Quantum Stability of Hamiltonian Evolution on a Finsler Manifold

Gil Elgressy, Lawrence Horwitz*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

This paper is a study of a generalization of the quantum Riemannian Hamiltonian evolution, previously analyzed by us, in the geometrization of quantum mechanical evolution in a Finsler geometry. We find results with dynamical equations governing the evolution of the trajectories defined by the expectation values of the position. The analysis appears to provide an underlying geometry described by a geodesic equation, with a connection form with a second term which is an essentially quantum effect. These dynamical equations provide a new geometric approach to the quantum evolution where we suggest a definition for “local instability” in the quantum theory.

Original languageEnglish
Article number1077
JournalSymmetry
Volume16
Issue number8
DOIs
StatePublished - Aug 2024

Keywords

  • Finsler geometry
  • geodesic deviation operator
  • geodesic equations
  • geometrization of quantum evolution
  • local instability
  • quantum effect
  • quantum stability

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