Asymptotic behavior of the quantum harmonic oscillator driven by a random time-dependent electric field (Q1806469)

This article considers a charged quantum particle in a harmonic oscillator driven by a time-dependent electric field, which randomly oscillates. The asymptotic behavior of this system is studied by letting the amplitude of the oscillations tending to 0 as \(\varepsilon\to 0\) and rescaling the time as \(t\varepsilon^{-2}\). This leads to an effective evolution equation of the state vector which corresponds to a stochastic partial differential equation. Transition probabilities for this model are explicitly derived as well as the exact statistical distribution of the energy of the particle.