Quantum Billiard-Based Control of Medium Response via Multi-Frequency Feedback in Graphene-hBN Heterostructures
Abstract
Chur Chin
We present a closed-loop optoelectronic control system that stabilizes and selectively forms the medium response state of a graphene–hexagonal boron nitride (hBN) heterostructure by exploiting quantum billiard dynamics. The active medium is patterned as a Sinai billiard mesa (100 × 100 nm) with a circular hBN potential scatterer (radius 25 nm) at its center. A multi-frequency drive signal V(t) = V0 + Σ ΔVn sin(2πfnt + φn) is generated from the imaginary parts γn of the nontrivial zeros of the Riemann zeta function, scaled to THz frequencies fn = α•γn. Because the paircorrelation statistics of Riemann zeros coincide with Gaussian Unitary Ensemble (GUE) random matrix theory, this drive is self-consistent with the GUE chaotic statistics of the Sinai billiard under an applied magnetic field Bc ≈ 0.4 T. The feedback loop continuously measures the optical response at λ0 ≈ 992 nm and the electrical resistance R(B), identifies the target state when a Giant Magnetoresistance (GMR) transition ΔR ≈ 34 Ω co-occurs with the optical intensity peak, and iteratively updates drive parameters until the strong-coupling condition g > (γc + γp)/4 is reached with gmax = 4.00 meV. Electron-beam lithography (EBL) at 100 kV with PMMA 950K resist and O2 reactive-ion etching are specified for device fabrication. This work bridges quantum chaos, topological condensed-matter physics, and real-time photonic feedback control.
