Tensor network trial states for chiral topological phases in two dimensions and a no-go theorem in any dimension

Trial wavefunctions that can be represented by summing over locally-coupled degrees of freedom are called tensor network states (TNSs); they have seemed difficult to construct for two-dimensional topological phases that possess protected gapless edge excitations. We show it can be done for chiral states of free fermions, using a Gaussian Grassmann integral, yielding $p_x \pm i p_y$ and Chern insulator states, in the sense that the fermionic excitations live in a topologically non-trivial bundle of the required type. We prove that any strictly short-range quadratic parent Hamiltonian for these states is gapless; the proof holds for a class of systems in any dimension of space. The proof also shows, quite generally, that sets of compactly-supported Wannier-type functions do not exist for band structures in this class. We construct further examples of TNSs that are analogs of fractional (including non-Abelian) quantum Hall phases; it is not known whether parent Hamiltonians for these are also gapless.Comment: 5 pages plus 4 pages supplementary material, inc 3 figures. v2: improved no-go theorem, additional references. v3: changed to regular article format; 16 pages, 3 figures, no supplemental material; main change is much extended proof of no-go theorem. v4: minor changes; as-published versio

The X-ray Evolution of Merging Galaxies

From a Chandra survey of nine interacting galaxy systems the evolution of X-ray emission during the merger process has been investigated. From comparing Lx/Lk and Lfir/Lb it is found that the X-ray luminosity peaks around 300 Myr before nuclear coalescence, even though we know that rapid and increasing star formation is still taking place at this time. It is likely that this drop in X-ray luminosity is a consequence of outflows breaking out of the galactic discs of these systems. At a time around 1 Gyr after coalescence, the merger-remnants in our sample are X-ray dim when compared to typical X-ray luminosities of mature elliptical galaxies. However, we do see evidence that these systems will start to resemble typical elliptical galaxies at a greater dynamical age, given the properties of the 3 Gyr system within our sample, indicating that halo regeneration will take place within low Lx merger-remnants.Comment: 4 pages, 1 figure, to appear in the Proceedings of the IAU Symposium No. 23

The traveling salesman problem, conformal invariance, and dense polymers

We propose that the statistics of the optimal tour in the planar random Euclidean traveling salesman problem is conformally invariant on large scales. This is exhibited in power-law behavior of the probabilities for the tour to zigzag repeatedly between two regions, and in subleading corrections to the length of the tour. The universality class should be the same as for dense polymers and minimal spanning trees. The conjectures for the length of the tour on a cylinder are tested numerically.Comment: 4 pages. v2: small revisions, improved argument about dimensions d>2. v3: Final version, with a correction to the form of the tour length in a domain, and a new referenc

Signatures of the Milky Way's Dark Disk in Current and Future Experiments

In hierarchical structure formation models of disk galaxies, a dark matter disk forms as massive satellites are preferentially dragged into the disk-plane where they dissolve. Here, we quantify the importance of this dark disk for direct and indirect dark matter detection. The low velocity of the dark disk with respect to the Earth enhances detection rates in direct detection experiments at low recoil energy. For WIMP masses M_{WIMP} >~ 50 GeV, the detection rate increases by up to a factor of 3 in the 5 - 20 keV recoil energy range. Comparing this with rates at higher energy is sensitive to M_{WIMP}, providing stronger mass constraints particularly for M_{WIMP}>~100 GeV. The annual modulation signal is significantly boosted by the dark disk and the modulation phase is shifted by ~3 weeks relative to the dark halo. The variation of the observed phase with recoil energy determines M_{WIMP}, once the dark disk properties are fixed by future astronomical surveys. The low velocity of the particles in the dark disk with respect to the solar system significantly enhances the capture rate of WIMPs in the Sun, leading to an increased flux of neutrinos from the Sun which could be detected in current and future neutrino telescopes. The dark disk contribution to the muon flux from neutrino back conversion at the Earth is increased by a factor of ~5 compared to the SHM, for rho_d/rho_h=0.5.Comment: 5 pages, 7 figures, To appear in the proceedings of Identification of Dark Matter 2008 (IDM2008), Stockholm, 18-22 August 2008; corrected one referenc

Vorticity imbalance and stability in relation to convection

A complete synoptic-scale vorticity budget was related to convection storm development in the eastern two-thirds of the United States. The 3-h sounding interval permitted a study of time changes of the vorticity budget in areas of convective storms. Results of analyses revealed significant changes in values of terms in the vorticity equation at different stages of squall line development. Average budgets for all areas of convection indicate systematic imbalance in the terms in the vorticity equation. This imbalance resulted primarily from sub-grid scale processes. Potential instability in the lower troposphere was analyzed in relation to the development of convective activity. Instability was related to areas of convection; however, instability alone was inadequate for forecast purposes. Combinations of stability and terms in the vorticity equation in the form of indices succeeded in depicting areas of convection better than any one item separately

Dark matter heats up in dwarf galaxies

Gravitational potential fluctuations driven by bursty star formation can kinematically 'heat up' dark matter at the centres of dwarf galaxies. A key prediction of such models is that, at a fixed dark matter halo mass, dwarfs with a higher stellar mass will have a lower central dark matter density. We use stellar kinematics and HI gas rotation curves to infer the inner dark matter densities of eight dwarf spheroidal and eight dwarf irregular galaxies with a wide range of star formation histories. For all galaxies, we estimate the dark matter density at a common radius of 150pc, $\rho_{\rm DM}(150\,\mathrm{pc})$. We find that our sample of dwarfs falls into two distinct classes. Those that stopped forming stars over 6Gyrs ago favour central densities $\rho_{\rm DM}(150\,\mathrm{pc})>10^8\,{\rm M}_\odot\,{\rm kpc}^{-3}$, consistent with cold dark matter cusps, while those with more extended star formation favour $\rho_{\rm DM}(150\,\mathrm{pc})<10^8\,{\rm M}_{\odot}\,{\rm kpc}^{-3}$, consistent with shallower dark matter cores. Using abundance matching to infer pre-infall halo masses, $M_{200}$, we show that this dichotomy is in excellent agreement with models in which dark matter is heated up by bursty star formation. In particular, we find that $\rho_{\rm DM}(150\,\mathrm{pc})$ steadily decreases with increasing stellar mass-to-halo mass ratio, $M_*/M_{200}$. Our results suggest that, to leading order, dark matter is a cold, collisionless, fluid that can be kinematically 'heated up' and moved around.Comment: 22 pages, 10 Figures. Final version accepted for publication in MNRA