Independent motionless two-level atoms emit thermal light statistics only when atom number and coherent-to-incoherent emission ratio meet specific conditions for each correlation order.
Isserlis, On a formula for the product-moment coefficient of any order of a normal frequency distribution in any number of variables, Biometrika12, 134 (1918)
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Deviations from thermal light statistics in ensembles of independent two-level emitters
Independent motionless two-level atoms emit thermal light statistics only when atom number and coherent-to-incoherent emission ratio meet specific conditions for each correlation order.