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Nonclassicality criteria: Quasiprobability distributions and correlation functions

We use the exact calculation of the quantum mechanical, temporal characteristic function $χ(η)$ and the degree of second-order coherence $g^{(2)}(τ)$ for a single-mode, degenerate parametric amplifier for a system in the Gaussian state, viz., a displaced-squeezed thermal state, to study the different criteria for nonclassicality. In particular, we contrast criteria that involve only one-time functions of the dynamical system, for instance, the quasiprobability distribution $P(β)$ of the Glauber-Sudarshan coherent or P-representation of the density of state and the Mandel $Q_{M}(τ)$ parameter, versus the criteria associated with the two-time correlation function $g^{(2)}(τ)$.