4,775 research outputs found
Threshold Singularities in the One Dimensional Hubbard Model
We consider excitations with the quantum numbers of a hole in the one
dimensional Hubbard model below half-filling. We calculate the finite-size
corrections to the energy. The results are then used to determine threshold
singularities in the single-particle Green's function for commensurate
fillings. We present the analogous results for the Yang-Gaudin model (electron
gas with delta-function interactions).Comment: 26 pages, 12 figures version to appear in Phys Rev
Quantum Quench in the Transverse Field Ising Chain
We consider the time evolution of observables in the transverse field Ising
chain (TFIC) after a sudden quench of the magnetic field. We provide exact
analytical results for the asymptotic time and distance dependence of one- and
two-point correlation functions of the order parameter. We employ two
complementary approaches based on asymptotic evaluations of determinants and
form-factor sums. We prove that the stationary value of the two-point
correlation function is not thermal, but can be described by a generalized
Gibbs ensemble (GGE). The approach to the stationary state can also be
understood in terms of a GGE. We present a conjecture on how these results
generalize to particular quenches in other integrable models.Comment: 4 pages, 1 figur
Dielectric function of the semiconductor hole liquid: Full frequency and wave vector dependence
We study the dielectric function of the homogeneous semiconductor hole liquid
of p-doped bulk III-V zinc-blende semiconductors within random phase
approximation. The single-particle physics of the hole system is modeled by
Luttinger's four-band Hamiltonian in its spherical approximation. Regarding the
Coulomb-interacting hole liquid, the full dependence of the zero-temperature
dielectric function on wave vector and frequency is explored. The imaginary
part of the dielectric function is analytically obtained in terms of
complicated but fully elementary expressions, while in the result for the real
part nonelementary one-dimensional integrations remain to be performed. The
correctness of these two independent calculations is checked via Kramers-Kronig
relations.
The mass difference between heavy and light holes, along with variations in
the background dielectric constant, leads to dramatic alternations in the
plasmon excitation pattern, and generically, two plasmon branches can be
identified. These findings are the result of the evaluation of the full
dielectric function and are not accessible via a high-frequency expansion. In
the static limit a beating of Friedel oscillations between the Fermi wave
numbers of heavy and light holes occurs.Comment: 16 pages, 11 figures included. Update: Minor additions and
adjustments, published versio
Spectral Models of Convection-Dominated Accretion Flows
For small values of the dimensionless viscosity parameter, namely
, the dynamics of non-radiating accretion flows is
dominated by convection; convection strongly suppresses the accretion of matter
onto the central object and transports a luminosity from small to large radii in the flow. A fraction of this convective
luminosity is likely to be radiated at large radii via thermal bremsstrahlung
emission. We show that this leads to a correlation between the frequency of
maximal bremsstrahlung emission and the luminosity of the source, . Accreting black holes with X-ray luminosities are expected to
have hard X-ray spectra, with photon indices , and sources with
are expected to have soft spectra, with
. This is testable with {\it Chandra} and {\it XMM}.Comment: final version accepted by ApJ; significant modifications from
previous versio
Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
We derive the Bethe ansatz equations describing the complete spectrum of the
transition matrix of the partially asymmetric exclusion process with the most
general open boundary conditions. For totally asymmetric diffusion we calculate
the spectral gap, which characterizes the approach to stationarity at large
times. We observe boundary induced crossovers in and between massive, diffusive
and KPZ scaling regimes.Comment: 4 pages, 2 figures, published versio
HARD: Hard Augmentations for Robust Distillation
Knowledge distillation (KD) is a simple and successful method to transfer
knowledge from a teacher to a student model solely based on functional
activity. However, current KD has a few shortcomings: it has recently been
shown that this method is unsuitable to transfer simple inductive biases like
shift equivariance, struggles to transfer out of domain generalization, and
optimization time is magnitudes longer compared to default non-KD model
training. To improve these aspects of KD, we propose Hard Augmentations for
Robust Distillation (HARD), a generally applicable data augmentation framework,
that generates synthetic data points for which the teacher and the student
disagree. We show in a simple toy example that our augmentation framework
solves the problem of transferring simple equivariances with KD. We then apply
our framework in real-world tasks for a variety of augmentation models, ranging
from simple spatial transformations to unconstrained image manipulations with a
pretrained variational autoencoder. We find that our learned augmentations
significantly improve KD performance on in-domain and out-of-domain evaluation.
Moreover, our method outperforms even state-of-the-art data augmentations and
since the augmented training inputs can be visualized, they offer a qualitative
insight into the properties that are transferred from the teacher to the
student. Thus HARD represents a generally applicable, dynamically optimized
data augmentation technique tailored to improve the generalization and
convergence speed of models trained with KD
Upper and lower bounds on the mean square radius and criteria for occurrence of quantum halo states
In the context of non-relativistic quantum mechanics, we obtain several upper
and lower limits on the mean square radius applicable to systems composed by
two-body bound by a central potential. A lower limit on the mean square radius
is used to obtain a simple criteria for the occurrence of S-wave quantum halo
sates.Comment: 12 pages, 2 figure
The variable OVIII Warm Absorber in MCG-6-30-15
We present the results of a 4 day ASCA observation of the Seyfert galaxy
MCG-6-30-15, focussing on the nature of the X-ray absorption by the warm
absorber, characterizd by the K-edges of the intermediately ionized oxygen,
OVII and OVIII. We confirm that the column density of OVIII changes on a
timescale of ~s when the X-ray continuum flux decreases. The
significant anti-correlation of column density with continuum flux gives direct
evidence that the warm absorber is photoionized by the X-ray continuum. From
the timescale of the variation of the OVIII column density, we estimate that it
originates from gas within a radius of about 10^{17}\cm of the central
engine. In contrast, the depth of the OVII edge shows no response to the
continuum flux, which indicates that it originates in gas at larger radii. Our
results strongly suggest that there are two warm absorbing regions; one located
near or within the Broad Line Region, the other associated with the outer
molecular torus, scattering medium or Narrow Line Region.Comment: 8 pages (including figures) uuencoded gziped PS file. Submitted to
Publications of the Astronomical Society of Japa
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