Clár na nÁbhar: :: Library Catalog

Sábháilte in:

Sonraí bibleagrafaíochta
Príomhchruthaitheoir:	Blanchette, Douglas
Formáid:	Recurso digital
Teanga:
Foilsithe / Cruthaithe:	Zenodo 2026
Ábhair:	Ammann-Beenker lattice, quasicrystal, Bogoliubov-de Gennes, topological defects, Jackiw-Rossi model, domain-wall mass, spectral flow, Majorana zero modes, Dirac operator, phason dynamics, cut-and-project method, E8 geometry, Coxeter projection, perpendicular space, topological matter, condensed matter physics, quantum geometry, localization, critical states, computational physics, lattice gauge theory, synthetic vacuum, Pure Monist Formulation, Collaborative Science Framework
Rochtain ar líne:	https://doi.org/10.5281/zenodo.19123146
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Clár na nÁbhar:

Synthetic Vacuum Laboratory: Rung 1 — Defect Physics and Topological Access on the Ammann–Beenker Lattice This report presents thirteen sequential computational experiments (E01–E13) investigating defect physics on a two-dimensional Ammann–Beenker (AB) quasicrystal equipped with a Dirac–Bogoliubov–de Gennes (BdG) operator. The study forms the first rung of a structured validation program for the Pure Monist Formulation, while also providing standalone results relevant to quasicrystal physics, topological matter, and geometric approaches to field theory. Several findings are of independent interest. Spectral flow is demonstrated on periodic AB approximants in symmetry class D, with crossing count invariant under system size—extending prior open-boundary analyses to a periodic setting. The Jackiw–Rossi and domain-wall defect constructions are shown to form a continuous family parameterized by the ratio m0/Δ0m_0 / \Delta_0m0/Δ0, with a crossover near m0/Δ0≈0.02m_0 / \Delta_0 \approx 0.02m0/Δ0≈0.02, unifying two commonly treated architectures within a single geometric framework. Under Coxeter projection, the E8E_8E8 root system exhibits complete vector–spinor shell separation in perpendicular space, with the 112 vector roots and 128 spinor roots occupying distinct radial shells; this separation is explicitly tabulated here. A quantitative link is established between perpendicular-space coordinates (V&perp;V_\perpV&perp;) and defect energy (correlation r=−0.84r = -0.84r=−0.84, p=0.009p = 0.009p=0.009 after environmental control), demonstrating that internal cut-and-project structure directly influences observable spectral properties. Phason perturbations produce discrete, reversible cluster-switching transitions with D8D_8D8 symmetry and exact loop closure, providing a controlled characterization of phason dynamics on the AB lattice. Finally, mass functions derived solely from V&perp;V_\perpV&perp; select defect locations without external tuning, indicating that geometry alone can determine the placement of particle-like bound states. Taken together, these results establish a consistent structural chain from geometry to topological protection: the AB lattice generates localized defect states, their energies are governed by perpendicular-space coordinates, effective mass arises from geometric structure, and stability is maintained under BdG symmetry constraints. All simulations are implemented as single-cell Python workflows and are fully reproducible without external dependencies. Each experiment includes pre-registered outcomes, adversarial review, and explicit kill-switch criteria; no kill switch was triggered. Rung 2, focusing on gauge dynamics and emergent transport, is currently in progress

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