Abstract We prove local in time, uniform in N, estimates for the solutions , Λ, and Γ of a coupled system of Hartree–Fock–Bogoliubov type with interaction potential , with and v a Schwartz function (satisfying additional technical requirements). The initial conditions are general functions in a Sobolev-type space, and the expected correlations in Λ develop dynamically in time. As shown in our previous work, as well as the work of Chong (both in the case ), using the conserved quantities of the system of equations, this type of local in time estimates can be extended globally. Also, they can be used to derive Fock space estimates for the approximation of the exact evolution of a Bosonic system by quasi-free states of the form . This will be addressed in detail in future work.

中文翻译：

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Hartree-Fock-Bogoliubov 型玻色子系统的 N 估计值一致

摘要 我们证明了在时间上是局部的，在 N 中是一致的，对具有相互作用势的 Hartree-Fock-Bogoliubov 型耦合系统的解 、Λ 和 Γ 的估计，具有 和 va Schwartz 函数（满足附加技术要求）。初始条件是 Sobolev 型空间中的一般函数，Λ 中的预期相关性随时间动态发展。正如我们之前的工作以及 Chong 的工作（均在 ）中所示，使用方程组的守恒量，这种局部时间估计可以在全球范围内扩展。此外，它们可用于推导出 Fock 空间估计，以通过 形式的准自由状态近似玻色系统的精确演化。这将在未来的工作中详细解决。