| _version_ | 1866901491052183552 |
|---|---|
| author | Adam, Marzuq Yussif Etsie |
| author_facet | Adam, Marzuq Yussif Etsie |
| contents | <p>This Jupyter Notebook is a supplementary computational artifact for Section 5.3 of "Isomorphic Emergence of Fermionic Excitations: Unifying Gravitational Particle Creation and Analogue Solid-State Horizons via an N-Dimensional Matrix Framework". It mathematically rederives the thermodynamic limit properties of a macroscopic graphene lattice—specifically the <span>$\pm 3t$</span> energy bounds and Dirac point symmetry established by Castro Neto et al. (2009).</p> <p>By representing the <span>$N$</span>-dimensional covariant Euler-Lagrange equations as a sparse bipartite Hamiltonian, this framework bypasses standard <span>$\mathcal{O}(N^3)$</span> dense matrix diagonalization. It evaluates the Rayleigh-Ritz bounds (<span>$R + \xi\mathcal{R} > m_{eff}^2$</span>) for <span>$N=181,200$</span> nodes in <span>$\mathcal{O}(N)$</span> time on consumer hardware.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18943894 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Supplementary Code for Section 5.3: Isomorphic Framework Replication of Graphene Adam, Marzuq Yussif Etsie Computational science Graphene O(N) Algorithms Isomorphic Framework Analogue Gravity Rayleigh-Ritz Method Tight-Binding Model Lanczos Algorithm <p>This Jupyter Notebook is a supplementary computational artifact for Section 5.3 of "Isomorphic Emergence of Fermionic Excitations: Unifying Gravitational Particle Creation and Analogue Solid-State Horizons via an N-Dimensional Matrix Framework". It mathematically rederives the thermodynamic limit properties of a macroscopic graphene lattice—specifically the <span>$\pm 3t$</span> energy bounds and Dirac point symmetry established by Castro Neto et al. (2009).</p> <p>By representing the <span>$N$</span>-dimensional covariant Euler-Lagrange equations as a sparse bipartite Hamiltonian, this framework bypasses standard <span>$\mathcal{O}(N^3)$</span> dense matrix diagonalization. It evaluates the Rayleigh-Ritz bounds (<span>$R + \xi\mathcal{R} > m_{eff}^2$</span>) for <span>$N=181,200$</span> nodes in <span>$\mathcal{O}(N)$</span> time on consumer hardware.</p> |
| title | Supplementary Code for Section 5.3: Isomorphic Framework Replication of Graphene |
| topic | Computational science Graphene O(N) Algorithms Isomorphic Framework Analogue Gravity Rayleigh-Ritz Method Tight-Binding Model Lanczos Algorithm |
| url | https://doi.org/10.5281/zenodo.18943894 |