Synthetic twist geometry in mesoscopic quantum circuits: geometric capacitance and chiral mode splitting

RESUMO

We propose a route for encoding a helicoidally twisted synthetic geometry in mesoscopic quantum circuits. A torsionless spatial metric with twist parameter $\Om$ defines an electrostatic capacitance kernel whose angular--axial sector contains the chiral coupling $-2\Om mk$. We show that this kernel can be implemented by a finite, quantizable circuit graph built only from positive two-node capacitors: diagonal bridges generate the cross term, and the dimensionless twist is the ratio of diagonal to total angular capacitance. The resulting capacitance matrix enters the Hamiltonian through $C^{-1}(\etaT)$ and splits counter-rotating synthetic modes. Exact finite-graph diagonalization confirms the analytic spectrum and shows that closed longitudinal circulation is required; with open boundaries the bridge phase is gauge removable and the doublets remain degenerate. Simulated spectroscopy resolves the chiral fan, while disorder simulations indicate that calibrated percent-level reactive disorder does not obscure the deterministic splitting in the parameter range considered. Twist textures produce interface modes, Josephson nonlinearities make the Kerr sector chirality dependent, and the same doublet provides a detuning knob for non-Hermitian exceptional-point control. For representative circuit-QED parameters the splitting is in the tens-of-MHz range, well above typical resonator linewidths.