Extreme Galaxies During Reionization: Testing ISM and Disk Models

We test the ability of equilibrium galactic disk and one-zone interstellar medium models to describe the physical and emission properties of quasar hosts, submillimeter galaxies, and Lyman-alpha emitters at z>~6. The size, line widths, star formation rates, black hole accretion rates, gas masses and temperatures, and the relationships between these properties are all well-described by our model, and we provide approximate fitting formulae for comparison with future observations. However, comparing our carbon line predictions to observations reveals differences between the ISM at low and high redshifts. Our underestimate of the [CII] line emission indicates either higher star formation efficiencies in high-redshift molecular clouds or less depletion of metals into dust at fixed metallicity. Further, our over-prediction of the CO(6-5)/CO(1-0) ratio suggests that molecular clouds in real high-redshift galaxies have a lower turbulent Mach number and more subthermal CO(6-5) emission than expected owing either to sizes smaller than the local Jeans mass or to a pressure support mechanism other than turbulence.Comment: Accepted in MNRAS; 19 pages; 10 figures; 4 table

A numerical canonical transformation approach to quantum many body problems

We present a new approach for numerical solutions of ab initio quantum chemistry systems. The main idea of the approach, which we call canonical diagonalization, is to diagonalize directly the second quantized Hamiltonian by a sequence of numerical canonical transformations.Comment: 10 pages, 3 encapsulated figures. Parts of the paper are substantially revised to refer to previous similar method

Surgery description of colored knots

The pair (K,r) consisting of a knot K and a surjective map r from the knot group onto a dihedral group is said to be a p-colored knot. D. Moskovich conjectured that for any odd prime p there are exactly p equivalence classes of p-colored knots up to surgery along unknots in the kernel of the coloring. We show that there are at most 2p equivalence classes. This is a vast improvement upon the previous results by Moskovich for p=3, and 5, with no upper bound given in general. T. Cochran, A. Gerges, and K. Orr, in "Dehn surgery equivalence relations of 3-manifolds", define invariants of the surgery equivalence class of a closed 3-manifold M in the context of bordisms. By taking M to be 0-framed surgery of the 3-sphere along K we may define Moskovich's colored untying invariant in the same way as the Cochran-Gerges-Orr invariants. This bordism definition of the colored untying invariant will be then used to establish the upper bound.Comment: 41 pages, 23 figures (Version 3) Minor revisions and typos fixed. Proofs of Propositions 4.1 and 4.8 revise

Enhanced Pairing in the "Checkerboard" Hubbard Ladder

We study signatures of superconductivity in a 2--leg "checkerboard" Hubbard ladder model, defined as a one--dimensional (period 2) array of square plaquettes with an intra-plaquette hopping $t$ and inter-plaquette hopping $t'$, using the density matrix renormalization group method. The highest pairing scale (characterized by the spin gap or the pair binding energy, extrapolated to the thermodynamic limit) is found for doping levels close to half filling, $U\approx 6t$ and $t'/t \approx 0.6$. Other forms of modulated hopping parameters, with periods of either 1 or 3 lattice constants, are also found to enhance pairing relative to the uniform two--leg ladder, although to a lesser degree. A calculation of the phase stiffness of the ladder reveals that in the regime with the strongest pairing, the energy scale associated with phase ordering is comparable to the pairing scale.Comment: 9 pages, 9 figures; Journal reference adde