FIG 1 - uploaded by Georges Jolicard
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Pulse with a total duration of 750a.u., carrier wave frequency 0.335a.u. and intensity 10 13 W.cm −2 .
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The constrained adiabatic trajectory method (CATM) allows us to compute solutions of the time-dependent Schrödinger 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 gen...
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Citations
... We now report results given by using time-dependent wavepacket propagations which take into acount all non-adiabatic exchanges. The wavepacket propagations use the constrained adiabatic trajectory method (CATM) explained in detail in [35,36,37,38]. ...
We present calculations for the action of laser pulses on vibrational transfer within the H2+ and Na2 molecules in the presence of dissipation due to photodissociation of the molecule. The laser fields perform closed loops surrounding exceptional points in the laser parameter plane of intensity and
wavelength. In principle the process should produce controlled vibrational transfers due to an adiabatic flip of the dressed eigenstates. We directly solve the Schr\"odinger equation with the complete time-dependent field instead of using the adiabatic Floquet formalism which initially suggested the design of the laser pulses. Results given by wavepacket propagations disagree with
predictions obtained using the adiabatic hypothesis. Thus we show that there are large non-adiabatic exchanges and that the dissipative character of the dynamics renders the adiabatic flip very difficult to obtain. Using much longer durations than expected from previous studies, the adiabatic flip is only obtained for the Na2 molecule and with strong dissociation.
... Le but de ce chapitre est de trouver une formule générale pour un potentiel absorbant capable de contraindre le vecteur propre de Floquet à une condition aux frontières quelconque [96]. Avec cette amélioration, la méthode CATM devient applicable à la propagation de fonctions d'onde initiales dispersées, et peut également calculer la solution sur des intervalles de temps très longs (impulsion laser longue, train d'impulsions...), puisque ces intervalles peuvent alors être découpés en fragments plus petits [0, T 1 ], [T 1 , T 2 ], . . . . ...
The Constrained Adiabatic Trajectory Method (CATM) allows us to compute global solutions of the time-dependent Schrödinger equation using the Floquet formalism and Fourier decomposition. The dynamical problem is thus transformed into a “static” problem, in the sense that the time will be included in an extended Hilbert space. This approach requires that suitable constraints are applied to the initial conditions for the relevant Floquet eigenstate.The CATM is well suited to the description of systems driven by Hamiltonians with explicit and complicated time variations. This method does not have cumulative errors and the only error sources are the non-completeness of the finite molecular and temporal basis sets used, and the imperfection of the time-dependent absorbing potential which is essential to impose the correct initial conditions. A general form is derived for the absorbing potential,which can reproduce any dispersed boundary conditions. Arguments on adiabatic tracking in the case of nonhermitian Hamiltonians are also presented. We insist on the role of geometric phase factors. The methods are applied to atomic and molecular systems illuminated by intense laser pulses, in connection with molecular control problems. We study several examples : two or three-level atomic models, hydrogen molecular ion, cold sodium molecules.
... In Sec. V, another important point emerges from a numerical problem that we have noted in previous CATM calculations, 16 in the case of a multistep propagation (if the time interval is too long to be treated with only one global step, it can be divided into several large steps treated in succession). Using the absorbing operator sometimes leads to high-frequency parasites characteristic of the Gibbs phenomenon. ...
... In the following we will denote by ⇒ the passage from the time-dependent to the stationary equations induced by this pure adiabatic limit and by =⇒ the non-passage. Evidently one cannot go from the Schrödinger equation (5) to the eigenvalue equation (16) by setting ∂/∂t → 0 in the first one, ...
... Within a one-dimensional (1D) subspace the wave operator representation becomes a column. In a pre-vious article, 16 we have studied the matrix expressions of a general time-dependent absorbing potential V for any initial wave function (x, t = 0). In this framework, the integration of ...
The constrained adiabatic trajectory method (CATM) is reexamined as an integrator for the Schrödinger 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 analyzed and illustrated by a numerical calculation describing the H(2)(+) 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.
In this review, a self-contained (although brief) introduction to electronic structure calculations for single molecule magnet (SMM) properties is provided in conjunction with several contemporary case studies on diverse mononuclear 3d-transition metal complexes. The adequacy of density functional and wavefunction based theories for the prediction and interpretation of magnetic properties is addressed. Furthermore, the connection between calculations and experimental properties is discussed in some detail, in particular with respect to the derivation of spin-Hamiltonian parameters. In addition, we present an outline of the most important features of the most commonly employed quasi-classical spin relaxation model. The presented case studies include Fe, Co and Ni complexes with orbitally degenerate and non-degenerate ground states. The focus is on establishing magneto-structural correlations on both, a qualitative and quantitative level.
A global solution of the Schrödinger 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.
We propose a scheme for preparing a set of bases constituted by equidistant states of a quantum system in prime dimension starting with a single entangled system-ancilla state. The required quantum correlations between the involved systems as a function of the separability constant are analyzed. A comparative analysis of errors in tomographic reconstruction process using bases of different separation is given in the frame of the Fisher information approach.
