发表机构
Gakushuin University（学习院大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究证明弱随机扰动的铁磁Ising模型中，典型扰动使所有初始态在宏观可观测量上热化，并在有序相周期边界下形成宏观薛定谔猫态，结合RSTTV理论与Ising大偏差估计。
AI 中文摘要
我们研究了具有弱一般性（高度非局域且多体）随机量子扰动的铁磁Ising模型中的宏观热化。我们证明，单个典型扰动使得指定能量壳层中的每个初始态$|\Phi(0)\rangle$都发生热化：在时间演化态$|\Phi(t)\rangle=e^{-i\widetilde H_Lt}|\Phi(0)\rangle$中测量一大类宏观可观测量，在足够大且典型的时间$t$，以压倒性概率在预定精度内得到其热平衡值。该结果覆盖整个有限温度范围，包括有序相，在有序相中我们采用正边界条件。在有序相采用周期性边界条件下，壳层中的每个能量本征态都被证明是几乎平衡的宏观薛定谔猫态。此外，每个纯初始态在足够大且典型的时间都会变成这样的猫态，其每个分支都处于相应的宏观热平衡中。该证明结合了Roos、Sugimoto、Teufel、Tumulka和Vogel的理论与严格的Ising大偏差估计。
英文摘要
We study macroscopic thermalization in the ferromagnetic Ising model with a weak generic (highly nonlocal and many-body) random quantum perturbation. We prove that a single typical perturbation makes every initial state $|Φ(0)\rangle$ in a specified energy shell thermalize: a measurement of a large class of macroscopic observables in the time-evolved state $|Φ(t)\rangle=e^{-i\widetilde H_Lt}|Φ(0)\rangle$ yields their thermal equilibrium values, within a prescribed precision and with overwhelming probability, at sufficiently large, typical times $t$. The result covers the full finite-temperature range, including the ordered phase, where we use plus boundary conditions. With periodic boundary conditions in the ordered phase, every energy eigenstate in the shell is shown to be an almost balanced macroscopic Schrödinger-cat state. Moreover, every pure initial state becomes such a cat at sufficiently large, typical times, with each branch in the corresponding macroscopic thermal equilibrium. The proof combines the theory of Roos, Sugimoto, Teufel, Tumulka, and Vogel with rigorous Ising large-deviation estimates.
Comments18 pages, no figures. Substantially extended version of arXiv:2409.09395, including results for the full temperature range and higher dimensions, a growing family of macroscopic observables, and the dynamical formation of balanced Schrödinger-cat states
