We investigate thermalization of a closed chaotic many-body quantum system by combining the Hartree–Fock approach with the Bohigas–Giannoni–Schmit conjecture. The conjecture implies that locally, the residual interaction causes the statistics of eigenvalues and eigenfunctions of the full Hamiltonian to agree with random-matrix predictions. The agreement is confined to an interval Δ (the correlation width). The results are used to calculate Tr(Aρ(t)) . Here ρ(t) is the time-dependent density matrix of the system, and A represents an observable. In the semiclassical regime, the average ⟨Tr(Aρ(t))⟩ decays on the time scale ℏ/Δ toward an asymptotic value. If the energy spread of the system is of order Δ, that value is given by Tr(Aρeq) where ρeq is the density matrix of statistical equilibrium. The correlation width Δ is the central parameter of our approach. We argue that Δ occurs generically in chaotic quantum systems and plays the same central role.

中文翻译：

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封闭混沌多体量子系统的热化

我们通过将 Hartree-Fock 方法与 Bohigas-Giannoni-Schmit 猜想相结合来研究封闭混沌多体量子系统的热化。该猜想意味着，在局部，残差相互作用导致完整哈密顿量的特征值和特征函数的统计与随机矩阵预测一致。该一致性仅限于区间 Δ（相关宽度）。结果用于计算 Tr（Aρ（t）） 。这里 ρ（t） 是系统随时间变化的密度矩阵，并且A代表一个可观察的。在半古典制度下，平均 ⟨Tr（Aρ（t））⟩ 在时间尺度上衰减 ℏ/Δ 趋向于渐近值。如果系统的能量扩散为 Δ 量级，则该值由下式给出 Tr（Aρ情商） 在哪里 ρ情商 是统计平衡的密度矩阵。相关宽度 Δ 是我们方法的核心参数。我们认为 Δ 通常出现在混沌量子系统中并发挥相同的核心作用。