6,616 research outputs found
Sparse seismic imaging using variable projection
We consider an important class of signal processing problems where the signal
of interest is known to be sparse, and can be recovered from data given
auxiliary information about how the data was generated. For example, a sparse
Green's function may be recovered from seismic experimental data using sparsity
optimization when the source signature is known. Unfortunately, in practice
this information is often missing, and must be recovered from data along with
the signal using deconvolution techniques.
In this paper, we present a novel methodology to simultaneously solve for the
sparse signal and auxiliary parameters using a recently proposed variable
projection technique. Our main contribution is to combine variable projection
with sparsity promoting optimization, obtaining an efficient algorithm for
large-scale sparse deconvolution problems. We demonstrate the algorithm on a
seismic imaging example.Comment: 5 pages, 4 figure
Many-body Green's function theory for electron-phonon interactions: ground state properties of the Holstein dimer
We study ground-state properties of a two-site, two-electron Holstein model
describing two molecules coupled indirectly via electron-phonon interaction by
using both exact diagonalization and self-consistent diagrammatic many-body
perturbation theory. The Hartree and self-consistent Born approximations used
in the present work are studied at different levels of self-consistency. The
governing equations are shown to exhibit multiple solutions when the
electron-phonon interaction is sufficiently strong whereas at smaller
interactions only a single solution is found. The additional solutions at
larger electron-phonon couplings correspond to symmetry-broken states with
inhomogeneous electron densities. A comparison to exact results indicates that
this symmetry breaking is strongly correlated with the formation of a bipolaron
state in which the two electrons prefer to reside on the same molecule. The
results further show that the Hartree and partially self-consistent Born
solutions obtained by enforcing symmetry do not compare well with exact
energetics, while the fully self-consistent Born approximation improves the
qualitative and quantitative agreement with exact results in the same symmetric
case. This together with a presented natural occupation number analysis
supports the conclusion that the fully self-consistent approximation describes
partially the bipolaron crossover. These results contribute to better
understanding how these approximations cope with the strong localizing effect
of the electron-phonon interaction.Comment: 9 figures, corrected typo
Diagrammatic expansion for positive density-response spectra: Application to the electron gas
In a recent paper [Phys. Rev. B 90, 115134 (2014)] we put forward a
diagrammatic expansion for the self-energy which guarantees the positivity of
the spectral function. In this work we extend the theory to the density
response function. We write the generic diagram for the density-response
spectrum as the sum of partitions. In a partition the original diagram is
evaluated using time-ordered Green's functions (GF) on the left-half of the
diagram, antitime-ordered GF on the right-half of the diagram and lesser or
greater GF gluing the two halves. As there exist more than one way to cut a
diagram in two halves, to every diagram corresponds more than one partition. We
recognize that the most convenient diagrammatic objects for constructing a
theory of positive spectra are the half-diagrams. Diagrammatic approximations
obtained by summing the squares of half-diagrams do indeed correspond to a
combination of partitions which, by construction, yield a positive spectrum. We
develop the theory using bare GF and subsequently extend it to dressed GF. We
further prove a connection between the positivity of the spectral function and
the analytic properties of the polarizability. The general theory is
illustrated with several examples and then applied to solve the long-standing
problem of including vertex corrections without altering the positivity of the
spectrum. In fact already the first-order vertex diagram, relevant to the study
of gradient expansion, Friedel oscillations, etc., leads to spectra which are
negative in certain frequency domain. We find that the simplest approximation
to cure this deficiency is given by the sum of the zero-th order bubble
diagram, the first-order vertex diagram and a partition of the second-order
ladder diagram. We evaluate this approximation in the 3D homogeneous electron
gas and show the positivity of the spectrum for all frequencies and densities.Comment: 19 pages, 19 figure
Diagrammatic expansion for positive spectral functions beyond GW: Application to vertex corrections in the electron gas
We present a diagrammatic approach to construct self-energy approximations
within many-body perturbation theory with positive spectral properties. The
method cures the problem of negative spectral functions which arises from a
straightforward inclusion of vertex diagrams beyond the GW approximation. Our
approach consists of a two-steps procedure: we first express the approximate
many-body self-energy as a product of half-diagrams and then identify the
minimal number of half-diagrams to add in order to form a perfect square. The
resulting self-energy is an unconventional sum of self-energy diagrams in which
the internal lines of half a diagram are time-ordered Green's functions whereas
those of the other half are anti-time-ordered Green's functions, and the lines
joining the two halves are either lesser or greater Green's functions. The
theory is developed using noninteracting Green's functions and subsequently
extended to self-consistent Green's functions. Issues related to the conserving
properties of diagrammatic approximations with positive spectral functions are
also addressed. As a major application of the formalism we derive the minimal
set of additional diagrams to make positive the spectral function of the GW
approximation with lowest-order vertex corrections and screened interactions.
