6,492 research outputs found
Superintegrability of the Tremblay-Turbiner-Winternitz quantum Hamiltonians on a plane for odd
In a recent FTC by Tremblay {\sl et al} (2009 {\sl J. Phys. A: Math. Theor.}
{\bf 42} 205206), it has been conjectured that for any integer value of ,
some novel exactly solvable and integrable quantum Hamiltonian on a plane
is superintegrable and that the additional integral of motion is a th-order
differential operator . Here we demonstrate the conjecture for the
infinite family of Hamiltonians with odd , whose first member
corresponds to the three-body Calogero-Marchioro-Wolfes model after elimination
of the centre-of-mass motion. Our approach is based on the construction of some
-extended and invariant Hamiltonian \chh_k, which can be interpreted
as a modified boson oscillator Hamiltonian. The latter is then shown to possess
a -invariant integral of motion \cyy_{2k}, from which can be
obtained by projection in the identity representation space.Comment: 14 pages, no figure; change of title + important addition to sect. 4
+ 2 more references + minor modifications; accepted by JPA as an FT
Pure-hydrogen 3D model atmospheres of cool white dwarfs
A sequence of pure-hydrogen CO5BOLD 3D model atmospheres of DA white dwarfs
is presented for a surface gravity of log g = 8 and effective temperatures from
6000 to 13,000 K. We show that convective properties, such as flow velocities,
characteristic granulation size and intensity contrast of the granulation
patterns, change significantly over this range. We demonstrate that these 3D
simulations are not sensitive to numerical parameters unlike the 1D structures
that considerably depend on the mixing-length parameters. We conclude that 3D
spectra can be used directly in the spectroscopic analyses of DA white dwarfs.
We confirm the result of an earlier preliminary study that 3D model spectra
provide a much better characterization of the mass distribution of white dwarfs
and that shortcomings of the 1D mixing-length theory are responsible for the
spurious high-log g determinations of cool white dwarfs. In particular, the 1D
theory is unable to account for the cooling effect of the convective overshoot
in the upper atmospheres.Comment: 14 pages, 17 figures, accepted for publication in Astronomy and
Astrophysic
Spectroscopic analysis of DA white dwarfs with 3D model atmospheres
We present the first grid of mean three-dimensional (3D) spectra for
pure-hydrogen (DA) white dwarfs based on 3D model atmospheres. We use CO5BOLD
radiation-hydrodynamics 3D simulations instead of the mixing-length theory for
the treatment of convection. The simulations cover the effective temperature
range of 6000 < Teff (K) < 15,000 and the surface gravity range of 7 < log g <
9 where the large majority of DAs with a convective atmosphere are located. We
rely on horizontally averaged 3D structures (over constant Rosseland optical
depth) to compute spectra. It is demonstrated that our spectra can be
smoothly connected to their 1D counterparts at higher and lower Teff where the
3D effects are small. Analytical functions are provided in order to convert
spectroscopically determined 1D effective temperatures and surface gravities to
3D atmospheric parameters. We apply our improved models to well studied
spectroscopic data sets from the Sloan Digital Sky Survey and the White Dwarf
Catalog. We confirm that the so-called high-log g problem is not present when
employing spectra and that the issue was caused by inaccuracies in the 1D
mixing-length approach. The white dwarfs with a radiative and a convective
atmosphere have derived mean masses that are the same within ~0.01 Msun, in
much better agreement with our understanding of stellar evolution. Furthermore,
the 3D atmospheric parameters are in better agreement with independent Teff and
log g values from photometric and parallax measurements.Comment: 15 pages, 18 figures, 10 pages online appendix, accepted for
publication in Astronomy and Astrophysic
Revisiting the Cooling Flow Problem in Galaxies, Groups, and Clusters of Galaxies
We present a study of 107 galaxies, groups, and clusters spanning ~3 orders
of magnitude in mass, ~5 orders of magnitude in central galaxy star formation
rate (SFR), ~4 orders of magnitude in the classical cooling rate (dM/dt) of the
intracluster medium (ICM), and ~5 orders of magnitude in the central black hole
accretion rate. For each system in this sample, we measure dM/dt using archival
Chandra X-ray data and acquire the SFR and systematic uncertainty in the SFR by
combining over 330 estimates from dozens of literature sources. With these
data, we estimate the efficiency with which the ICM cools and forms stars,
finding e_cool = SFR/(dM/dt) = 1.4 +/- 0.4% for systems with dM/dt > 30
Msun/yr. For these systems, we measure a slope in the SFR-dM/dt relation
greater than unity, suggesting that the systems with the strongest cool cores
are also cooling more efficiently. We propose that this may be related to, on
average, higher black hole accretion rates in the strongest cool cores, which
could influence the total amount (saturating near the Eddington rate) and
dominant mode (mechanical vs radiative) of feedback. For systems with dM/dt <
30 Msun/yr, we find that the SFR and dM/dt are uncorrelated, and show that this
is consistent with star formation being fueled at a low (but dominant) level by
recycled ISM gas in these systems. We find an intrinsic log-normal scatter in
SFR at fixed dM/dt of 0.52 +/- 0.06 dex, suggesting that cooling is tightly
self-regulated over very long timescales, but can vary dramatically on short
timescales. There is weak evidence that this scatter may be related to the
feedback mechanism, with the scatter being minimized (~0.4 dex) in systems for
which the mechanical feedback power is within a factor of two of the cooling
luminosity.Comment: 16 pages, 10 figures, 6 tables. Submitted to ApJ. Comments welcome
Quantum Monte Carlo Study of Strongly Correlated Electrons: Cellular Dynamical Mean-Field Theory
We study the Hubbard model using the Cellular Dynamical Mean-Field Theory
(CDMFT) with quantum Monte Carlo (QMC) simulations. We present the algorithmic
details of CDMFT with the Hirsch-Fye QMC method for the solution of the
self-consistently embedded quantum cluster problem. We use the one- and
two-dimensional half-filled Hubbard model to gauge the performance of CDMFT+QMC
particularly for small clusters by comparing with the exact results and also
with other quantum cluster methods. We calculate single-particle Green's
functions and self-energies on small clusters to study their size dependence in
one- and two-dimensions.Comment: 14 pages, 18 figure
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