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Article Dans Une Revue Journal of Physics A: Mathematical and Theoretical Année : 2016

Global integration of the Schrödinger equation within the wave operator formalism: the role of the effective Hamiltonian in multidimensional active spaces

Résumé

A global solution of the Schrodinger equation, obtained recently within the wave operator formalism for explicitly time-dependent Hamiltonians (Leclerc and Jolicard 2015 J. Phys. A: Math. Theor. 48 225205), 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.

Dates et versions

hal-01317483 , version 1 (18-05-2016)

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Citer

G. Jolicard, A. Leclerc, D. Viennot, J.P. Killingbeck. Global integration of the Schrödinger equation within the wave operator formalism: the role of the effective Hamiltonian in multidimensional active spaces. Journal of Physics A: Mathematical and Theoretical, 2016, 49 (19), pp.195305. ⟨10.1088/1751-8113/49/19/195305⟩. ⟨hal-01317483⟩
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