Windowed Actions and Finite-Domain Localization Across Five Quantum Experiments

A smooth window function ♢(x)∈[0,1] that restricts a field-theory action to a finite spacetime domain generates a common conservation structure across diverse experimentally realized finite-time quantum phenomena. Applying the windowed action principle yields windowed Noether identities of the form ∂μ(♢Jμ)=0: exact conservation of the windowed current, with apparent non-conservation of local currents confined to the boundary layer where ∂μ♢≠0. This boundary-layer structure is mathematically identical to open-system flux terms in decoherence theory. The formalism is applied to five experimentally established settings: the timelike Unruh effect in trapped-ion detectors, the dynamical Casimir effect in superconducting circuits, quench-induced currents in cold-atom systems, ultrafast coherent control with femtosecond laser pulses, and finite-time scattering theory. In each case, the experimentally specified control window—switching function, drive envelope, quench ramp, pulse envelope, or scattering window—is shown to be an instance of the same formal object ♢, and the windowed Noether identity is derived for each setting in this unified form for the first time. Two results are new: the cross-case identification of all five control functions as instances of ♢ under a single formalism, and the formal consequence that systems with the same ungated Hamiltonian operator content but different temporal control profiles generically produce inequivalent unitary evolutions, formulated here as a structural consequence of explicit domain specification. Here, ♢ is fixed by the experimentally specified control protocol and is neither a new dynamical degree of freedom nor an additional fit function. Although it may be absorbed algebraically into a time-dependent coupling or interaction Hamiltonian, retaining it explicitly exposes the common finite-domain conservation structure across the five settings. In the purely temporal measurement limit, g(t)=λ♢(t) reproduces the standard von Neumann system–apparatus coupling, while the action-level extension to ♢(x) permits finite spacetime support and makes the associated boundary-supported current balance explicit.