Year: 2026
Type: preprint
Abstract: We determine the time required for local weak measurements to collapse to one occupied site in an initial superposition of $N$ alternatives in the model of PRA 111, 032217 (2025). For equal initial occupation probabilities and a fixed confidence threshold $1-δ$, we prove $T_N/\ln N\to1/2$ in $L^1$, with time measured in units of the characteristic measurement time $τ_m$ of each detector. We also connect the asymptotic stabilization theorem of that work to a finite measurement: the first site to reach $1-δ$ is the eventual outcome with conditional probability exactly $1-δ$. The result corrects the previously proposed double-logarithmic asymptotic scaling. The finite-range numerical fit does not determine a constant asymptotic correction or a precise finite-$N$ law.
Source: arXiv (Cornell University)
Authors: Van, Truong-Son P., Snoke, David W.
Institution: Ho Chi Minh City University of Technology
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220689264