In this paper, global well-posedness of the non-Markovian Unruh–Zurek and Hu–Paz–Zhang master equations with nonlinear electrostatic coupling is demonstrated. They both consist of a Wigner–Poisson like equation subjected to a dissipative Fokker–Planck mechanism with time-dependent coefficients of integral type, which makes necessary to take into account the full history of the open quantum system under consideration to describe its present state. From a mathematical viewpoint this feature makes particularly elaborated the calculation of the propagators that take part of the corresponding mild formulations, as well as produces rather strong decays near the initial time (\(t=0\)) of the magnitudes involved, which would be reflected in the subsequent derivation of a priori estimates and a significant lack of Sobolev regularity when compared with their Markovian counterparts. The existence of local-in-time solutions is deduced from a Banach fixed point argument, while global solvability follows from appropriate kinetic energy estimates.

在本文中，证明了具有非线性静电耦合的非Markovian Unruh-Zurek和Hu-Paz-Zhang主方程的整体适定性。它们都由服从耗散Fokker-Planck机理的Wigner-Poisson方程组成，具有随时间变化的整数型系数，这有必要考虑所考虑的开放量子系统的完整历史来描述其当前状态。从数学角度来看，此功能特别详细地计算了采用相应温和配方一部分的传播子的计算，并且在初始时间附近会产生相当强的衰减（\（t = 0 \））所涉及的数量级，这将反映在随后的先验估计推导中，并且与马尔可夫模型相比，索伯列夫规则性明显不足。实时解决方案的存在是根据Banach不动点论证得出的，而全局可解性则是根据适当的动能估算得出的。