Section: New Results

Well-posedness and convergence of the Lindblad master equation for a quantum harmonic oscillator with multi-photon drive and damping

Participants: Remi Azouit, Pierre Rouchon, Alain Sarlette

The main motivation for this result was to finally treat in a rigorous way the convergence of a non-trivial infinite-dimensional system (harmonic oscillator Hilbert space) that is of relevance to physicists. The essential tools for this proof are the choice of an appropriate metric leading to contraction, and the Hille-Yosida theorem ensuring well-posedness of the problem. This could be a valuable basis towards a more general, yet easily invocable argument to treat the many other infinite-dimensional quantum dynamics which intuitively "should never escape towards infinite energies."

This result has been published in [13].