thus, differently from what obtained in the classical case, the power spectral density is not exactly frequency-symmetric in the quantum limit. Consistently, ⟨ ⟨ x ^ ^ ( t ) x ^ ^ ( 0 ) ⟩ ⟩ has an imaginary part originating from the commutation rules of operators. The additional " + 1 " term in the expression of S x ( ω ω ) at positive frequencies can also be thought of as linked to spontaneous emission. An often cited result is also the symmetrized power spectral density