A Hamiltonian for cavity decay

We derive from first principles the phenomenological Hamiltonian for high-Q cavity damping that is often adopted in quantum optics and show that it is a far better approximation than was previously thought. We also obtain an explicit expression for the coupling strength between the discrete cavity q uasimodes and the continuum that reveals the fast-time non-Markovian nature of cavity damping and the limit of validity of the independent reservoir a ssumption.