Quantum Evolution And Sub-laplacian Operators On Groups Of Heisenberg Type

Clotilde Fermanian-Kammerer; Véronique Fischer

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arXiv · 1910.14486

Quantum Evolution And Sub-laplacian Operators On Groups Of Heisenberg Type

Clotilde Fermanian-Kammerer·Véronique Fischer

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Abstract

In this paper we analyze the evolution of the time averaged energy densities associated with a family of solutions to a Schr{\"o}dinger 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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Clotilde Fermanian-Kammerer, Véronique Fischer. 2019-10-31. Quantum Evolution And Sub-laplacian Operators On Groups Of Heisenberg Type. https://arxiv.org/abs/1910.14486

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