The method is then applied to vertex corrections in the three-dimensional
homogeneous electron gas by using a combination of analytical frequency
integrations and numerical Monte-Carlo momentum integrations to evaluate the
diagrams.Comment: 19 pages, 19 figure
Vertex corrections for positive-definite spectral functions of simple metals
We present a systematic study of vertex corrections in the homogeneous
electron gas at metallic densities. The vertex diagrams are built using a
recently proposed positive-definite diagrammatic expansion for the spectral
function. The vertex function not only provides corrections to the well known
plasmon and particle-hole scatterings, but also gives rise to new physical
processes such as generation of two plasmon excitations or the decay of the
one-particle state into a two-particles-one-hole state. By an efficient Monte
Carlo momentum integration we are able to show that the additional scattering
channels are responsible for the bandwidth reduction observed in photoemission
experiments on bulk sodium, appearance of the secondary plasmon satellite below
the Fermi level, and a substantial redistribution of spectral weights. The
feasibility of the approach for first-principles band-structure calculations is
also discussed
A Note on Wetting Transition for Gradient Fields
We prove existence of a wetting transition for two types of gradient fields:
1) Continuous SOS models in any dimension and 2) Massless Gaussian model in two
dimensions. Combined with a recent result showing the absence of such a
transition for Gaussian models above two dimensions by Bolthausen et al, this
shows in particular that absolute-value and quadratic interactions can give
rise to completely different behaviors.Comment: 6 pages, latex2
Topology of Pulsar Profiles (ToPP). I. Graph theory method and classification of the EPN
Some of the most important information on a radio pulsar is derived from its
average pulse profile. Many early pulsar studies were necessarily based on only
few such profiles. There, discrete profile components were linked to emission
mechanism models for individual stars through human interpretation. For the
population as a whole, profiles morphology must reflect the geometry and
overall evolution of the radio emitting regions. The problem, however, is that
this population is becoming too large for intensive studies of all sources
individually. Moreover, connecting profiles from a large collection of pulsars
rapidly becomes cumbersome. In this article, we present ToPP, the first-ever
unsupervised method to sort pulsars by profile-shape similarity, using graph
topology. We apply ToPP to the publicly available European Pulsar Network
profile database, providing the first organised visual overview of
multi-frequency profiles representing 90 individual pulsars. We find discrete
evolutionary tracks, varying from simple, single component profiles at all
frequencies, towards diverse mixtures of more complex profiles with frequency
evolution. The profile evolution is continuous, extending out to millisecond
pulsars, and does not fall in sharp classes. We interpret the profiles as a
mixture of pulsar core/cone emission type, spin-down energetics, and the
line-of-sight impact angle towards the magnetic axis. We show how ToPP can
systematically classify sources into the Rankin empirical profile scheme. ToPP
forms one of the key unsupervised methods that will be essential to explore
upcoming pulsar census data such as expected by the Square Kilometer Array.Comment: Submitte
Correlation effects in bistability at the nanoscale: steady state and beyond
The possibility of finding multistability in the density and current of an
interacting nanoscale junction coupled to semi-infinite leads is studied at
various levels of approximation. The system is driven out of equilibrium by an
external bias and the non-equilibrium properties are determined by real-time
propagation using both time-dependent density functional theory (TDDFT) and
many-body perturbation theory (MBPT). In TDDFT the exchange-correlation effects
are described within a recently proposed adiabatic local density approximation
(ALDA). In MBPT the electron-electron interaction is incorporated in a
many-body self-energy which is then approximated at the Hartree-Fock (HF),
second-Born (2B) and GW level. Assuming the existence of a steady-state and
solving directly the steady-state equations we find multiple solutions in the
HF approximation and within the ALDA. In these cases we investigate if and how
these solutions can be reached through time evolution and how to reversibly
switch between them. We further show that for the same cases the inclusion of
dynamical correlation effects suppresses bistability.Comment: 13 pages, 12 figure
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