Model specification: Passive capture port

The effective interaction is defined first on one-particle amplitudes $z(t)$ of the memory and incoming amplitudes $u(t)$:

Its quantum evolution is the bosonic second quantization of this one-particle input–output map.

The memory is initially independent of the radiation, spectators, and references. Its specified preparation is the geometric state of mean $m_0\ge 0$. A subsequent storage interval of duration $T_s$ has vacuum attenuation rate ${\kappa }_s\ge 0$, implemented by an independent auxiliary loss port. Define

All phases are defined in a fixed interaction picture. Its clock is the predecessor's asymptotic retarded-time coordinate, up to a fixed translation.