驱动非厄米系统中的放大记忆与有限时间正则性

中文摘要 AI 辅助

我们研究了有限时间驱动的非厄米费米子动力学中破缺谱与奇异点的作用。为此，我们计算了Nambu双正交关联矩阵。非平衡配对Kitaev链作为我们的具体实现。瞬态通过破缺谱区域会放大制备记忆。当最终哈密顿量回到实谱区域时，该效应仍然存在。负失衡迫使静态端点态具有谱非正性。我们通过减去这一基线来隔离真实的驱动历史，留下的超出部分严格受累积虚能量作用控制，并在整个斜坡后时间窗口内持续存在。一个连接的纵向关联反映了这一物理。其慢斜坡增长追踪相应的加倍作用。如果驱动在破缺谱区域内停止，不稳定扇区反而在斜坡后继续放大。奇异点产生不同的物理。有限时间传播子和子系统关联矩阵在奇异端点附近完全保持正则，即使准粒子间隙表现出其特征性的平方根闭合。这种有限时间正则性反映了矩阵演化在端点参数中的解析性；可对角化端点并非严格必需。一个发散的长时间交叉最终揭示了奇异尺度。我们恰好将驱动停止在奇异点，发现关联投影子和连接的纵向关联共享一个相同的弹道前沿。子系统饱和长度建立了一个不同但可比较的空间尺度。记忆和奇异端点标度在测试的负失衡范围内没有发散。记忆标度由驱动固定，对实谱最终端点的具体选择不敏感。

英文摘要

We study the roles of broken spectra and exceptional points in finite-time driven non-Hermitian fermionic dynamics. We compute the Nambu biorthogonal correlation matrix for this purpose. The imbalanced-pairing Kitaev chain serves as our concrete realization. Transient passage through a broken-spectrum region amplifies preparation memory. The effect survives when the final Hamiltonian returns to a real-spectrum regime. Negative imbalance forces spectral nonpositivity in the static endpoint state. We isolate the genuine drive history by subtracting out this baseline, leaving an excess that is strictly controlled by the accumulated imaginary-energy action and persists over the entire post-ramp time window. A connected longitudinal correlation mirrors this physics. Its slow-ramp growth tracks the corresponding doubled action. Unstable sectors instead continue amplifying post-ramp if the drive halts inside the broken-spectrum region. Exceptional points yield distinct physics. The finite-time propagator and subsystem correlation matrix remain entirely regular near an exceptional endpoint, even as the quasiparticle gap exhibits its characteristic square-root closing. This finite-time regularity reflects the analyticity of the matrix evolution in the endpoint parameter; a diagonalizable endpoint is strictly not required. A diverging long-time crossover eventually reveals the exceptional scale. We halt the drive exactly at the exceptional point to find that the correlation projector and the connected longitudinal correlation share an identical ballisti front. The subsystem saturation length establishes a distinct but comparable spatial scale. Memory and exceptional-endpoint scalings show no divergence across the tested negative-imbalance range. Memory scaling is fixed by the drive and remains insensitive to the specific choice of real-spectrum final endpoint.

发表机构

• Beijing Institute of Mathematical Sciences and Applications (BIMSA)（北京数学与应用研究所）
• Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS)（基础科学高等研究院物理系）
• School of Quantum Physics and Matter Science, Institute for Research in Fundamental Sciences (IPM)（基本科学研究院量子物理与物质科学学院）
• Max Planck Institute for the Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）

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