with maximal and minimal cutoff scales, we derive the velocity dispersion imparted to the halo particles and the relevant relaxation time. We further perform numerical simulations, with fluctuations realised as a Gaussian random field, which confirm the formation of a core within a timescale comparable to that derived analytically. Non-radial collective modes enhance the energy transport process that erases the cusp, though the parametrisations of the analytical model persist. In our model, the dominant contribution to the dynamical coupling driving the cusp-core transformation comes from the largest scale fluctuations. Yet, the efficiency of the transformation is independent of the value of the largest scale and depends weakly (linearly) on the power law exponent; it effectively depends on two parameters: the gas mass fraction and the normalisation of the power spectrum. This suggests that cusp-core transformations observed in hydrodynamic simulations of galaxy formation may be understood and parametrised in simple terms, the physical and numerical complexities of the various implementations notwithstanding.Comment: Minor revisions to match version to appear in MNRAS; Section~2.3 largely rewritten for clarit

Renormalization Group Approach to Low Temperature Properties of a Non-Fermi Liquid Metal

We expand upon on an earlier renormalization group analysis of a non-Fermi liquid fixed point that plausibly govers the two dimensional electron liquid in a magnetic field near filling fraction $\nu=1/2$. We give a more complete description of our somewhat unorthodox renormalization group transformation by relating both our field-theoretic approach to a direct mode elimination and our anisotropic scaling to the general problem of incorporating curvature of the Fermi surface. We derive physical consequences of the fixed point by showing how they follow from renormalization group equations for finite-size scaling, where the size may be set by the temperature or by the frequency of interest. In order fully to exploit this approach, it is necessary to take into account composite operators, including in some cases dangerous ``irrelevant'' operators. We devote special attention to gauge invariance, both as a formal requirement and in its positive role providing Ward identities constraining the renormalization of composite operators. We emphasize that new considerations arise in describing properties of the physical electrons (as opposed to the quasiparticles.) We propose an experiment which, if feasible, will allow the most characteristic feature of our results, that isComment: 42 pages, 5 figures upon request, uses Phyzzx, IASSNS-HEP 94/6

The Private Higgs

We introduce Higgs democracy in the Yukawa sector by constructing a model with a private Higgs and a dark scalar for each fermion thus addressing the large hierarchy among fermion masses. The model has interesting implications for the LHC, while the Standard Model phenomenology is recovered at low energies. We discuss some phenomenological implications such as FCNC, new Higgses at the TeV scale and dark matter candidates.Comment: 8 pages, no figures. Version published in Phys. Lett.

Transformation of Statistics in Fractional Quantum Hall Systems

A Fermion to Boson transformation is accomplished by attaching to each Fermion a tube carrying a single quantum of flux oriented opposite to the applied magnetic field. When the mean field approximation is made in Haldane's spherical geometry, the Fermion angular momentum l_F is replaced by l_B=l_F-(N-1)/2. The set of allowed total angular momentum multiplets is identical in the two different pictures. The Fermion and Boson energy spectra in the presence of many body interactions are identical only if the pseudopotential V (interaction energy as a function of pair angular momentum L_12) increases as L_12(L_12+1). Similar bands of low energy states occur in the two spectra if V increases more quickly than this.Comment: 4 pages, 1 figure, poster at ARW in Queenstown, New Zealand (2001

A remark on interacting anyons in magnetic field

In this remark, we note that the anyons, interacting with each other through pairwise potential in external magnetic field, exhibit a simple quantum group symmetry.Comment: IPT-EPFL preprint, typos fixed, minor corrections, references updated, submitted to Physics Letter A

Obtaining the Neutrino Mixing Matrix with the Tetrahedral Group

We discuss various "minimalist'' schemes to derive the neutrino mixing matrix using the tetrahedral group $A_{4}.

On Charge Quantization and Abelian Gauge Horizontal Symmetries

Under the assumption that there exists a local gauge horizontal symmetry $G_H$ wich allows only for a top quark mass at tree level, we look for the constraints that charge quatization and the family structure of the standard model imposes on that symmetry.Comment: 13 pages, LaTeX, Acepted in Physics Letters

Quantum gates with topological phases

We investigate two models for performing topological quantum gates with the Aharonov-Bohm (AB) and Aharonov-Casher (AC) effects. Topological one- and two-qubit Abelian phases can be enacted with the AB effect using charge qubits, whereas the AC effect can be used to perform all single-qubit gates (Abelian and non-Abelian) for spin qubits. Possible experimental setups suitable for a solid state implementation are briefly discussed.Comment: 2 figures, RevTex

Unbroken supersymmetry in the Aharonov-Casher effect

We consider the problem of the bound states of a spin 1/2 chargless particle in a given Aharonov-Casher configuration. To this end we recast the description of the system in a supersymmetric form. Then the basic physical requirements for unbroken supersymmetry are established. We comment on the possibility of neutron confinement in this system

Skyrmion Excitations in Quantum Hall Systems

Using finite size calculations on the surface of a sphere we study the topological (skyrmion) excitation in quantum Hall system with spin degree of freedom at filling factors around $\nu=1$. In the absence of Zeeman energy, we find, in systems with one quasi-particle or one quasi-hole, the lowest energy band consists of states with $L=S$, where $L$ and $S$ are the total orbital and spin angular momentum. These different spin states are almost degenerate in the thermodynamic limit and their symmetry-breaking ground state is the state with one skyrmion of infinite size. In the presence of Zeeman energy, the skyrmion size is determined by the interplay of the Zeeman energy and electron-electron interaction and the skyrmion shrinks to a spin texture of finite size. We have calculated the energy gap of the system at infinite wave vector limit as a function of the Zeeman energy and find there are kinks in the energy gap associated with the shrinking of the size of the skyrmion. breaking ground state is the state with one skyrmion of infinite size. In the presence of Zeeman energy, the skyrmion size is determined by the interplay of the Zeeman energy and electron-electronComment: 4 pages, 5 postscript figures available upon reques