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| Auteur principal: | |
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| Format: | Recurso digital |
| Langue: | anglais |
| Publié: |
Zenodo
2026
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| Sujets: | |
| Accès en ligne: | https://doi.org/10.5281/zenodo.20395773 |
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- <pre class="language-markup"><code><p>We present a comprehensive numerical and analytical study of the Hamiltonian constraint spectrum for 2+1D quantum gravity with a positive cosmological constant \( \Lambda \propto 1/k^2 \) on a spatial torus. Using the Turaev-Viro topological quantum field theory formalism at roots of unity \( q = e^{\pi i / (k+2)} \), we exactly diagonalize the Hamiltonian operator on the minimal triangulation (up to \( k=12 \)) and on refined 2×2 and 3×2 periodic lattices (at \( k=3 \) and partially at \( k=4,5 \)). The ground state exhibits the predicted topological degeneracy of \( k+1 \), and we confirm the existence of a non-zero physical excitation gap \( \Delta_{\text{phys}} \) for any finite \( \Lambda \). Statistical scaling analysis demonstrates that the physical gap follows a smooth power-law decay, scaling as \( \Delta_{\text{phys}} \propto \Lambda^{0.895 \pm 0.010} \). Importantly, the asymptotic offset is statistically consistent with zero, meaning the gap vanishes in the flat-space limit \( \Lambda \to 0 \). We therefore characterize this as an <strong>IR-regulated gap</strong> or <strong>curvature-induced gap</strong>, not a fundamental topological mass. Analysis of the spatial wavefunctions reveals that the vacuum state acts as a topological condensate favoring an equilibrium curvature, while the first excited state represents a macroscopic quantum "breathing mode" of the spatial geometry.</p></code></pre>