Wigner Cat Phases: A finely tunable system for exploring the transition to quantum chaos

arXiv:2512.22169v4 Announce Type: replace Abstract: A quantum mechanical setting consisting of a frozen qubit composed with a fully thermalized chaotic system of N states is proposed, with potential relevance to quantum control. Observing the states of the composed system selectively retaining the states leads to the observation of novel localization in the subsystem. At a tuning parameter of 1.0, implying no selection, the system exhibits Wigner-Dyson level spacing statistics, indicative of quantum chaos. As the tuning parameter is reduced and selection occurs at a cutoff, the nearest-neighbor level spacing distribution develops heavier tails, a signature of suppressed spectral mixing and the emergence of non-thermal dynamics. In these regimes, the eigendensity develops a pronounced "cat-ears" structure, reflecting the formation of spatially localized bimodal eigenstates. These topological features persist without transitioning to Poisson statistics, indicating a transition from quantum chaos to a non-thermal, novel many-body localized (MBL) regime-referred to as Wigner Cat Phases. The proposed mixed random matrix ensemble offers a practical probe for sustaining this novel quantum localization setting. Results from our rigorous spectral statistics analysis show how "cat-ears" form in spectral densities based on the degree of selection or disorder and indicate that gap ratio statistics must be used with caution in detecting the full integrable limit due to the possibility of heavy-tailed Wigner-Dyson distributions.

Abstract:A quantum mechanical setting consisting of a frozen qubit composed with a fully thermalized chaotic system of N states is proposed, with potential relevance to quantum control. Observing the states of the composed system selectively retaining the states leads to the observation of novel localization in the subsystem. At a tuning parameter of 1.0, implying no selection, the system exhibits Wigner-Dyson level spacing statistics, indicative of quantum chaos. As the tuning parameter is reduced and selection occurs at a cutoff, the nearest-neighbor level spacing distribution develops heavier tails, a signature of suppressed spectral mixing and the emergence of non-thermal dynamics. In these regimes, the eigendensity develops a pronounced "cat-ears" structure, reflecting the formation of spatially localized bimodal eigenstates. These topological features persist without transitioning to Poisson statistics, indicating a transition from quantum chaos to a non-thermal, novel many-body localized (MBL) regime-referred to as Wigner Cat Phases. The proposed mixed random matrix ensemble offers a practical probe for sustaining this novel quantum localization setting. Results from our rigorous spectral statistics analysis show how "cat-ears" form in spectral densities based on the degree of selection or disorder and indicate that gap ratio statistics must be used with caution in detecting the full integrable limit due to the possibility of heavy-tailed Wigner-Dyson distributions.

JMP formatted 9 pages 7 figures. Additional analyses: permutation operator, participation distributions and analytic moments ratio, enhanced notation and presentation. Data is released on Zenodo this https URL with associated Python package released this https URL

Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)

arXiv:2512.22169 [quant-ph]

(or arXiv:2512.22169v4 [quant-ph] for this version)

From: Mehmet A. Süzen PhD [view email] [v1] Wed, 17 Dec 2025 11:40:38 UTC (327 KB) [v2] Thu, 12 Feb 2026 08:29:48 UTC (328 KB) [v3] Mon, 9 Mar 2026 16:02:09 UTC (327 KB) [v4] Wed, 10 Jun 2026 14:11:55 UTC (511 KB)

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Wigner Cat Phases: A finely tunable system for exploring the transition to quantum chaos

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