12,814 research outputs found
Development of a general time-dependent absorbing potential for the constrained adiabatic trajectory method
The Constrained Adiabatic Trajectory Method (CATM) allows us to compute
solutions of the time-dependent Schr\"odinger equation using the Floquet
formalism and Fourier decomposition, using matrix manipulation within a
non-orthogonal basis set, provided that suitable constraints can be applied to
the initial conditions for the Floquet eigenstate. A general form is derived
for the inherent absorbing potential, which can reproduce any dispersed
boundary conditions. This new artificial potential acting over an additional
time interval transforms any wavefunction into a desired state, with an error
involving exponentially decreasing factors. Thus a CATM propagation can be
separated into several steps to limit the size of the required Fourier basis.
This approach is illustrated by some calculations for the molecular ion
illuminated by a laser pulse.Comment: 8 pages, 7 figure
Fluorescence from a few electrons
Systems containing few Fermions (e.g., electrons) are of great current
interest. Fluorescence occurs when electrons drop from one level to another
without changing spin. Only electron gases in a state of equilibrium are
considered. When the system may exchange electrons with a large reservoir, the
electron-gas fluorescence is easily obtained from the well-known Fermi-Dirac
distribution. But this is not so when the number of electrons in the system is
prevented from varying, as is the case for isolated systems and for systems
that are in thermal contact with electrical insulators such as diamond. Our
accurate expressions rest on the assumption that single-electron energy levels
are evenly spaced, and that energy coupling and spin coupling between electrons
are small. These assumptions are shown to be realistic for many systems.
Fluorescence from short, nearly isolated, quantum wires is predicted to drop
abruptly in the visible, a result not predicted by the Fermi-Dirac
distribution. Our exact formulas are based on restricted and unrestricted
partitions of integers. The method is considerably simpler than the ones
proposed earlier, which are based on second quantization and contour
integration.Comment: 10 pages, 3 figures, RevTe
Statistical Network Analysis for Functional MRI: Summary Networks and Group Comparisons
Comparing weighted networks in neuroscience is hard, because the topological
properties of a given network are necessarily dependent on the number of edges
of that network. This problem arises in the analysis of both weighted and
unweighted networks. The term density is often used in this context, in order
to refer to the mean edge weight of a weighted network, or to the number of
edges in an unweighted one. Comparing families of networks is therefore
statistically difficult because differences in topology are necessarily
associated with differences in density. In this review paper, we consider this
problem from two different perspectives, which include (i) the construction of
summary networks, such as how to compute and visualize the mean network from a
sample of network-valued data points; and (ii) how to test for topological
differences, when two families of networks also exhibit significant differences
in density. In the first instance, we show that the issue of summarizing a
family of networks can be conducted by adopting a mass-univariate approach,
which produces a statistical parametric network (SPN). In the second part of
this review, we then highlight the inherent problems associated with the
comparison of topological functions of families of networks that differ in
density. In particular, we show that a wide range of topological summaries,
such as global efficiency and network modularity are highly sensitive to
differences in density. Moreover, these problems are not restricted to
unweighted metrics, as we demonstrate that the same issues remain present when
considering the weighted versions of these metrics. We conclude by encouraging
caution, when reporting such statistical comparisons, and by emphasizing the
importance of constructing summary networks.Comment: 16 pages, 5 figure
Detection of gravitational wave bursts by interferometric detectors
We study in this paper some filters for the detection of burst-like signals
in the data of interferometric gravitational-wave detectors. We present first
two general (non-linear) filters with no {\it a priori} assumption on the
waveforms to detect. A third filter, a peak correlator, is also introduced and
permits to estimate the gain, when some prior information is known about the
waveforms. We use the catalogue of supernova gravitational-wave signals built
by Zwerger and M\"uller in order to have a benchmark of the performance of each
filter and to compare to the performance of the optimal filter. The three
filters could be a part of an on-line triggering in interferometric
gravitational-wave detectors, specialised in the selection of burst events.Comment: 15 pages, 8 figure
Accurate numerical potential and field in razor-thin axisymmetric discs
We demonstrate the high accuracy of the density splitting method to compute
the gravitational potential and field in the plane of razor-thin, axially
symmetric discs, as preliminarily outlined in Pierens & Hure (2004).
Because residual kernels in Poisson integrals are not C^infinity-class
functions, we use a dynamical space mapping in order to increase the efficiency
of advanced quadrature schemes. In terms of accuracy, results are better by
orders of magnitude than for the classical FFT-methods.Comment: 11 pages, 5 color figures, 2 table
Global integration of the Schr\"odinger equation within the wave operator formalism: The role of the effective Hamiltonian in multidimensional active spaces
A global solution of the Schr\"odinger equation, obtained recently within the
wave operator formalism for explicitly time-dependent Hamiltonians [J. Phys. A:
Math. Theor. 48, 225205 (2015)], is generalized to take into account the case
of multidimensional active spaces. An iterative algorithm is derived to obtain
the Fourier series of the evolution operator issuing from a given
multidimensional active subspace and then the effective Hamiltonian
corresponding to the model space is computed and analysed as a measure of the
cyclic character of the dynamics. Studies of the laser controlled dynamics of
diatomic models clearly show that a multidimensional active space is required
if the wavefunction escapes too far from the initial subspace. A suitable
choice of the multidimensional active space, including the initial and target
states, increases the cyclic character and avoids divergences occuring when
one-dimensional active spaces are used. The method is also proven to be
efficient in describing dissipative processes such as photodissociation.Comment: 33 pages, 11 figure
Constrained Adiabatic Trajectory Method (CATM): a global integrator for explicitly time-dependent Hamiltonians
The Constrained Adiabatic Trajectory Method (CATM) is reexamined as an
integrator for the Schr\"odinger equation. An initial discussion places the
CATM in the context of the different integrators used in the literature for
time-independent or explicitly time-dependent Hamiltonians. The emphasis is put
on adiabatic processes and within this adiabatic framework the interdependence
between the CATM, the wave operator, the Floquet and the (t,t') theories is
presented in detail. Two points are then more particularly analysed and
illustrated by a numerical calculation describing the ion submitted to
a laser pulse. The first point is the ability of the CATM to dilate the
Hamiltonian spectrum and thus to make the perturbative treatment of the
equations defining the wave function possible, possibly by using a Krylov
subspace approach as a complement. The second point is the ability of the CATM
to handle extremely complex time-dependencies, such as those which appear when
interaction representations are used to integrate the system.Comment: 15 pages, 14 figure
- âŠ