Decay of a Bound State under a Time-Periodic Perturbation: a Toy Case

We study the time evolution of a three dimensional quantum particle, initially in a bound state, under the action of a time-periodic zero range interaction with ``strength'' (\alpha(t)). Under very weak generic conditions on the Fourier coefficients of (\alpha(t)), we prove complete ionization as (t \to \infty). We prove also that, under the same conditions, all the states of the system are scattering states.Comment: LaTeX2e, 15 page

μ\mu--PhotoZ: Photometric Redshifts by Inverting the Tolman Surface Brightness Test

Surface brightness is a fundamental observational parameter of galaxies. We show, for the first time in detail, how it can be used to obtain photometric redshifts for galaxies, the $\mu$-PhotoZ method. We demonstrate that the Tolman surface brightness relation, $\mu \propto (1+z)^{-4}$, is a powerful tool for determining galaxy redshifts from photometric data. We develop a model using $\mu$ and a color percentile (ranking) measure to demonstrate the $\mu$-PhotoZ method. We apply our method to a set of galaxies from the SHELS survey, and demonstrate that the photometric redshift accuracy achieved using the surface brightness method alone is comparable with the best color-based methods. We show that the $\mu$-PhotoZ method is very effective in determining the redshift for red galaxies using only two photometric bands. We discuss the properties of the small, skewed, non-gaussian component of the error distribution. We calibrate $\mu_r, (r-i)$ from the SDSS to redshift, and tabulate the result, providing a simple, but accurate look up table to estimate the redshift of distant red galaxies.Comment: Accepted for publication in the Astronomical Journa

Multiparticle Schrodinger operators with point interactions in the plane

We study a system of N bosons in the plane interacting with delta function potentials. After a coupling constant renormalization we show that the Hamiltonian defines a self-adjoint operator and obtain a lower bound for the energy. The same results hold if one includes a regular inter-particle potential.Comment: 17 pages, Late

A study of the Gribov copies in linear covariant gauges in Euclidean Yang-Mills theories

The Gribov copies and their consequences on the infrared behavior of the gluon propagator are investigated in Euclidean Yang-Mills theories quantized in linear covariant gauges. Considering small values of the gauge parameter, it turns out that the transverse component of the gluon propagator is suppressed, while its longitudinal part is left unchanged. A Green function, G_{tr}, which displays infrared enhancement and which reduces to the ghost propagator in the Landau gauge is identified. The inclusion of the dimension two gluon condensate is also considered. In this case, the transverse component of the gluon propagator and the Green function G_{tr} remain suppressed and enhanced, respectively. Moreover, the longitudinal part of the gluon propagator becomes suppressed. A comparison with the results obtained from the studies of the Schwinger-Dyson equations and from lattice simulations is provided.Comment: 20 page

Effective Schroedinger dynamics on ϵ \epsilon -thin Dirichlet waveguides via Quantum Graphs I: star-shaped graphs

We describe the boundary conditions at the vertex that one must choose to obtain a dynamical system that best describes the low-energy part of the evolution of a quantum system confined to a very small neighbourhood of a star-shaped metric graph.Comment: in memory of Pierre Duclo

Asymptotics for the number of eigenvalues of three-particle Schr\"{o}dinger operators on lattices

We consider the Hamiltonian of a system of three quantum mechanical particles (two identical fermions and boson)on the three-dimensional lattice $\Z^3$ and interacting by means of zero-range attractive potentials. We describe the location and structure of the essential spectrum of the three-particle discrete Schr\"{o}dinger operator $H_{\gamma}(K),$ $K$ being the total quasi-momentum and $\gamma>0$ the ratio of the mass of fermion and boson. We choose for $\gamma>0$ the interaction $v(\gamma)$ in such a way the system consisting of one fermion and one boson has a zero energy resonance. We prove for any $\gamma> 0$ the existence infinitely many eigenvalues of the operator $H_{\gamma}(0).$ We establish for the number $N(0,\gamma; z;)$ of eigenvalues lying below $z<0$ the following asymptotics $$\lim_{z\to 0-}\frac{N(0,\gamma;z)}{\mid \log \mid z\mid \mid}={U} (\gamma) .$$ Moreover, for all nonzero values of the quasi-momentum $K \in T^3$ we establish the finiteness of the number $N(K,\gamma;\tau_{ess}(K))$ of eigenvalues of $H(K)$ below the bottom of the essential spectrum and we give an asymptotics for the number $N(K,\gamma;0)$ of eigenvalues below zero.Comment: 25 page

