Scrambling Separates Superradiance from Quantum Chaos
Abstract
Early studies on the Dicke model linked superradiance to quantum chaos, whereas later anisotropic Dicke and Rabi studies reached apparently conflicting conclusions. We resolve this tension by distinguishing global chaos from local instability. Along the isotropic Dicke path, a sweep at fixed low excitation energy crosses both the superradiant boundary and a nearby chaotic window, explaining the reported correlation. However, the anisotropic Dicke model can be chaotic in the normal phase and regular in the superradiant phase, making superradiance neither necessary nor sufficient for global chaos. A fidelity out-of-time-order correlator (FOTOC), in contrast, probes the local stability of the stationary point selected by the initial wave packet. The superradiant transition destabilizes the origin, whereas a change in anisotropy can restore its stability and create displaced saddles. Wave packets centered at these saddles exhibit exponential FOTOC growth even on a classically regular Dicke energy shell with Poisson statistics. This local sensitivity also enables quantitative spectroscopy: combined with the topology of stationary points and local density of states relations, FOTOC dynamics reconstructs the absolute amplitudes of spectral singularities in both models without fitting the density of states.
Related
- Chaos and scrambling in anisotropic Dicke and Rabi models
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BibTeX
@misc{li2026scrambling,
title = {{Scrambling Separates Superradiance from Quantum Chaos}},
author = {Long-Jie Li and Li-Li Gao and Zi-Cheng Liu and Zi-Min Li and Murray T. Batchelor},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28412},
eprint = {2610.28412},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28412},
}
RIS
TY - UNPB
TI - Scrambling Separates Superradiance from Quantum Chaos
AU - Long-Jie Li
AU - Li-Li Gao
AU - Zi-Cheng Liu
AU - Zi-Min Li
AU - Murray T. Batchelor
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28412
UR - https://arxiv.org/abs/2610.28412
AB - Early studies on the Dicke model linked superradiance to quantum chaos, whereas later anisotropic Dicke and Rabi studies reached apparently conflicting conclusions. We resolve this tension by distinguishing global chaos from local instability. Along the isotropic Dicke path, a sweep at fixed low excitation energy crosses both the superradiant boundary and a nearby chaotic window, explaining the reported correlation. However, the anisotropic Dicke model can be chaotic in the normal phase and regular in the superradiant phase, making superradiance neither necessary nor sufficient for global chaos. A fidelity out-of-time-order correlator (FOTOC), in contrast, probes the local stability of the stationary point selected by the initial wave packet. The superradiant transition destabilizes the origin, whereas a change in anisotropy can restore its stability and create displaced saddles. Wave packets centered at these saddles exhibit exponential FOTOC growth even on a classically regular Dicke energy shell with Poisson statistics. This local sensitivity also enables quantitative spectroscopy: combined with the topology of stationary points and local density of states relations, FOTOC dynamics reconstructs the absolute amplitudes of spectral singularities in both models without fitting the density of states.
ER -