12,597 research outputs found
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
On the Executability of Interactive Computation
The model of interactive Turing machines (ITMs) has been proposed to
characterise which stream translations are interactively computable; the model
of reactive Turing machines (RTMs) has been proposed to characterise which
behaviours are reactively executable. In this article we provide a comparison
of the two models. We show, on the one hand, that the behaviour exhibited by
ITMs is reactively executable, and, on the other hand, that the stream
translations naturally associated with RTMs are interactively computable. We
conclude from these results that the theory of reactive executability subsumes
the theory of interactive computability. Inspired by the existing model of ITMs
with advice, which provides a model of evolving computation, we also consider
RTMs with advice and we establish that a facility of advice considerably
upgrades the behavioural expressiveness of RTMs: every countable transition
system can be simulated by some RTM with advice up to a fine notion of
behavioural equivalence.Comment: 15 pages, 0 figure
Compact two-electron wave function for bond dissociation and Van der Waals interactions: A natural amplitude assessment
Electron correlations in molecules can be divided in short range dynamical
correlations, long range Van der Waals type interactions and near degeneracy
static correlations. In this work we analyze for a one-dimensional model of a
two-electron system how these three types of correlations can be incorporated
in a simple wave function of restricted functional form consisting of an
orbital product multiplied by a single correlation function
depending on the interelectronic distance . Since the three types of
correlations mentioned lead to different signatures in terms of the natural
orbital (NO) amplitudes in two-electron systems we make an analysis of the wave
function in terms of the NO amplitudes for a model system of a diatomic
molecule. In our numerical implementation we fully optimize the orbitals and
the correlation function on a spatial grid without restrictions on their
functional form. Due to this particular form of the wave function, we can prove
that none of the amplitudes vanishes and moreover that it displays a distinct
sign pattern and a series of avoided crossings as a function of the bond
distance in agreement with the exact solution. This shows that the wave
function Ansatz correctly incorporates the long range Van der Waals
interactions. We further show that the approximate wave function gives an
excellent binding curve and is able to describe static correlations. We show
that in order to do this the correlation function needs to diverge
for large at large internuclear distances while for shorter bond
distances it increases as a function of to a maximum value after which
it decays exponentially. We further give a physical interpretation of this
behavior.Comment: 16 pages, 13 figure
Invariance of the Kohn (sloshing) mode in a conserving theory
It is proven that the center of mass (COM or Kohn) oscillation of a many-body
system in a harmonic trap coincides with the motion of a single particle as
long as conserving approximations are applied to treat the interactions. The
two conditions formulated by Kadanoff and Baym \cite{kb-book} are shown to be
sufficient to preserve the COM mode. The result equally applies to zero and
finite temperature, as well as to nonequilibrium situations, and to the linear
and nonlinear response regimes
Image charge dynamics in time-dependent quantum transport
In this work we investigate the effects of the electron-electron interaction
between a molecular junction and the metallic leads in time-dependent quantum
transport. We employ the recently developed embedded Kadanoff-Baym method
[Phys. Rev. B 80, 115107 (2009)] and show that the molecule-lead interaction
changes substantially the transient and steady-state transport properties. We
first show that the mean-field Hartree-Fock (HF) approximation does not capture
the polarization effects responsible for the renormalization of the molecular
levels neither in nor out of equilibrium. Furthermore, due to the time-local
nature of the HF self-energy there exists a region in parameter space for which
the system does not relax after the switch-on of a bias voltage. These and
other artifacts of the HF approximation disappear when including correlations
at the second-Born or GW levels. Both these approximations contain polarization
diagrams which correctly account for the screening of the charged molecule. We
find that by changing the molecule-lead interaction the ratio between the
screening and relaxation time changes, an effect which must be properly taken
into account in any realistic time-dependent simulation. Another important
finding is that while in equilibrium the molecule-lead interaction is
responsible for a reduction of the HOMO-LUMO gap and for a substantial
redistribution of the spectral weight between the main spectral peaks and the
induced satellite spectrum, in the biased system it can have the opposite
effect, i.e., it sharpens the spectral peaks and opens the HOMO-LUMO gap.Comment: 18 pages, 26 figure
[Review of: Y. Yamanaka, T. Nishio (2006) The Arabian Nights and Orientalism: perspectives from East & West]
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