Classically Forbidden Signatures of Quantum Coherence in the Mesoscopic Lipkin-Meshkov-Glick Model

Quantum Physics [Submitted on 19 Apr 2026] Classically Forbidden Signatures of Quantum Coherence in the Mesoscopic Lipkin-Meshkov-Glick Model Stavros Mouslopoulos We derive strict quantitative conditions under which a collective quantum system of N~370 spins exhibits classically forbidden temporal correlations in a spinor Bose-Einstein condensate (BEC). The Lipkin-Meshkov-Glick (LMG) model near its Z_2-breaking quantum critical point supports a mesoscopic superposition a|P> + b|R> of two macroscopic ordered phases (|P>: m_z ~ +m_*; |R>: m_z ~ -m_*) at the Goldilocks crossover N ~ N_c, where the tunnel splitting equals k_B T and macroscopic susceptibility chi ~ N coexists with finite quantum coherence. We establish two quantum-discriminating predictions. P4 (Landau-Zener crossover, proposed discriminator): quantum tunnelling drives P_error -> 0 exponentially with quench time, while the classically non-ergodic system remains kinetically frozen at P_error -> 1 - a parametrically large, computable separation that rests on a specific kinetic foil. P5 (Leggett--Garg inequality violation, strictly model-independent): K_3 > 1 is forbidden by macrorealism for all classical models satisfying non-invasive measurability. A five-level Lindblad simulation yields K_3 ~ 1.32 and dephasing threshold gamma_phi < 0.289 s^{-1} at the BEC target (gamma_phi = 0.05 s^{-1}, N = 370, Gamma/J = 0.95) - a margin of 8.8x above the optimal measurement interval, well within current experimental reach. The threshold has a precise physical origin in the emergent collective Z_2 symmetry: exact parity eliminates the dominant dephasing cross-term and renders the LGI correlator immune to T_1 population mixing without requiring ground-state preparation (2.35x improvement over the naive mean-field estimate); constructive dynamical phase alignment of higher odd-parity states at the benchmark parameters contributes a further 2.47x. All results are reproducible from the provided self-tested Python code. Subjects: Quantum Physics (quant-ph); High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th) Cite as: arXiv:2604.18638 [quant-ph]   (or arXiv:2604.18638v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.18638 Focus to learn more Submission history From: Stavros Mouslopoulos Dr [view email] [v1] Sun, 19 Apr 2026 05:45:56 UTC (50 KB) Access Paper: view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: hep-ph hep-th References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)