165 research outputs found
Calculating vibrational spectra with sum of product basis functions without storing full-dimensional vectors or matrices
We propose an iterative method for computing vibrational spectra that
significantly reduces the memory cost of calculations. It uses a direct product
primitive basis, but does not require storing vectors with as many components
as there are product basis functions. Wavefunctions are represented in a basis
each of whose functions is a sum of products (SOP) and the factorizable
structure of the Hamiltonian is exploited. If the factors of the SOP basis
functions are properly chosen, wavefunctions are linear combinations of a small
number of SOP basis functions. The SOP basis functions are generated using a
shifted block power method. The factors are refined with a rank reduction
algorithm to cap the number of terms in a SOP basis function. The ideas are
tested on a 20-D model Hamiltonian and a realistic CHCN (12 dimensional)
potential. For the 20-D problem, to use a standard direct product iterative
approach one would need to store vectors with about components and
would hence require about GB. With the approach of this
paper only 1 GB of memory is necessary. Results for CHCN agree well with
those of a previous calculation on the same potential.Comment: 15 pages, 6 figure
Global integration of the Schr\"odinger equation: a short iterative scheme within the wave operator formalism using discrete Fourier transforms
A global solution of the Schr\"odinger equation for explicitly time-dependent
Hamiltonians is derived by integrating the non-linear differential equation
associated with the time-dependent wave operator. A fast iterative solution
method is proposed in which, however, numerous integrals over time have to be
evaluated. This internal work is done using a numerical integrator based on
Fast Fourier Transforms (FFT). The case of a transition between two potential
wells of a model molecule driven by intense laser pulses is used as an
illustrative example. This application reveals some interesting features of the
integration technique. Each iteration provides a global approximate solution on
grid points regularly distributed over the full time propagation interval.
Inside the convergence radius, the complete integration is competitive with
standard algorithms, especially when high accuracy is required.Comment: 25 pages, 14 figure
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
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
Controlling vibrational cooling with Zero-Width Resonances: An adiabatic Floquet approach
In molecular photodissociation, some specific combinations of laser
parameters (wavelength and intensity) lead to unexpected Zero-Width Resonances
(ZWR), with in principle infinite lifetimes. Their interest in inducing basic
quenching mechanisms have recently been devised in the laser control of
vibrational cooling through filtration strategies [O. Atabek et al., Phys. Rev.
A87, 031403(R) (2013)]. A full quantum adiabatic control theory based on the
adiabatic Floquet Hamiltonian is developed to show how a laser pulse could be
envelop-shaped and frequency-chirped so as to protect a given initial
vibrational state against dissociation, taking advantage from its continuous
transport on the corresponding ZWR, all along the pulse duration. As compared
with previous control scenarios actually suffering from non-adiabatic
contamination, drastically different and much more efficient filtration goals
are achieved. A semiclassical analysis helps in finding and interpreting a
complete map of ZWRs in the laser parameter plane. In addition, the choice of a
given ZWR path, among the complete series identified by the semiclassical
approach, amounts to be crucial for the cooling scheme, targeting a single
vibrational state population left at the end of the pulse, while all others
have almost completely decayed. The illustrative example, offering the
potentiality to be transposed to other diatomics, is Na2 prepared by
photoassociation in vibrationally hot but translationally and rotationally cold
states.Comment: 15 pages, 14 figure
The interaction between warming and enrichment accelerates foodâweb simplification in freshwater systems
Nutrient enrichment and climate warming threaten freshwater systems. Metabolic theory and the paradox of enrichment predict that both stressors independently can lead to simpler foodâwebs having fewer nodes, shorter foodâchains and lower connectance, but cancel each other's effects when simultaneously present. Yet, these theoretical predictions remain untested in complex natural systems. We inferred the foodâweb structure of 256 lakes and 373 streams from standardized fish community samplings in France. Contrary to theoretical predictions, we found that warming shortens fish foodâchain length and that this effect was magnified in enriched streams and lakes. Additionally, lakes experiencing enrichment exhibit lower connectance in their fish foodâwebs. Our study suggests that warming and enrichment interact to magnify foodâweb simplification in nature, raising further concerns about the fate of freshwater systems as climate change effects will dramatically increase in the coming decades
Teaching Sodium Fast Reactor Technology and Operation for the Present and Future Generations of SFR Users
International audienceThis paper provides a description of the education and training activities related to sodium fast reactors, carried out respectively in the French Sodium and Liquid Metal School (ESML) created in 1975 and located in France (at the CEA Cadarache Research Centre), in the Fast Reactor Operation and Safety School (FROSS) created in 2005 at the Phenix plant, and in the Institut National des Sciences et Techniques Nucle'aires (INSTN). It presents their recent developments and the current collaborations throughout the world with some other nuclear organizations and industrial companies. Owing to these three entities, CEA provides education and training sessions for students, researchers, and operators involved in the operation or development of sodium fast reactors and related experimental facilities. The sum of courses provided by CEA through its sodium school, FROSS, and INSTN organizations is a unique valuable amount of knowledge on sodium fast reactor design, technology, safety and operation experience, decommissioning aspects and practical exercises. It is provided for the national demand and, since the last ten years, it is extensively opened to foreign countries. Over more than 35 years, the ESML, FROSS, and INSTN have demonstrated their flexibility in adapting their courses to the changing demand in the sodium fast reactor field, operation of PHENIX and SUPERPHENIX plants, and decommissioning and dismantling operations. The results of this ambitious and constant strategy are first sharing of knowledge obtained from experimental studies carried out in research laboratories and operational feedback from reactors, secondly standardized information on safety, and finally the creation of a ''sodium community'' that debates, shares the knowledge, and suggests new tracks for a better definition of design and operating rules
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