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

Abstract : 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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https://hal.archives-ouvertes.fr/hal-02337447
Contributor : Clotilde Fermanian Kammerer <>
Submitted on : Saturday, November 2, 2019 - 5:51:08 PM
Last modification on : Thursday, November 7, 2019 - 1:15:26 AM

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  • HAL Id : hal-02337447, version 2
  • ARXIV : 1910.14486

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Clotilde Fermanian-Kammerer, Véronique Fischer. QUANTUM EVOLUTION AND SUB-LAPLACIAN OPERATORS ON GROUPS OF HEISENBERG TYPE. 2019. ⟨hal-02337447v2⟩

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