27,787 research outputs found
N electrons in a quantum dot: Two-point Pade approximants
We present analytic estimates for the energy levels of N electrons (N = 2 -
5) in a two-dimensional parabolic quantum dot. A magnetic field is applied
perpendicularly to the confinement plane. The relevant scaled energy is shown
to be a smooth function of the parameter \beta=(effective Rydberg/effective dot
energy)^{1/6}. Two-point Pade approximants are obtained from the series
expansions of the energy near the oscillator () and Wigner
() limits. The approximants are expected to work with an error
not greater than 2.5% in the entire interval .Comment: 27 pages. LaTeX. 6 figures not include
Prospects for indirect MeV Dark Matter detection with Gamma Rays in light of Cosmic Microwave Background Constraints
The self-annihilation of dark matter particles with mass in the MeV range can
produce gamma rays via prompt or secondary radiation. The annihilation rate for
such light dark matter particles is however tightly constrained by cosmic
microwave background (CMB) data. Here we explore the possibility of discovering
MeV dark matter annihilation with future MeV gamma-ray telescopes taking into
account the latest and future CMB constraints. We study the optimal energy
window as a function of the dominant annihilation final state. We consider both
the (conservative) case of the dwarf spheroidal galaxy Draco and the (more
optimistic) case of the Galactic center. We find that for certain channels,
including those with one or two monochromatic photon(s) and one or two neutral
pion(s), a detectable gamma-ray signal is possible for both targets under
consideration, and compatible with CMB constraints. For other annihilation
channels, however, including all leptonic annihilation channels and two charged
pions, CMB data rule out any significant signal of dark matter annihilation at
future MeV gamma-ray telescopes from dwarf galaxies, but possibly not for the
Galactic center.Comment: 10 pages, 6 figures, version to appear on PR
Higher-order symmetry energy and neutron star core-crust transition with Gogny forces
We study the symmetry energy and the core-crust transition in neutron stars
using the finite-range Gogny nuclear interaction and examine the deduced
crustal thickness and crustal moment of inertia. We start by analyzing the
second-, fourth- and sixth-order coefficients of the Taylor expansion of the
energy per particle in powers of the isospin asymmetry for Gogny forces. These
coefficients provide information about the departure of the symmetry energy
from the widely used parabolic law. The neutron star core-crust transition is
evaluated by looking at the onset of thermodynamical instability of the liquid
core. The calculation is performed with the exact (i.e., without Taylor
expansion) Gogny EoS for the core, and also with its Taylor expansion in order
to assess the influence of isospin expansions on locating the inner edge of
neutron star crusts. It is found that the properties of the core-crust
transition derived from the exact EoS differ from the predictions of the Taylor
expansion even when the expansion is carried through sixth order in the isospin
asymmetry. Gogny forces, using the exact EoS, predict the ranges for the transition
density and for the transition pressure. The transition densities show an
anticorrelation with the slope parameter of the symmetry energy. The
transition pressures are not found to correlate with . Neutron stars
obtained with Gogny forces have maximum masses below and
relatively small moments of inertia. The crustal mass and moment of inertia are
evaluated and comparisons are made with the constraints from observed glitches
in pulsars.Comment: 24 pages, 15 figures, discussions and bibliography updated, to appear
in Physical Review
Consistent Approximations for the Optimal Control of Constrained Switched Systems
Though switched dynamical systems have shown great utility in modeling a
variety of physical phenomena, the construction of an optimal control of such
systems has proven difficult since it demands some type of optimal mode
scheduling. In this paper, we devise an algorithm for the computation of an
optimal control of constrained nonlinear switched dynamical systems. The
control parameter for such systems include a continuous-valued input and
discrete-valued input, where the latter corresponds to the mode of the switched
system that is active at a particular instance in time. Our approach, which we
prove converges to local minimizers of the constrained optimal control problem,
first relaxes the discrete-valued input, then performs traditional optimal
control, and then projects the constructed relaxed discrete-valued input back
to a pure discrete-valued input by employing an extension to the classical
Chattering Lemma that we prove. We extend this algorithm by formulating a
computationally implementable algorithm which works by discretizing the time
interval over which the switched dynamical system is defined. Importantly, we
prove that this implementable algorithm constructs a sequence of points by
recursive application that converge to the local minimizers of the original
constrained optimal control problem. Four simulation experiments are included
to validate the theoretical developments
- …