Keldysh Approach to Driven-Dissipative Phase Transition in a Kerr Oscillator*

We study open quantum many-body physics using a minimal model, namely a Kerr non-linear oscillator subject to two-photon driving and single-photon dissipation. Exact solutions are provided by coherently tying together several methods such as mean field theory, exact diagonalization, and Keldysh field theory. Spectral properties are given analytically using the Keldysh formalism (both the spectral function of the oscillator and the power-spectrum of the emitted photons). Then using the quantum Langevin equation, finite-size scaling is calculated exactly.

Ref: arXiv:2007.01422