ResearchPod Summary
Traditional studies of quantum chaos and transport typically rely on microscopic disorder or many-body interactions to generate complex dynamics. This paper investigates whether these phenomena can arise solely from the geometric arrangement of a graph. Specifically, the authors examine non-interacting quantum particles on random locally tree-like layered (RLTL) graphs, where the randomness is encoded in the connections between layers rather than in the hopping amplitudes themselves.
The authors model the system as a tight-binding Hamiltonian on RLTL graphs, which can be viewed as multi-component one-dimensional chains with random links between components. They analyze two distinct regimes: an effective two-dimensional case where the number of sites per layer scales with the number of layers, and a quasi-one-dimensional limit where the number of sites per layer remains constant. They employ level-spacing statistics, inverse participation ratios (IPRs), wavepacket dynamics, and entanglement entropy to characterize the spectral properties and transport behavior.
In the two-dimensional regime, the system exhibits robust quantum chaos, characterized by Wigner-Dyson level repulsion, delocalized eigenstates, and diffusive transport. Conversely, in the quasi-one-dimensional limit, the system displays a coexistence of localized and delocalized states. While the localized states suppress level repulsion, the delocalized states—identified as Bloch waves—drive ballistic transport. The study confirms that geometric randomness is a fundamental mechanism capable of tuning quantum chaos and transport properties independently of traditional disorder.
This work provides a new perspective on the origins of quantum chaos, showing that structural geometry alone can drive complex dynamics. By mapping these properties to graph dimensionality, the authors offer a framework for understanding how transport transitions occur in non-interacting systems, which has implications for both condensed matter physics and the study of many-body localization in higher-dimensional Fock-space graphs.
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