Five-Phase Bulk-Dressed Extension and Adjacency-Induced Directional Asymmetry
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| Format: | Recurso digital |
| Langue: | anglais |
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2026
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| _version_ | 1866901314275901440 |
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| author | Holdway, Craig Edwin |
| author_facet | Holdway, Craig Edwin |
| contents | <p>We show that the mediated three-sector system underlying Theorems 10 and 11 arises as the effective active core of a five-phase bulk-dressed architecture. Integrating out two outer bulk phases via Schur-complement reduction produces dressed detunings that sharpen the detuning-controlled transport asymmetry mechanism without altering its structure.</p> <p>We then introduce an adjacency-structured bulk and derive the leading correction to the dressed detuning difference under asymmetric adjacency coupling. In the symmetric-bulk regime, adjacency enters only at second order, yielding the explicit shift</p> <p><strong>ΔR−ΔL=δ+(EM−B2)(EM−B1)2u2(a′2−a2)+O(u2a4,u4)</strong>,</p> <p>which provides a compact algebraic relation linking bulk-core coupling, adjacency structure, and left-right asymmetry.</p> <p>A conditional proposition shows that, under a monotonicity assumption, adjacency asymmetry alone can reverse the directional ordering of local recovery failure in the reduced model.</p> <p>We further establish an operator realization of the leading correction on the dressed core as a diagonal side-asymmetry operator PR−PL. While no natural bare-basis global asymmetry operator projects to this form, we construct an explicit lifted realization via a core-bath mixing unitary, and exhibit an exact dynamical implementation within a parameter-tuned regime of the same five-phase Hamiltonian architecture. The question of whether such a lift is structurally forced by the underlying Q5 geometry remains open.</p> <h1> </h1> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19393422 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Five-Phase Bulk-Dressed Extension and Adjacency-Induced Directional Asymmetry Holdway, Craig Edwin quantum transport effective Hamiltonian Schur complement reduction detuning asymmetry perturbation theory operator theory Q5 hypercube Q5 hypercube Gray code structure Möbius Hamiltonian graded operator systems bulk-dressed systems adjacency-induced correction directional asymmetry multi-phase reduction core-bath coupling Rabi dynamics operator lifting non-uniform environments quantum information quantum dynamics emergent behavior networked systems <p>We show that the mediated three-sector system underlying Theorems 10 and 11 arises as the effective active core of a five-phase bulk-dressed architecture. Integrating out two outer bulk phases via Schur-complement reduction produces dressed detunings that sharpen the detuning-controlled transport asymmetry mechanism without altering its structure.</p> <p>We then introduce an adjacency-structured bulk and derive the leading correction to the dressed detuning difference under asymmetric adjacency coupling. In the symmetric-bulk regime, adjacency enters only at second order, yielding the explicit shift</p> <p><strong>ΔR−ΔL=δ+(EM−B2)(EM−B1)2u2(a′2−a2)+O(u2a4,u4)</strong>,</p> <p>which provides a compact algebraic relation linking bulk-core coupling, adjacency structure, and left-right asymmetry.</p> <p>A conditional proposition shows that, under a monotonicity assumption, adjacency asymmetry alone can reverse the directional ordering of local recovery failure in the reduced model.</p> <p>We further establish an operator realization of the leading correction on the dressed core as a diagonal side-asymmetry operator PR−PL. While no natural bare-basis global asymmetry operator projects to this form, we construct an explicit lifted realization via a core-bath mixing unitary, and exhibit an exact dynamical implementation within a parameter-tuned regime of the same five-phase Hamiltonian architecture. The question of whether such a lift is structurally forced by the underlying Q5 geometry remains open.</p> <h1> </h1> |
| title | Five-Phase Bulk-Dressed Extension and Adjacency-Induced Directional Asymmetry |
| topic | quantum transport effective Hamiltonian Schur complement reduction detuning asymmetry perturbation theory operator theory Q5 hypercube Q5 hypercube Gray code structure Möbius Hamiltonian graded operator systems bulk-dressed systems adjacency-induced correction directional asymmetry multi-phase reduction core-bath coupling Rabi dynamics operator lifting non-uniform environments quantum information quantum dynamics emergent behavior networked systems |
| url | https://doi.org/10.5281/zenodo.19393422 |