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

Clotilde Fermanian-Kammerer, Véronique Fischer

OAI: oai:purehost.bath.ac.uk:openaire_cris_publications/e93ba63c-e1d3-4b21-8dd5-a5789e0dda85 • DOI: https://doi.org/10.4171/JST/375

In this paper we analyze the evolution of the time averaged energy densities associatedwith a family of solutions to a Schrödinger equation on a Lie group ofHeisenberg 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.

Abstract harmonic analysis Analysis on nilpotent Lie groups C -algebra theory Evolution of solutions to the Schrodinger 7equation Semi-classical analysis for sub-elliptic operators /dk/atira/pure/subjectarea/asjc/3100/3109 name=Statistical and Nonlinear Physics /dk/atira/pure/subjectarea/asjc/2600/2610 name=Mathematical Physics /dk/atira/pure/subjectarea/asjc/2600/2608 name=Geometry and Topology