9,845 research outputs found
First-principles nonequilibrium Green's function approach to transient photoabsorption: Application to atoms
We put forward a first-principle NonEquilibrium Green's Function (NEGF)
approach to calculate the transient photoabsorption spectrum of optically thin
samples. The method can deal with pump fields of arbitrary strength, frequency
and duration as well as for overlapping and nonoverlapping pump and probe
pulses. The electron-electron repulsion is accounted for by the correlation
self-energy, and the resulting numerical scheme deals with matrices that scale
quadratically with the system size. Two recent experiments, the first on helium
and the second on krypton, are addressed. For the first experiment we explain
the bending of the Autler-Townes absorption peaks with increasing the
pump-probe delay \t, and relate the bending to the thickness and density of
the gas. For the second experiment we find that sizable spectral structures of
the pump-generated admixture of Kr ions are fingerprints of {\em dynamical
correlation} effects, and hence they cannot be reproduced by time-local
self-energy approximations. Remarkably, the NEGF approach also captures the
retardation of the absorption onset of Kr with respect to Kr as a
function of \t.Comment: 13 pages, 8 captioned figure
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
Conserving Approximations in Time-Dependent Density Functional Theory
In the present work we propose a theory for obtaining successively better
approximations to the linear response functions of time-dependent density or
current-density functional theory. The new technique is based on the
variational approach to many-body perturbation theory (MBPT) as developed
during the sixties and later expanded by us in the mid nineties. Due to this
feature the resulting response functions obey a large number of conservation
laws such as particle and momentum conservation and sum rules. The quality of
the obtained results is governed by the physical processes built in through
MBPT but also by the choice of variational expressions. We here present several
conserving response functions of different sophistication to be used in the
calculation of the optical response of solids and nano-scale systems.Comment: 11 pages, 4 figures, revised versio
Crossover from Reptation to Rouse dynamics in the Extended Rubinstein-Duke Model
The competition between reptation and Rouse Dynamics is incorporated in the
Rubinstein-Duke model for polymer motion by extending it with sideways motions,
which cross barriers and create or annihilate hernias. Using the Density-Matrix
Renormalization-Group Method as solver of the Master Equation, the renewal time
and the diffusion coefficient are calculated as function of the length of the
chain and the strength of the sideways motion. These new types of moves have a
strong and delicate influence on the asymptotic behavior of long polymers. The
effects are analyzed as function of the chain length in terms of effective
exponents and crossover scaling functions.Comment: 16 Pages RevTeX and 13 PostScript figures included, accepted for
publication in Phys. Rev.
Ultra-nonlocality in density functional theory for photo-emission spectroscopy
We derive an exact expression for the photo-current of photo-emission
spectroscopy using time-dependent current density functional theory (TDCDFT).
This expression is given as an integral over the Kohn-Sham spectral function
renormalized by effective potentials that depend on the exchange-correlation
kernel of current density functional theory. We analyze in detail the physical
content of this expression by making a connection between the
density-functional expression and the diagrammatic expansion of the
photo-current within many-body perturbation theory. We further demonstrate that
the density functional expression does not provide us with information on the
kinetic energy distribution of the photo-electrons. Such information can, in
principle, be obtained from TDCDFT by exactly modeling the experiment in which
the photo-current is split into energy contributions by means of an external
electromagnetic field outside the sample, as is done in standard detectors. We
find, however, that this procedure produces very nonlocal correlations between
the exchange-correlation fields in the sample and the detector.Comment: 11 pages, 11 figure
Charge dynamics in molecular junctions: Nonequilibrium Green's Function approach made fast
Real-time Green's function simulations of molecular junctions (open quantum
systems) are typically performed by solving the Kadanoff-Baym equations (KBE).
The KBE, however, impose a serious limitation on the maximum propagation time
due to the large memory storage needed. In this work we propose a simplified
Green's function approach based on the Generalized Kadanoff-Baym Ansatz (GKBA)
to overcome the KBE limitation on time, significantly speed up the
calculations, and yet stay close to the KBE results. This is achieved through a
twofold advance: first we show how to make the GKBA work in open systems and
then construct a suitable quasi-particle propagator that includes correlation
effects in a diagrammatic fashion. We also provide evidence that our GKBA
scheme, although already in good agreement with the KBE approach, can be
further improved without increasing the computational cost.Comment: 13 pages, 13 figure
Crossover from reptation to Rouse dynamics in a one-dimensional model
A simple one-dimensional model is constructed for polymer motion. It exhibits
the crossover from reptation to Rouse dynamics through gradually allowing
hernia creation and annihilation. The model is treated by the density matrix
technique which permits an accurate finite-size-scaling analysis of the
behavior of long polymers.Comment: 5 Pages RevTeX and 5 PostScript figures included (to appear in
Physical Review E
Crossover behavior for long reptating polymers
We analyze the Rubinstein-Duke model for polymer reptation by means of
density matrix renormalization techniques. We find a crossover behavior for a
series of quantities as function of the polymer length. The crossover length
may become very large if the mobility of end groups is small compared to that
of the internal reptons. Our results offer an explanation to a controversy
between theory, experiments and simulations on the leading and subleading
scaling behavior of the polymer renewal time and diffusion constant.Comment: 4 Pages, RevTeX, and 4 PostScript figures include
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