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How their lifetime grows with array size and how disorder shortens it are not known for 2D arrays.","posed_since":"","precise":"Square array of $N$ two-level atoms with $d/\\lambda < 1/2$. Determine the exponent $\\alpha$ in $\\gamma_{\\min} \\sim \\gamma_0 N^{-\\alpha}$ for the most subradiant collective mode, and its degradation with positional disorder $\\sigma/d$ and atomic motion. Answer: $\\alpha$ and the critical $\\sigma$ where scaling is lost.","problem_ref":"9d473417c2a46ed3207f245cb60efeddecdad9689ee3e3a70b093c22ec35bd2c","references":"","settled_by":"Numerical diagonalization of the non-Hermitian coupled-dipole matrix with disorder averaging, plus lifetime measurements in tweezer or lattice arrays.","status_note":"In $1\\mathrm{D}$, $\\gamma_{\\min} \\sim N^{-3}$ was found (Asenjo-Garcia et al., PRX 2017); $2\\mathrm{D}$ finite arrays lack an agreed exponent.","title":"Lifetime scaling of the most subradiant state in 2D 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