近日，美国达特茅斯学院的Lorenza Viola及其研究团队取得一项新进展。经过不懈努力，他们揭示二次玻色子林德布拉德中有限和无限尺寸稳定性的相互作用。相关研究成果已于2024年9月9日在国际知名学术期刊《物理评论A》上发表。

该研究团队提供了一个框架，用于理解自由玻色子开放多体系统中的动力学亚稳性，其中系统在无限大（热力学）极限下的动力学稳定性特性可能与任何有限大小截断系统的特性截然不同，并可能导致异常瞬态动力学。

通过利用伪谱技术，研究人员将渐近动力学与瞬态动力学之间的差异归因于底层二次玻色子林德布拉德算符（QBL）生成元的非简正性，并展示了两种不同类型的动力学亚稳性可能出现。之前在讨论异常瞬态放大时提及的I型动力学亚稳性QBL[《物理评论快报》127, 245701 (2021)]，在无限大极限下是动力学不稳定的，但在施加开放边界条件后变得稳定。

相比之下，该研究团队在本研究中发现的II型动力学亚稳性QBL，在无限大时是动力学稳定的，但在任意有限系统大小的开放边界条件下变得不稳定。研究人员在耗散以及封闭系统（哈密顿量）设置中展示了这两种亚稳性类型的代表性模型，并分析了它们可能引发的独特行为。

他们证明了动力学亚稳性通过反映无限大（而非实际有限）系统的稳定性阶段的瞬态，在生成纠缠熵的过程中表现出来，并因此与I型系统中出现的超体积纠缠标度直接相关。最后，他们展示了即使在厄米，尤其是高度非简正体系的情况下，无限大QBL的谱特性如何通过共振伪谱模式反映在相应有限QBL的线性响应函数中。

附：英文原文

Title: Interplay of finite- and infinite-size stability in quadratic bosonic Lindbladians

Author: Mariam Ughrelidze, Vincent P. Flynn, Emilio Cobanera, Lorenza Viola

Issue&Volume: 2024/09/09

Abstract: We provide a framework for understanding dynamical metastability in open many-body systems of free bosons, whereby the dynamical stability properties of the system in the infinite-size (thermodynamic) limit may sharply differ from those of any finite-size truncation, and anomalous transient dynamics may arise. By leveraging pseudospectral techniques, we trace the discrepancy between asymptotic and transient dynamics to the non-normality of the underlying quadratic bosonic Lindbladian (QBL) generator and show that two distinct flavors of dynamical metastability can arise. QBLs exhibiting type I dynamical metastability, previously discussed in the context of anomalous transient amplification [Phys. Rev. Lett. 127, 245701 (2021)], are dynamically unstable in the infinite-size limit yet stable once open boundaries are imposed. In contrast, type II dynamically metastable QBLs, which we uncover in this work, are dynamically stable for infinite size but become unstable under open boundary conditions for arbitrary finite system size. We exhibit representative models for both types of metastability in the dissipative, as well as the closed-system (Hamiltonian) settings, and analyze distinctive behavior they can engender. We show that dynamical metastability manifests itself in the generation of entanglement entropy by way of a transient which reflects the stability phase of the infinite (rather than the actual finite) system and, as a result, is directly tied to the emergence of supervolume entanglement scaling in type I systems. Finally, we demonstrate how, even in Hermitian, and especially in highly non-normal regimes, the spectral properties of an infinite-size QBL are reflected in the linear response functions of the corresponding finite QBLs by way of resonant pseudospectral modes.

DOI: 10.1103/PhysRevA.110.032207

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.032207