Bethe Ansatz for a Quantum Supercoset Sigma Model

We study an integrable conformal OSp(2m + 2|2m) supercoset model as an analog to the AdS_5 X S^5 superstring world-sheet theory. Using the known S-matrix for this system, we obtain integral equations for states of large particle density in an SU(2) sector, which are exact in the sigma model coupling constant. As a check, we derive as a limit the general classical Bethe equation of Kazakov, Marshakov, Minahan, and Zarembo. There are two distinct quantum expansions around the well-studied classical limit, the lambda^{-1/2} effects and the 1/J effects. Our approach captures the first type, but not the second.Comment: 30 pages, 1 figure, v2: references adde

They are Small Worlds After All: Revised Properties of Kepler M Dwarf Stars and their Planets

We classified the reddest ($r-J>2.2$) stars observed by the NASA $Kepler$ mission into main sequence dwarf or evolved giant stars and determined the properties of 4216 M dwarfs based on a comparison of available photometry with that of nearby calibrator stars, as well as available proper motions and spectra. We revised the properties of candidate transiting planets using the stellar parameters, high-resolution imaging to identify companion stars, and, in the case of binaries, fitting light curves to identify the likely planet host. In 49 of 54 systems we validated the primary as the host star. We inferred the intrinsic distribution of M dwarf planets using the method of iterative Monte Carlo simulation. We compared several models of planet orbital geometry and clustering and found that one where planets are exponentially distributed and almost precisely coplanar best describes the distribution of multi-planet systems. We determined that $Kepler$ M dwarfs host an average of $2.2 \pm 0.3$ planets with radii of 1-4$R_{\oplus}$ and orbital periods of 1.5-180 d. The radius distribution peaks at $\sim 1.2R_{\oplus}$ and is essentially zero at $4R_{\oplus}$, although we identify three giant planet candidates other than the previously confirmed Kepler-45b. There is suggestive but not significant evidence that the radius distribution varies with orbital period. The distribution with logarithmic orbital period is flat except for a decline for orbits less than a few days. Twelve candidate planets, including two Jupiter-size objects, experience an irradiance below the threshold level for a runaway greenhouse on an Earth-like planet and are thus in a "habitable zone".Comment: MNRAS, in press. Tables 1, 3, and 4 are available in electronic form in the "anc" director

Quasiclassical Coarse Graining and Thermodynamic Entropy

Our everyday descriptions of the universe are highly coarse-grained, following only a tiny fraction of the variables necessary for a perfectly fine-grained description. Coarse graining in classical physics is made natural by our limited powers of observation and computation. But in the modern quantum mechanics of closed systems, some measure of coarse graining is inescapable because there are no non-trivial, probabilistic, fine-grained descriptions. This essay explores the consequences of that fact. Quantum theory allows for various coarse-grained descriptions some of which are mutually incompatible. For most purposes, however, we are interested in the small subset of ``quasiclassical descriptions'' defined by ranges of values of averages over small volumes of densities of conserved quantities such as energy and momentum and approximately conserved quantities such as baryon number. The near-conservation of these quasiclassical quantities results in approximate decoherence, predictability, and local equilibrium, leading to closed sets of equations of motion. In any description, information is sacrificed through the coarse graining that yields decoherence and gives rise to probabilities for histories. In quasiclassical descriptions, further information is sacrificed in exhibiting the emergent regularities summarized by classical equations of motion. An appropriate entropy measures the loss of information. For a ``quasiclassical realm'' this is connected with the usual thermodynamic entropy as obtained from statistical mechanics. It was low for the initial state of our universe and has been increasing since.Comment: 17 pages, 0 figures, revtex4, Dedicated to Rafael Sorkin on his 60th birthday, minor correction

