bibkey: kato1950adiabatic authors: Tosio Kato year: 1950 title: On the Adiabatic Theorem of Quantum Mechanics doi: 10.1143/JPSJ.5.435 claim: A smoothly varying spectral projection admits adiabatic parallel transport generated by its projector derivative. strata_touched:

• D5/S3/Quantum/Transport/MatrixUnitGenerator license: citation-only triage: anchor

Projector transport and the complete logical algebra

Journal of the Physical Society of Japan 5(6), 435-439 (1950). Primary publication metadata: https://www.jstage.jst.go.jp/browse/jpsj/5/6/_contents/-char/ja DOI: https://doi.org/10.1143/JPSJ.5.435

Kato’s adiabatic work is the classical source for projector-based adiabatic transport. In the finite skew-adjoint convention, the projector generator is [Pdot,P]. The present module gives a self-contained algebraic construction for a moving full system of logical matrix units:

K = (1/d) sum_ij D_ij F_ji - P Pdot,
P = sum_i F_ii,  Pdot = sum_i D_ii.

The differentiated matrix-unit and adjoint laws imply K* = -K and [K,F_ij] = D_ij. For d=1 this reduces to the projector mechanism. For d>1 a constant support can still contain a moving logical algebra, so transporting P alone cannot determine every logical operation.

The real-path adapter derives the tangent laws from actual entrywise HasDerivAt hypotheses. The general full-matrix-unit averaging formula is not attributed as a theorem of Kato’s paper. No new universal adiabatic estimate, Dyson-series convergence, parameter-bundle trivialization, or physical control cost theorem is claimed by the algebraic declarations.

Verified locator

• DOI: https://doi.org/10.1143/JPSJ.5.435 resolves to the Journal of the Physical Society of Japan article titled above. The publisher page returned HTTP 403 here.
• The citation is for projector-based adiabatic transport. The finite matrix-unit generator in this note is the repository’s separate construction.