耗散量子行走动力学中源于谱几何的自加速
Self acceleration from spectral geometry in dissipative quantum-walk dynamics
AI总结：
本研究利用损耗型光子量子行走实验，证明了一维、二维量子行走中局域激发的瞬态自加速分别与非厄米本征谱围成的面积、体积成正比，揭示了谱拓扑与瞬态动力学的普适对应，为非厄米系统相关现象提供灵敏探测手段。
摘要：
物理系统的动力学行为通常源于其谱特性。在开放系统中，有效的非厄米描述可在复平面上产生丰富的谱结构，相应的动力学也得到显著丰富，但识别和理解二者间的内在关联颇具挑战。本研究利用损耗型光子量子行走，通过实验证明了局域激发的瞬态自加速与非厄米谱拓扑之间的对应关系。我们首先聚焦一维量子行走，发现测得的波函数短时加速度与本征谱围成的面积成正比。随后我们在二维量子行走中揭示了类似的对应关系：自加速与复参数空间中本征谱围成的体积成正比。在两种维度下，瞬态自加速都会过渡到由漂移速度下的恒定流主导的长时行为。本研究结果揭示了谱拓扑与瞬态动力学之间的普适对应关系，为非厄米系统中源于谱几何的现象提供了一种灵敏的探测手段。
英文摘要：
Dynamic behaviors of a physical system often originate from its spectral properties. In open systems, where the effective non-Hermitian description enables a wealth of spectral structures on the complex plane, the concomitant dynamics is significantly enriched, whereas the identification and comprehension of the underlying connections are challenging. Here we experimentally demonstrate the correspondence between the transient self acceleration of local excitations and the non-Hermitian spectral topology using lossy photonic quantum walks. Focusing first on one-dimensional quantum walks, we show that the measured short-time acceleration of the wave function is proportional to the area enclosed by the eigenspectrum. We then reveal similar correspondence in two-dimension quantum walks, where the self acceleration is proportional to the volume enclosed by the eigenspectrum in the complex parameter space. In both dimensions, the transient self acceleration crosses over to a long-time behavior dominated by a constant flow at the drift velocity. Our results unveil the universal correspondence between spectral topology and transient dynamics, and offer a sensitive probe for phenomena in non-Hermitian systems that originate from spectral geometry.
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