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Bibliographische Detailangaben
1. Verfasser:	Trees, Nala
Format:	Recurso digital
Sprache:
Veröffentlicht:	Zenodo 2026
Online-Zugang:	https://doi.org/10.5281/zenodo.19580746
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

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This paper establishes the arithmetic Aharonov-Bohm package for the SGOC programme in the bounded-domain setting.   Given a primitive Dirichlet character chi of conductor q and a compact swallowed window O with a character-seeded placed screen complex, the residual period vector encodes a U(1)-valued arithmetic holonomy class on the cycle basis of H_1(O; Z). Conditional on the continuum flat U(1) realisation of the residual period class and cut-neighbourhood trivialisation, a nodal-free stationary state acquires the Aharonov-Bohm phase Delta_phi = Arg(Per_{chi,O}(Gamma)) around every cycle class Gamma. Once the residual periods are fixed on basis cycles, the phase on any remaining cycle is predicted exactly.   The paper makes the theorem concrete with the first worked example: the primitive character modulo 5 with chi(2) = i. For a one-cycle bouquet this gives the quarter-flux ring ladder E_n(pi/2) = (hbar^2 / 2mR^2)(n - 1/4)^2, and for a two-cycle screen it yields the phase predictions theta_1 = pi/2, theta_2 = -pi/2 with trivial and half-flux classes on the sum and difference cycles.   The bouquet-class continuum realisation theorem is proved unconditionally: on a planar bouquet screen every arithmetic period homomorphism is realised by a flat U(1) connection on a trivial line bundle. The arithmetic scale is fixed by coherence matching rather than by spectral fitting.   Keywords: Aharonov-Bohm effect, Dirichlet characters, arithmetic topology, holonomy, residual periods, SGOC, ring spectrum, flux quantisation   Related Programme: Spectral Geometry of Coherence (SGOC)

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