Regulated reconstruction of long-time spin--boson dynamics and emergent zero-bias transverse measurement primitive

Abstract

Time--convolutionless (TCL) master equations can break down at long times: time-local perturbative generators develop secular growth in correlation-dominated regimes. We mitigate this by a regulated, partially resummed reconstruction of the dynamical map around a Davies reference semigroup, expressed through a non--Markovian density-matrix correlator C(t) that remains bounded at late times. An exactly solvable rotating-wave benchmark links generator growth to interference-induced near-zeros of the coherence and shows how the reconstruction regulates the map. Applying the method to the unbiased spin--boson model reveals an emergent transverse measurement primitive: bath memory and counter--rotating terms induce phase lock-in that irreversibly erases the relative phase between $σ_x$ eigenspaces on a finite timescale $t_P$, yielding an effective zero-bias transverse ($σ_x$) measurement channel. The selected transverse basis is not assumed a priori; it follows from the reconstructed reduced dynamics. The effect disappears in the rotating-wave approximation and in the Davies weak-coupling limit, demonstrating its non--Markovian interference origin.