孤立量子多体系统中的涌现经典性与波函数分支
Emergent classicality and wavefunction branching in an isolated quantum many-body system
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中文总结 AI 辅助
本文证明孤立多体系统中经典性可从内部涌现：通过集体自旋与微观置换扇区的相互作用，推导出有效Lindblad方程，并在热力学极限下收敛为经典混沌Fokker-Planck方程，波函数分支形成正交记录，实现量子-经典对应。
中文摘要 AI 辅助
量子系统中的退相干通常被建模为与外部环境相互作用的结果。然而，这种描述排除了孤立的多体系统，而后者在宏观尺度上也被预期表现出经典行为。在孤立系统中，退相干必须从宏观描述不可见的微观自由度内部涌现。在这里，我们明确展示了经典性可以以这种方式涌现。我们考虑一个由 $N$ 个量子比特组成的弱无序、$3$-局域混沌踢顶模型，其中集体自旋扇区作为宏观描述，而微观置换扇区充当内部浴，使集体自旋扇区退相干。从封闭的幺正动力学出发，我们推导并数值确认了集体自旋变量的有效 Lindblad 方程。在热力学极限下，这些约化动力学收敛到球面相空间上具有极小扩散的经典混沌 Fokker-Planck 方程，从而产生超越 Ehrenfest 时间的量子-经典对应。混沌动力学将纯多体波函数演化为与不同经典轨迹相关的连续分支分量。这些分支在置换扇区中获得近乎正交的微观记录，阻止量子干涉并确保相应的历史保持一致。
英文摘要
Decoherence in quantum systems is conventionally modeled as the effect of interactions with an external environment. However, such a prescription excludes isolated many-body systems, which are also expected to display classical behavior at macroscopic scales. In isolated systems, decoherence must emerge internally from microscopic degrees of freedom that are invisible to the macroscopic description. Here we explicitly show that classicality can emerge in such a fashion. We consider a weakly disordered, $3$-local chaotic kicked top of $N$ qubits, where the collective spin sector serves as the macroscopic description, while the microscopic permutation sector acts as an internal bath, decohering the collective spin sector. Starting from closed unitary dynamics, we derive and numerically confirm an effective Lindblad equation for the collective spin variables. In the thermodynamic limit these reduced dynamics converge to a classical chaotic Fokker--Planck equation with vanishingly small diffusion on the spherical phase space, producing a quantum-classical correspondence beyond the Ehrenfest time. The chaotic dynamics evolve the pure many-body wavefunction into continuously branching components associated with distinct classical trajectories. These branches acquire nearly orthogonal microscopic records in the permutation sector, preventing quantum interferences and ensuring the corresponding histories remain consistent.
发表机构
- Center for Theoretical Physics — a Leinweber Institute, Massachusetts Institute of Technology（麻省理工学院理论物理中心）
- Harvard University（哈佛大学）
- California Institute of Technology（加州理工学院）
- NTT Research, Inc.（日本电报电话公司研究所）
机构由 AI 辅助整理，请以论文原文为准。
