Spectral Analysis of Birth-and-Death Processes with and without Killing via Perturbation

Quadratic open quantum harmonic oscillator

“…As an example, if one looks at the action on the abelian algebra of functions of the number operator, one finds a birth-and-death process with quadratic jump rates for which explicit representations for transition probabilities, to the best of our knowledge (see Ref. [25]), are not known.…”