Quantum Stability of Hamiltonian
Evolution on a Finsler Manifold

GIL ELGRESSY; LAWRENCE HORWITZ

doi:10.20944/preprints202405.1475.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 21 May 2024 / Approved: 22 May 2024 / Online: 23 May 2024 (02:55:42 CEST)

This paper is a study of a generalization of the quantum Riemannian Hamiltonian evolution, previously analyzed by us in our work [6], 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 position. The analysis appears to provide an underlying geometry described by a geodesic equation, with 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.

geometrization of quantum mechanical evolution; Finsler geometry; geodesic equation; quantum effect; local instability

Physical Sciences, Mathematical Physics

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Quantum Stability of Hamiltonian Evolution on a Finsler Manifold

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