Energy-localized Egorov theorem for matrix-valued Schrödinger operator without Cordes's hyperbolicity condition
Year: 2025
Type: article
Abstract: We establish a semi-classical Egorov type theorem for a matrix-valued Schr\"{o}dinger operator, frequently arising in important applications, which does not satisfy typically imposed hypotheses, e.g., Cordes's hyperbolicity condition. The proof combines a number of new ideas and the techniques involve $h$-pseudodifferential operator calculus, Riesz projection formula, energy localization, and detailed study of the Heisenberg equations on symbol level using the time-dependent Schr\"{o}dinger equation to justify an auxiliary localized initial condition which allows for a detailed analysis of the Hamiltonian flow and the derivation of key estimates for the solutions to new auxiliary Heisenberg equations.
Source: Figshare
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7019050652
FWCI:
Cites:
Cited by:
Related to: