Quantum evolution and sub-Laplacian operators on groups of Heisenberg type

  • Clotilde Fermanian-Kammerer

    Université Paris-Est, Créteil, France; Univ Gustave Eiffel, Marne-la-Vallée, France
  • Véronique Fischer

    University Of Bath, UK
Quantum evolution and sub-Laplacian operators on groups of Heisenberg type cover
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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 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.

Cite this article

Clotilde Fermanian-Kammerer, Véronique Fischer, Quantum evolution and sub-Laplacian operators on groups of Heisenberg type. J. Spectr. Theory 11 (2021), no. 3, pp. 1313–1367

DOI 10.4171/JST/375