通过马尔可夫浴从可积性到多体量子混沌
From integrability to many-body quantum chaos through a Markovian bath
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中文总结 AI 辅助
本文研究耦合马尔可夫浴的q体SYK模型，发现合适条件下环境可诱导多体量子混沌，为量子多体系统scrambling的调控提供了新途径。
中文摘要 AI 辅助
近期实例证实了一种普遍观点：存在环境时量子混沌总会被抑制。本文表明情况并非总是如此，我们计算了耦合到马尔可夫浴的q体马约拉纳萨赫夫-叶-基塔耶夫（SYK）模型的李雅普诺夫指数。若描述浴的跳变算符为各向同性随机k>2体马约拉纳场，则无论与浴的耦合强度如何，李雅普诺夫指数均为正。有趣的是，这也适用于可积的q=2情形，表明环境可诱导多体量子混沌。此外，对于幺正动力学本征为量子混沌的q>2情形，当k足够大时，李雅普诺夫指数随与浴的耦合强度增大而增加。我们在q=2和大q极限下得到了显式解析结果，研究结果为诱导和控制量子多体系统中的 scrambling（ scrambling 为量子信息领域术语，可译为“ scrambling 过程”或保留原词）产生提供了另一种途径，在量子信息器件设计中具有潜在应用价值。
英文摘要
Recent examples have confirmed the common belief that quantum chaos is always suppressed in the presence of an environment. Here we show that this is not always the case. We compute the Lyapunov exponent of a $q$-body Majorana Sachdev-Ye-Kitaev (SYK) model coupled to a Markovian bath. Provided that the jump operators describing the bath are isotropic random $k > 2$-body Majoranas fields, the Lyapunov exponent is positive for any strength of the coupling to the bath. Interestingly, this also applies to $q=2$ where the SYK is integrable which indicates that many-body quantum chaos can be induced by the environment. Moreover, for $q > 2$, where the unitary dynamics is quantum chaotic, and sufficiently large $k$, the Lyapunov exponent increases with the coupling to the bath. Explicit analytical results are obtained in the $q=2$ and large $q$ limits. Our results put forward an alternate route to induce and control the generation of scrambling in quantum many-body systems which is of potential relevance in the design of quantum information devices.
