Self-sustained harmonic oscillators in the quantum regime*

Self-sustained harmonic oscillators play an important role in the self-organization of dynamical classical systems. Recent work [1] clarified the classical-to-quantum correspondence for three different types of oscillators, namely the Raleigh oscillator, the van der Pol oscillator, and the Raleigh-van der Pol oscillator. In the classical regime, these oscillators are characterized by non-linearities that are proportional to the square of the velocity, proportional to the square of the position, and proportional to the kinetic energy, respectively. Using a master equation-based formulation, this contribution will present results for the quantum dynamics of self-sustained oscillators. Comparisons with classical trajectory calculations will also be presented. [1] L.B. Arosh, M.C. Cross, and R. Lifshitz, Physical Review Research 3, 013130 (2021).