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Short Hartree-Refreshed Pulses: Endpoint Transfer and Post-Pulse Mean-Field Closure

Panasenko

Published Apr 12, 2026• 0 citations

Abstract

This preprint is Paper IV in the research series “Operator Properties and Mathematical Structure of Nonlocal Morphing”. We study short pulse windows in which the phase generator is refreshed along a self-consistent Hartree reference path and the microscopic pulse is driven by the corresponding Hartree-refreshed field lifted to the many-body level. On the pulse window we construct the refreshed reference branch by a local Picard argument, compare the refreshed and frozen microscopic pulse propagators by Duhamel’s formula, and transfer the resulting mismatch to an explicit one-body endpoint defect. We then formulate an abstract restart mechanism showing that any endpoint defect controlled at time τ can be propagated by the standard post-pulse mean-field closure. In the theorem-clean regular regime, and on every fixed post-pulse window [τ, τ+T], we prove that the one-body defect is bounded by C_T·(τ + N^{-1}), provided the frozen regular-regime endpoint scale is available. The main new contribution is the endpoint-transfer mechanism for short Hartree-refreshed pulses: the pulse-window discrepancy is converted into an explicit one-body endpoint defect, and the post-pulse evolution is then handled by a restarted mean-field closure. Thus the frozen bridge remains the leading-order law for short Hartree-refreshed pulses, while the refreshed pulse enters the post-pulse theory only through an explicit endpoint defect. This record is published as a citable preprint in order to provide a public reference point for the companion mean-field arguments used in the present paper and to make the manuscript openly accessible prior to journal submission.

DOI: 10.5281/zenodo.19542177

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