OP-QM-004 · Dynamical Origin of Born Statistics
A linearly driven detector’s mean absorbed power is proportional to the envelope modulus squared. Fixed energy per event and negligible leakage, dead time and saturation give an event rate and a conditional position distribution after time/thickness integration. The manuscript also supplies phase-flow equivariance and a nonlinear detector-response expansion. These are established results within their stated conditions.
Based on the final manuscript · 第五章
NEEDS THEORY · Needs theory
Discuss this task01Established results
A linearly driven detector’s mean absorbed power is proportional to the envelope modulus squared. Fixed energy per event and negligible leakage, dead time and saturation give an event rate and a conditional position distribution after time/thickness integration. The manuscript also supplies phase-flow equivariance and a nonlinear detector-response expansion. These are established results within their stated conditions.
Mathematical result
The first follows from near-monochromatic average work after subtracting independent noise; the second additionally requires fixed absorbed energy per event and negligible leakage, dead time and saturation.
Chapter reference: Ch. 5 (5.3.19) and following text · ASD-BOOK-ddbade997b45
Mathematical result
Nonzero total detection rate with stated efficiency, thickness and time window. For normal-flux sampling jn=vn|Ψ|²; normalized squared modulus also requires constant or cancelling vn across compared positions.
Chapter reference: Ch. 5 (5.3.20)–(5.3.21) · ASD-BOOK-ddbade997b45
02Research still required
Build nonlinear competition dynamics for the core, accompanying field and detector array to obtain one record per excitation. Test relaxation toward a Born-type distribution from independently specified initial ensembles, retaining efficiency, normal-flux weighting, time windows and noise calibration.
03The next reproducible deliverable
First deliver a complete response model, conservation accounting, event definition and calibration for one detector. Provide a proof, numerical result or counterexample for single-record exclusivity and initial-state convergence, without using the target probability as a preset sampling rule.
04Scope and research links
Equivariance preserves an already matched initial ensemble; it does not prove convergence from arbitrary ensembles. Uniform efficiency alone also does not remove a varying normal-flow velocity from the count distribution.
detection statistics · master equation · detection statistics · electron solution · master equation · quantum
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Adopted source, conditions and previous versions
第五章 §3.3—§3.4 式（5.3.11）—（5.3.22）；§7
已得结果、继续研究任务与下一份交付；保留原问题 ID、优先级及状态。
Conditions retained in this adoption
- Equivariance preserves an already matched initial ensemble; it does not prove convergence from arbitrary ensembles. Uniform efficiency alone also does not remove a varying normal-flow velocity from the count distribution.
Specific unresolved source issues
- 式（5.3.21）后的通量归一化需保留法向速度权重；相同速度条件方可约去
Source locators: p1943 · p1945 · p1954 · p1955 · p1959 · p1963 · p2305
Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e
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Previous source, retained as history
QM-0accdcbe7725 · Ch. 5 §§3.3–3.4
CH5-ca737ec4e327 · 第五章-出版整理稿.docxca737ec4e327d72c5507bbc8e00295b6e56029c7583ebad8e505cdb9c68c6262
Position within the framework
These links index inputs and research relationships. The completion status of each derivation is specified in its text. Untranslated supporting pages open in Chinese.
Revision history
第五章 · 第五章 §3.3—§3.4 式（5.3.11）—（5.3.22）；§7
This research task is based on the cited final Chinese manuscript. It is not a new canonical result. Both languages use the same source snapshot; original equation numbers and website IDs remain distinct.
Knowledge scopeASD: OP-QM-004 · Dynamical Origin of Born Statistics. OP-QM-004-EN. Version 1.0.0; 2026-10-24. https://asd-physics.org/en/open-problems/quantum/born-statistics. 第五章 §3.3—§3.4 式（5.3.11）—（5.3.22）；§7. Source ASD-BOOK-ddbade997b45.
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