2,392 research outputs found
Non-autonomous double phase eigenvalue problems with indefinite weight and lack of compactness
In this paper, we consider eigenvalues to the following double phase problem
with unbalanced growth and indefinite weight, -\Delta_p^a u-\Delta_q u
=\lambda m(x) |u|^{q-2}u \quad \mbox{in} \,\, \R^N, where {},
{, }, , and is {an indefinite sign weight which may admit
nontrivial positive and negative parts}. Here is the -Laplacian
operator and is the weighted -Laplace operator defined by
. The problem
can be degenerate, in the sense that the infimum of in may be zero.
Our main results distinguish between the cases and . In the first
case, we establish the existence of a {\it continuous} family of eigenvalues,
starting from the principal frequency of a suitable single phase eigenvalue
problem. In the latter case, we prove the existence of a {\it discrete} family
of positive eigenvalues, which diverges to infinity.Comment: 16 page
Modeling GRB 050904: Autopsy of a Massive Stellar Explosion at z=6.29
GRB 050904 at redshift z=6.29, discovered and observed by Swift and with
spectroscopic redshift from the Subaru telescope, is the first gamma-ray burst
to be identified from beyond the epoch of reionization. Since the progenitors
of long gamma-ray bursts have been identified as massive stars, this event
offers a unique opportunity to investigate star formation environments at this
epoch. Apart from its record redshift, the burst is remarkable in two respects:
first, it exhibits fast-evolving X-ray and optical flares that peak
simultaneously at t~470 s in the observer frame, and may thus originate in the
same emission region; and second, its afterglow exhibits an accelerated decay
in the near-infrared (NIR) from t~10^4 s to t~3 10^4 s after the burst,
coincident with repeated and energetic X-ray flaring activity. We make a
complete analysis of available X-ray, NIR, and radio observations, utilizing
afterglow models that incorporate a range of physical effects not previously
considered for this or any other GRB afterglow, and quantifying our model
uncertainties in detail via Markov Chain Monte Carlo analysis. In the process,
we explore the possibility that the early optical and X-ray flare is due to
synchrotron and inverse Compton emission from the reverse shock regions of the
outflow. We suggest that the period of accelerated decay in the NIR may be due
to suppression of synchrotron radiation by inverse Compton interaction of X-ray
flare photons with electrons in the forward shock; a subsequent interval of
slow decay would then be due to a progressive decline in this suppression. The
range of acceptable models demonstrates that the kinetic energy and circumburst
density of GRB 050904 are well above the typical values found for low-redshift
GRBs.Comment: 45 pages, 7 figures, and ApJ accepted. Revised version, minor
modifications and 1 extra figur
Radiative efficiency and thermal spectrum of accretion onto Schwarzschild black holes
Recent general relativistic magneto-hydrodynamic (MHD) simulations of
accretion onto black holes have shown that, contrary to the basic assumptions
of the Novikov-Thorne model, there can be substantial magnetic stress
throughout the plunging region. Additional dissipation and radiation can
therefore be expected. We use data from a particularly well-resolved simulation
of accretion onto a non-spinning black hole to compute both the radiative
efficiency of such a flow and its spectrum if all emitted light is radiated
with a thermal spectrum whose temperature matches the local effective
temperature. This disk is geometrically thin enough (H/r ~= 0.06) that little
heat is retained in the flow. In terms of light reaching infinity (i.e., after
allowance for all relativistic effects and for photon capture by the black
hole), we find that the radiative efficiency is at least ~=6-10% greater than
predicted by the Novikov-Thorne model (complete radiation of all heat might
yield another ~6%). We also find that the spectrum more closely resembles the
Novikov-Thorne prediction for a/M ~= 0.2--0.3 than for the correct value,
a/M=0. As a result, if the spin of a non-spinning black hole is inferred by
model-fitting to a Novikov-Thorne model with known black hole mass, distance,
and inclination, the inferred a/M is too large by ~= 0.2--0.3.Comment: Submitted to ApJ, 26 pages, 12 figures (some in color), AASTE
Stationary wave patterns generated by an impurity moving with supersonic velocity through a Bose-Einstein condensate
Formation of stationary 3D wave patterns generated by a small point-like
impurity moving through a Bose-Einstein condensate with supersonic velocity is
studied. Asymptotic formulae for a stationary far-field density distribution
are obtained. Comparison with three-dimensional numerical simulations
demonstrates that these formulae are accurate enough already at distances from
the obstacle equal to a few wavelengths.Comment: 7 pages, 3 figure
Dark pair coherent states of the motion of a trapped ion
We propose a scheme for generating vibrational pair coherent states of the
motion of an ion in a two-dimensional trap. In our scheme, the trapped ion is
excited bichromatically by three laser beams along different directions in the
X-Y plane of the ion trap. We show that if the initial vibrational state is
given by a two-mode Fock state, the final steady state, indicated by the
extinction of the fluorescence emitted by the ion, is a pure state. The
motional state of the ion in the equilibrium realizes that of the
highly-correlated pair coherent state.Comment: 14 pages, 3 figure
Nonlinear Decoherence in Quantum State Preparation of a Trapped Ion
We present a nonlinear decoherence model which models decoherence effect
caused by various decohereing sources in a quantum system through a nonlinear
coupling between the system and its environment, and apply it to investigating
decoherence in nonclassical motional states of a single trapped ion. We obtain
an exactly analytic solution of the model and find very good agreement with
experimental results for the population decay rate of a single trapped ion
observed in the NIST experiments by Meekhof and coworkers (D. M. Meekhof, {\it
et al.}, Phys. Rev. Lett. {\bf 76}, 1796 (1996)).Comment: 5 pages, Revte
Quantum-state synthesis of multi-mode bosonic fields: Preparation of arbitrary states of 2-D vibrational motion of trapped ions
We present a universal algorithm for an efficient deterministic preparation
of an arbitrary two--mode bosonic state. In particular, we discuss in detail
preparation of entangled states of a two-dimensional vibrational motion of a
trapped ion via a sequence of laser stimulated Raman transitions. Our formalism
can be generalized for multi-mode bosonic fields. We examine stability of our
algorithm with respect to a technical noise.Comment: 8 pages, revtex, including 2 ps-figures, section about physical
implementation added, references updated, submitted to Phys. Rev. A, computer
program available at http://www.savba.sk/sav/inst/fyzi/qo
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