Liquid Crystal-Driven Navier–Stokes and Riemann Zeta Function Transformations as Solutions to Hardware Limitations in Graphene-Based Spintronic Neuromorphic Ising Machines

Abstract

Chur Chin

The convergence of graphene-based spintronics, stochastic neurons, Ising machines, and neuromorphic architectures represents a transformative frontier in computing hardware. However, this convergence confronts fundamental physical and computational limitations: thermal decoherence, the von Neumann memory wall, nonlinear intractability of governing partial differential equations, and insufficient entropy generation for true random number synthesis. This paper proposes a novel theoretical and engineering framework in which liquid crystal (LC) systems governed by Navier–Stokes fluid dynamics for anisotropic media serve as a room-temperature physical computing substrate capable of resolving these hardware constraints. By transforming the Navier–Stokes equations (NSE) through Riemann zeta function spectral mappings, we establish that the eigen spectrum of the LC Stokes operator follows Gaussian Unitary Ensemble (GUE) statistics identical to those of the Riemann zeros, per the Montgomery–Dyson conjecture. This correspondence enables

(i) Replacement of computationally intractable NSE integration with analytically structured zeta spectral computation (projected speedup:107×);

(ii) LC-based optical matrix-vector multiplication approaching the Land Auer energy limit (~10−Z1 J/op), dissolving the memory wall;

(iii) Riemann-resonance-tuned graphene quantum billiard true random number generators achieving 10–10Z Gbit/s entropy rates. We further propose a hybrid architecture integrating graphene photonic cavities, LC spatial light modulators, and Riemann resonance-tuned TRNGs, offering a pathway to room-temperature neuromorphic Ising machines at scales (N ~ 106 spins) beyond all current implementations.

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