Quantum-Mechanical Harmonic Oscillator under a Random Quadratic Perturbation
B. R. Mollow · Physical Review A · 1970
The behavior of a quantum-mechanical harmonic oscillator under a random perturbation of the form $f(t){q}^{2}$ is discussed. Equations are obtained governing the time evolution of the Wigner function and the weight function for the $P$ representation. The latter function satisfies a fourth-order differential equation, in contrast to the simpler second-order equation obeyed by the Wigner function.