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Dynamique quantique en temps longs d'états cohérents dans un champ magnétique fort

Abstract : The propagation of coherent states was extensively studied over past decades. A coherent state is the quantum version of a classical particle. The trajectory of a charged particle under strong magnetic field, that is a non-vanishing field, is given by the center guide motion : it is high speeds oscillations around a virtual center that moves slowly along the field lines of the magnetic field. The aim of this thesis is the study of the quantum translation of this. It is well-known that for short times, i.e. bounded times with respect to the semiclassical parameter h, the dynamics of such a state is given by the classical trajectory of the associated particle. The thing is to study the dynamics of coherent states for long times, that are times going to infinite as h goes to 0. For low energy coherent states, using normal form and magnetic elliptical regularity results, we prove the following long time magnetic propagation result. A coherent state under strong magnetic field is propagated as a sum of coherent states following the same dynamics, but with different speeds.
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Grégory Boil. Dynamique quantique en temps longs d'états cohérents dans un champ magnétique fort. Physique mathématique [math-ph]. Université Rennes 1, 2018. Français. ⟨NNT : 2018REN1S061⟩. ⟨tel-02064166⟩

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