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Article Dans Une Revue Journal of Spectral Theory Année : 2021

QUANTUM EVOLUTION AND SUB-LAPLACIAN OPERATORS ON GROUPS OF HEISENBERG TYPE

Résumé

In this paper we analyze the evolution of the time averaged energy densities associated with a family of solutions to a Schrödinger equation on a Lie group of Heisenberg type. We use a semi-classical approach adapted to the stratified structure of the group and describe the semi-classical measures (also called quantum limits) that are associated with this family. This allows us to prove an Egorov's type Theorem describing the quantum evolution of a pseudodifferential semi-classical operator through the semi-group generated by a sub-Laplacian.
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Dates et versions

hal-02337447 , version 1 (29-10-2019)
hal-02337447 , version 2 (02-11-2019)

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Clotilde Fermanian-Kammerer, Véronique Fischer. QUANTUM EVOLUTION AND SUB-LAPLACIAN OPERATORS ON GROUPS OF HEISENBERG TYPE. Journal of Spectral Theory, 2021. ⟨hal-02337447v2⟩
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