A little inflation at the cosmological QCD phase transition

We reexamine the recently proposed "little inflation" scenario that allows for a strong first order phase-transition of QCD at non-negligible baryon number in the early universe and its possible observable consequences. The scenario is based on the assumptions of a strong mechanism for baryogenesis and a quasistable QCD-medium state which triggers a short inflationary period of inflation diluting the baryon asymmetry to the value observed today. The cosmological implications are reexamined, namely effects on primordial density fluctuations up to dark matter mass scales of M_{max} \sim 1 M_{\astrosun}, change in the spectral slope up to M_{max} \sim 10^6 M_{\astrosun}, production of seeds for the present galactic and extragalactic magnetic fields and a gravitational wave spectrum with a peak frequency around $\nu_{peak} \sim 4 \cdot 10^{-8} Hz$. We discuss the issue of nucleation in more detail and employ a chiral effective model of QCD to study the impact on small scale structure formation.Comment: 18 pages, 12 figures, several extensions to the text and structure formation part was rephrased for better readabilit

Multicomponent dense electron gas as a model of Si MOSFET

We solve two-dimensional model of $N$-component dense electron gas in the limit of large $N$ and in a range of the Coulomb interaction parameter: $N^{-3/2}\ll r_s\ll 1$. The quasiparticle interaction on the Fermi circle vanishes as 1/N. The ground state energy and the effective mass are found as series in powers of $r_s^{2/3}$. In the quantum Hall state on the lowest Landau level at integer filling: $1\ll\nu<N$, the charge activation energy gap and the exchange constant are found.Comment: 10 pages, 4 figure

Strong contraction of the representations of the three dimensional Lie algebras

For any Inonu-Wigner contraction of a three dimensional Lie algebra we construct the corresponding contractions of representations. Our method is quite canonical in the sense that in all cases we deal with realizations of the representations on some spaces of functions; we contract the differential operators on those spaces along with the representation spaces themselves by taking certain pointwise limit of functions. We call such contractions strong contractions. We show that this pointwise limit gives rise to a direct limit space. Many of these contractions are new and in other examples we give a different proof

Quasiclassical Equations of Motion for Nonlinear Brownian Systems

Following the formalism of Gell-Mann and Hartle, phenomenological equations of motion are derived from the decoherence functional formalism of quantum mechanics, using a path-integral description. This is done explicitly for the case of a system interacting with a ``bath'' of harmonic oscillators whose individual motions are neglected. The results are compared to the equations derived from the purely classical theory. The case of linear interactions is treated exactly, and nonlinear interactions are compared using classical and quantum perturbation theory.Comment: 24 pages, CALT-68-1848 (RevTeX 2.0 macros

Composition of Jupiter irregular satellites sheds light on their origin

Irregular satellites of Jupiter with their highly eccentric, inclined and distant orbits suggest that their capture took place just before the giant planet migration. We aim to improve our understanding of the surface composition of irregular satellites of Jupiter to gain insight into a narrow time window when our Solar System was forming. We observed three Jovian irregular satellites, Himalia, Elara, and Carme, using a medium-resolution 0.8-5.5 micro m spectrograph on the National Aeronautics and Space Administration (NASA) Infrared Telescope Facility (IRTF). Using a linear spectral unmixing model we have constrained the major mineral phases on the surface of these three bodies. Our results confirm that the surface of Himalia, Elara, and Carme are dominated by opaque materials such as those seen in carbonaceous chondrite meteorites. Our spectral modeling of NIR spectra of Himalia and Elara confirm that their surface composition is the same and magnetite is the dominant mineral. A comparison of the spectral shape of Himalia with the two large main C-type asteroids, Themis (D 176 km) and Europa (D 352 km), suggests surface composition similar to Europa. The NIR spectrum of Carme exhibits blue slope up to 1.5 microm and is spectrally distinct from those of Himalia and Elara. Our model suggests that it is compositionally similar to amorphous carbon. Himalia and Elara are compositionally similar but differ significantly from Carme. These results support the hypotheses that the Jupiter irregular satellites are captured bodies that were subject to further breakup events and clustered as families based on their similar physical and surface compositions