Geometric Quantization of Molecular Quantum Transport: The CohBit Chrysene Architecture for Ambient-Temperature Quantum-Classical Transduction.

Abstract

The construction of macroscopic single-molecule architectures that combine coherent quantum transport with classical control remains limited by two thermodynamic obstacles: stochastic self-assembly in continuous manifolds and rapid thermal decoherence at ambient temperature. This work introduces the CohBit architecture, in which dual-channel molecular quantum transport is formalized by geometric quantization on a discrete, non-commutative manifold---the Chrysene Instantiation Space---canonically identified with the integer lattice.

A 3,6,9,12-tetrasubstituted chrysene core is taken as the elementary geometric basis tensor. Its C2h symmetry, together with hard Dirichlet boundaries at every (sp2 to sp3) termination, yields an algebraic Zero-Divisor Theorem that enforces strict orthogonality between longitudinal ballistic data channels and transverse electrostatic control channels. The principal logic operation is resonant Stark tuning of molecular orbitals; persistent ring currents on the aromatic perimeter supply secondary geometric phases and topologically protected molecular flux degrees of freedom. Vertical co-facial stacking produces bipartite dimers that realize single-electron Coulomb blockade and memristive hysteresis whose thermodynamic cost is bounded from below by the Landauer limit.

Supramolecular polymerization of these nodes via conjugated polyene bridges generates an orthogonal crossbar that functions as a field-programmable neural array supporting native four-quadrant analog matrix multiplication. Thermal decoherence is controlled by a hierarchy of mechanisms: C2h Fröhlich selection rules, acoustic reflection at Ricci-curvature singularities, Anderson localization of phonons inside an interstitial \(\alpha\)-helical scaffold, and irreversible dissipation into a Caldeira--Leggett continuum. Under these mechanisms the effective electron-phonon coupling is driven toward zero, furnishing a theoretical lower bound on phase-coherence time compatible with ballistic transit at ambient temperature.

The resulting construction supplies a coherent algebraic and open-system framework for ambient-temperature quantum-classical transduction. Quantitative first-principles parameters, realistic geometric-phase magnitudes, and experimental realization of the interstitial scaffold remain open problems that must be addressed before the architecture can be regarded as a physical blueprint.