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    Solving Dicke superradiance analytically: A compendium of methods
    (American Physical Society, 2026-01-01)
    We present several analytical approaches to the Dicke superradiance problem, which involves determining the time evolution of the density operator for an initially inverted ensemble of N identical two-level systems undergoing collective spontaneous emission. This serves as one of the simplest cases of open quantum system dynamics that allows for a fully analytical solution. We explore multiple methods to tackle this problem, yielding a solution valid for any time and any number of emitters. These approaches range from solving coupled rate equations and identifying exceptional points in non-Hermitian evolution to employing combinatorial and probabilistic techniques, as well as utilizing a quantum jump unraveling of the master equation. The analytical solution is expressed as a residue sum obtained from a contour integral in the complex plane, suggesting the possibility of fully analytical solutions for a broader class of open quantum system dynamics problems.
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    Finite Mixtures of Birnbaum-Saunders Distributions Under a Skew Scale-Mixture Framework: Accepted April 2026
    (2026-04-08)
    We introduce finite mixtures of Birnbaum–Saunders distributions generated from the scale-mixture-of-skew-normal family (FM–BS–SMSN) to model positive data with asymmetry, multimodality, heterogeneous tails, and latent heterogeneity. The class includes skew-normal, skew-t, skew-slash, and skew-contaminated normal components. Under a common mixing parameter, we establish identifiability of minimal mixtures and, for two components, derive a criterion for strict unimodality. We develop an ECM algorithm and compute standard errors using the outer-product-of-gradients approximation. Simulations show satisfactory finite-sample performance. An application to NHANES BMI data indicates that the FM–BS–ST model provides the best fit, with the BIC favoring two components.
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