Pair Creation in Space–Time Modulated Media III: Loss, Gain, Noise and Nonlinearity

A space–time symmetric medium creates photon pairs only in the channels its sector rule allows, and a single-harmonic modulation of its inertial term keeps the even degenerate channels closed. This article asks which closures survive loss, gain, noise and a nonlinear response. A loss that commutes with the symmetry keeps the sectors, and a forbidden channel still crosses exactly, inside the unit circle. A static loss keeps the silent zero mode: the periodic solutions still come in conjugate halves, and an isolated pair whose determinant falls below 1 cannot pass the multiplier +1. The first-order coupling of a crossing pair by a static, reciprocal loss that breaks the symmetry is anti-Hermitian. At a degenerate channel it is a total derivative and vanishes, and at a sum channel it repels the pair along the unit circle. Such a passive loss opens no forbidden pair channel at first order, whatever its shape, although the same loss breaks reciprocity linearly. A loss that follows the modulation, a nonreciprocal loss matrix and a permittivity defect open forbidden channels linearly; a passive loss that follows the modulation keeps them below threshold, and gain opens them. The noise of a symmetric loss keeps the block structure of the covariance at every temperature, so forbidden channels carry neither vacuum nor thermal pairs. The noise of a symmetry-breaking loss correlates the sectors at first order. A slab emits thermally from each face what the same face of its twin absorbs, harmonic by harmonic, and a grating whose period runs along its faces is its own twin. A nonlinearity that commutes with the symmetry keeps the sector of a periodic saturated orbit, also with a depleted pump; a Kerr-type one that does not drives the opposite sector in proportion to its strength. Design rules and refutable predictions follow.