由相互作用量子记忆驱动的酉演化：封闭量子系统利用其状态历史自我引导
Unitary Evolutions Sourced By Interacting Quantum Memories: Closed Quantum Systems Directing Themselves Using Their State Histories
AI总结：
本文提出由量子记忆相互作用驱动的酉演化框架，通过非局域非线性方程实现系统自我引导，并分类了丰富的相图与相变行为。
摘要：
我们提出、阐述并研究新型量子系统及行为相，在这些系统中，系统记忆的瞬时选择相互作用，以产生系统内部的相互作用和酉时间演化。在这种封闭系统中，酉演化算符通过由系统的“经验”（即其量子态历史）重新构造而逐时刻更新。生成这些酉演化的“量子记忆制造”哈密顿量（QMM-Hs）是厄米非局域时间算符，由封闭系统或其任意子系统的任意选择的从过去到现在的密度算符组成。这类时间演化由新型非局域非线性冯·诺依曼和薛定谔方程描述。我们证明，非平凡的纯QMM酉演化是“稳健非马尔可夫的”，这意味着所选量子记忆之间的最大时间距离必须超过由相互作用耦合设定的有限下界。在一般性表述和考虑之后，我们聚焦于一项足够复杂的任务：获取并分类由一阶至三阶多项式QMM-Hs（由一、二和三个量子记忆构成）生成的单量子比特纯态演化的行为相。由QMM-Hs产生的行为吸引子通过使用QMM两点函数可观测量作为自然探针，结合解析方法和广泛数值分析进行表征和分类。QMM相图被证明极其丰富，具有多种前所未有的酉演化类别，展现出物理上显著的行为。此外，我们表明QMM相互作用引起新颖的纯内部动力学相变。最后，我们提出独立的基础和应用领域，在这些领域中，所提出的“经验中心”酉演化可以自然且有利地应用。
英文摘要：
We propose, formulate and examine novel quantum systems and behavioral phases in which momentary choices of the system's memories interact in order to source the internal interactions and unitary time evolutions of the system. In a closed system of the kind, the unitary evolution operator is updated, moment by moment, by being remade out of the system's `experience', that is, its quantum state history. The `Quantum Memory Made' Hamiltonians (QMM-Hs) which generate these unitary evolutions are Hermitian nonlocal-in-time operators composed of arbitrarily-chosen past-until-present density operators of the closed system or its arbitrary subsystems. The time evolutions of the kind are described by novel nonlocal nonlinear von Neumann and Schrödinger equations. We establish that nontrivial Purely-QMM unitary evolutions are `Robustly Non-Markovian', meaning that the maximum temporal distances between the chosen quantum memories must exceed finite lower bounds which are set by the interaction couplings. After general formulation and considerations, we focus on the sufficiently-involved task of obtaining and classifying behavioral phases of one-qubit pure-state evolutions generated by first-to-third order polynomial QMM-Hs made out of one, two and three quantum memories. The behavioral attractors resulted from QMM-Hs are characterized and classified using QMM two-point-function observables as the natural probes, upon combining analytical methods with extensive numerical analyses. The QMM phase diagrams are shown to be outstandingly rich, having diverse classes of unprecedented unitary evolutions with physically remarkable behaviors. Moreover, we show that QMM interactions cause novel purely-internal dynamical phase transitions. Finally, we suggest independent fundamental and applied domains where the proposed `Experience Centric' Unitary Evolutions can be applied natuarlly and advantageously.
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