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This research investigates the "zoology" of patterns emerging in quantum systems governed by Lindblad equations, revealing how stable morphologies like stripes persist even as specific witness thresholds cross zero. The study provides a quantitative framework for separating pattern stability from measurement noise, offering new insights into self-organization within open quantum lattices.
A Zoology of Quantum Turing Patterns
arXiv:2608.20151v1 Announce Type: new Abstract: We explore quantum Turing pattern zoology, where the same Lindblad equation supports a morphology atlas of stripes, spots, holes, labyrinths, and defects. The stable stripe species provides a quantitatively controlled case in which morphology and Gaussian witness loss separate parametrically. In particular, visible Turing stripes can remain after two Gaussian witness margins associated with the same $k_*$ mode cross zero in a completely positive Lindblad lattice. The witness thresholds on the exact shell fall as $\mathcal{N}^{-1}$. The stripe nematic threshold tends to a nonzero value at fixed lattice size, time window, and morphology criterion. The ratio of the morphology threshold to either witness threshold therefore grows with $\mathcal{N}$. Imaging and momentum-resolved covariance measurements probe these sectors separately.
Abstract:We explore quantum Turing pattern zoology, where the same Lindblad equation supports a morphology atlas of stripes, spots, holes, labyrinths, and defects. The stable stripe species provides a quantitatively controlled case in which morphology and Gaussian witness loss separate parametrically. In particular, visible Turing stripes can remain after two Gaussian witness margins associated with the same $k_*$ mode cross zero in a completely positive Lindblad lattice. The witness thresholds on the exact shell fall as $\mathcal{N}^{-1}$. The stripe nematic threshold tends to a nonzero value at fixed lattice size, time window, and morphology criterion. The ratio of the morphology threshold to either witness threshold therefore grows with $\mathcal{N}$. Imaging and momentum-resolved covariance measurements probe these sectors separately.
A related work is available at arXiv:2607.26331. Code is publicly available in the author's GitHub repository. this https URL
Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph); Adaptation and Self-Organizing Systems (nlin.AO); Pattern Formation and Solitons (nlin.PS)
arXiv:2608.20151 [quant-ph]
(or arXiv:2608.20151v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2608.20151 arXiv-issued DOI via DataCite (pending registration)
Full text under the publisher's open licence · 170 words
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