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 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.

Original languageEnglish
Pages (from-to)1313-1367
Number of pages1
JournalJournal of Spectral Theory
Volume11
Issue number3
DOIs
Publication statusPublished - 25 Sept 2021

Keywords

  • 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

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Geometry and Topology

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