Massless Thirring model in canonical quantization scheme

It is shown that the exact solvability of the massless Thirring model in the canonical quantization scheme originates from the intrinsic linearizability of its Heisenberg equations in the method of dynamical mappings. The corresponding role of inequivalent representations of free massless Dirac field is elucidated.Comment: 10 page

Deep Multi-object Spectroscopy to Enhance Dark Energy Science from LSST

Community access to deep (i ~ 25), highly-multiplexed optical and near-infrared multi-object spectroscopy (MOS) on 8-40m telescopes would greatly improve measurements of cosmological parameters from LSST. The largest gain would come from improvements to LSST photometric redshifts, which are employed directly or indirectly for every major LSST cosmological probe; deep spectroscopic datasets will enable reduced uncertainties in the redshifts of individual objects via optimized training. Such spectroscopy will also determine the relationship of galaxy SEDs to their environments, key observables for studies of galaxy evolution. The resulting data will also constrain the impact of blending on photo-z's. Focused spectroscopic campaigns can also improve weak lensing cosmology by constraining the intrinsic alignments between the orientations of galaxies. Galaxy cluster studies can be enhanced by measuring motions of galaxies in and around clusters and by testing photo-z performance in regions of high density. Photometric redshift and intrinsic alignment studies are best-suited to instruments on large-aperture telescopes with wider fields of view (e.g., Subaru/PFS, MSE, or GMT/MANIFEST) but cluster investigations can be pursued with smaller-field instruments (e.g., Gemini/GMOS, Keck/DEIMOS, or TMT/WFOS), so deep MOS work can be distributed amongst a variety of telescopes. However, community access to large amounts of nights for surveys will still be needed to accomplish this work. In two companion white papers we present gains from shallower, wide-area MOS and from single-target imaging and spectroscopy.Comment: Science white paper submitted to the Astro2020 decadal survey. A table of time requirements is available at http://d-scholarship.pitt.edu/36036

Anyons and the Bose-Fermi duality in the finite-temperature Thirring model

Solutions to the Thirring model are constructed in the framework of algebraic QFT. It is shown that for all positive temperatures there are fermionic solutions only if the coupling constant is $\lambda=\sqrt{2(2n+1)\pi}, n\in {\bf N}$. These fermions are inequivalent and only for $n=1$ they are canonical fields. In the general case solutions are anyons. Different anyons (which are uncountably many) live in orthogonal spaces and obey dynamical equations (of the type of Heisenberg's "Urgleichung") characterized by the corresponding values of the statistic parameter. Thus statistic parameter turns out to be related to the coupling constant $\lambda$ and the whole Hilbert space becomes non-separable with a different "Urgleichung" satisfied in each of its sectors. This feature certainly cannot be seen by any power expansion in $\lambda$. Moreover, since the latter is tied to the statistic parameter, it is clear that such an expansion is doomed to failure and will never reveal the true structure of the theory. The correlation functions in the temperature state for the canonical dressed fermions are shown by us to coincide with the ones for bare fields, that is in agreement with the uniqueness of the $\tau$-KMS state over the CAR algebra ($\tau$ being the shift automorphism). Also the $\alpha$-anyon two-point function is evaluated and for scalar field it reproduces the result that is known from the literature.Comment: 25 pages, LaTe