Quantum decoherence is considered a core obstacle in quantum computing; therefore, suppressing decoherence is a primary task. Based on the integral representation of the solution to the thermal master equation, we focus on the evolution of decoherence in a degenerate parametric amplifier system described by a known Hamiltonian in a thermal environment. We also investigate the evolution of the photon number distribution, Wigner distribution, and von Neumann entropy in a thermal environment. This work can provide a theoretical reference for experimental studies of degenerate parametric amplifier systems.

We investigate the skin effect and localization characteristics in a one-dimensional non-Hermitian Su−Schrieffer−Heeger (SSH) chain induced by unidirectional Anderson disorder. Based on the theory of the renormalized generalized Brillouin zone, we observe that this system exhibits an energy-dependent skin effect (EDSE), whose directions are strongly dependent on the competitive interplay between the disorder strength and the averaged hopping amplitudes along the two directions. The emergence of EDSE gives rise to multiple localization transitions in this system, manifesting as repeated transitions between different types of EDSE and Anderson localization. Furthermore, the EDSEs differ distinctly between topologically nontrivial and trivial regions. These findings offer novel insights into understanding the role of unidirectional disorder in one-dimensional non-Hermitian SSH structures.