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Journal of Electrical Systems and Information Technology

Geometric collapse engineering: a framework for sub-1·5 nm transistor design via environment-induced quantum state reduction

Lefliti Mohamed

Published Sep 8, 2026• 0 citations
Publisher

Abstract

Abstract The miniaturization of field-effect transistors has reached a critical juncture at the 1.5 nm technology node, where conventional drift-diffusion models fail due to dominant quantum effects. We present a device engineering framework grounded in geometric collapse theory, wherein environmental coupling is harnessed as an active switching mechanism rather than treated as a parasitic effect. By exploiting the inherent structure of quantum state space–the Riemann sphere for two-level systems–we demonstrate that asymmetric environmental coupling can force deterministic wavefunction collapse to a desired pointer state within switching timescales. Our approach provides explicit design rules: (1) environmental coupling rates $$\kappa_{S}$$ and $$\kappa_{D}$$ must differ by at least $$10^{13}$$ s $${}^{-1}$$ , (2) effective mass engineering using III-V materials achieves this condition, and (3) symmetry breaking through gate geometry or material composition yields collapse times $$\tau_{\mathrm{collapse}} < 0.1$$ ps. This framework reconciles quantum measurement theory with semiconductor device physics, offering a pathway to extend Moore’s Law beyond the 1.5 nm barrier. We analyze the validity of the geometric flow equation, competition with thermal effects at 300 K, the transition from deterministic to probabilistic regimes, and fundamental limits below 1 nm. A comprehensive NEGF simulation with realistic parameters ( $$\alpha = 0.5$$ ) confirms the theoretical predictions, demonstrating a $$3.86 \times 10^5$$ improvement in $$I_{\mathrm{on}}/I_{\mathrm{off}}$$ ratio compared to conventional tunneling transport. The comprehensive NEGF simulation results, including key parameters and performance metrics, are summarized in Tables 6-12.

DOI
10.1186/s43067-026-00395-1

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Abstract The miniaturization of field-effect transistors has reached a critical juncture at the 1.5 nm technology node, where conventional drift-diffusion models fail due to dominant quantum effects. We present a device engineering framework grounded in geometric collapse theory, wherein environmental coupling is harnessed as an active switching mechanism rather than treated as a parasitic effect. By exploiting the inherent structure of quantum state space–the Riemann sphere for two-level systems–we demonstrate that asymmetric environmental coupling can force deterministic wavefunction collapse to a desired pointer state within switching timescales. Our approach provides explicit design rules: (1) environmental coupling rates κS\kappa_{S}κS​ and κD\kappa_{D}κD​ must differ by at least 101310^{13}1013 s −1{}^{-1}−1 , (2) effective mass engineering using III-V materials achieves this condition, and (3) symmetry breaking through gate geometry or material composition yields collapse times τcollapse<0.1\tau_{\mathrm{collapse}} < 0.1τcollapse​<0.1 ps. This framework reconciles quantum measurement theory with semiconductor device physics, offering a pathway to extend Moore’s Law beyond the 1.5 nm barrier. We analyze the validity of the geometric flow equation, competition with thermal effects at 300 K, the transition from deterministic to probabilistic regimes, and fundamental limits below 1 nm. A comprehensive NEGF simulation with realistic parameters ( α=0.5\alpha = 0.5α=0.5 ) confirms the theoretical predictions, demonstrating a 3.86×1053.86 \times 10^53.86×105 improvement in Ion/IoffI_{\mathrm{on}}/I_{\mathrm{off}}Ion​/Ioff​ ratio compared to conventional tunneling transport. The comprehensive NEGF simulation results, including key parameters and performance metrics, are summarized in Tables 6-12.
This paper presents a geometric framework for objective wavefunction collapse that addresses core challenges in quantum foundations. We develop a complete mathematical formulation using the Riemann sphere as the natural state space for two-level quantum systems. The theory provides explicit dynamical equations for collapse as a deterministic geometric flow, resolves the preferred-basis problem through environmental coupling, derives the Born rule statistically from the uniform Fubini–Study measure, and explains the system-size dependence of collapse via a mass-squared scaling of the collapse rate. The parameter λ0 = (6.0 ± 2.0) × 10−16 s−1 (referenced to 1 atomic mass unit) yields precise, falsifiable predictions—from electrons maintaining coherence for over 1016 years to 1 kg objects collapsing in 0.27 µs. These predictions are consistent with all current experimental bounds from LIGO, molecular interferometry, and optomechanics. By grounding collapse in the intrinsic geometry of quantum state space, our approach avoids ad hoc modifications to quantum dynamics and offers a mathematically natural resolution to the measurement problem.
We show that any objective collapse model satisfying (i) Markovian dynamics, (ii) Lindblad consistency, and (iii) pointer-basis localization is necessarily geometry-dependent: collapse rates are controlled by the spectral bottleneck D∗Σ, not by particle number, entanglement, or Hilbert-space dimension. This follows from the structure of pointer-diagonal Lindblad generators and does not require interpretational assumptions. Building on this foundation, we develop a min-imal completion of quantum mechanics—in the same technical sense as GRW/CSL—with two additional physical commitments: (A) the noise record is ontologically real, making outcomes deterministic given the record; and (B) the noise metric has gravitational origin, Σ = Σ(G)/ℏ, where the 1/r spatial structure is derived from linearized quantum gravity and the amplitude is fixed up to order-unity regularization. This yields the Penrose-Di´osi timescale τ ∼ℏ/∆EG as a derived result rather than an ansatz. The framework predicts that GHZ and Cluster states with the same particle number collapse at rates differing by a factor of n—a ratio that constitutes a parameter-free experimental test. This prediction has been validated on IBM quantum hardware, with sub-percent prefactor agreement for the theorem applied to environmental noise. We iden-tify a window λ0 ∈[10−20,10−10] Hz for the fundamental collapse rate, consistent with current bounds. Applications include: intrinsic geometric robustness of quantum error-correcting codes,Noise Geometry Tomography for reverse-engineering transport coefficients, and testable cosmo-logical implications. Within the class of Markovian CPTP collapse models that localize in a pointer basis, geometry-dependence is a theorem; models outside this class (e.g., non-Markovian,Everettian, or contextual) are not constrained by our result.
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Title of Works: Geometric Origin of Spontaneous Collapse from a Compactified Timelike Dimension Supplementary Material: Experimental Tests of Geometric Collapse Overview: This integrated body of work proposes a novel geometric resolution to the quantum measurement problem. By extending spacetime with a compactified timelike dimension on a Z2\mathbb{Z}_2Z2​ orbifold, the author derives the phenomenological GRW collapse rate from first principles. The mechanism identifies the QCD confinement scale as the fundamental driver of wave-function localization via the Jackiw-Rebbi mechanism, bridging the gap between quantum foundations and high-energy physics. Key Contributions: Geometric Micro-physics: Provides the full derivation of the Lindblad Master Equation and the Continuous Spontaneous Localization (CSL) dynamics directly from 5D bulk-brane interactions. Chromatic Coupling: Introduces a unique "chromatic" mechanism where only color-charged particles (nucleons) undergo spontaneous collapse. This predicts that leptons and photons remain transparent to the mechanism, a feature that distinguishes it from standard mass-proportional models. Quantum Computing Scalability: Establishes a quantitative "effective mass budget" for qubit design, defining a geometric ceiling for the scalability of quantum architectures based on nucleon count. Experimental Predictions & Falsifiability: The accompanying supplementary material details a comprehensive roadmap for testing the model using next-generation matter-wave interferometers such as MAQRO and OTIMA. Key testable signatures include: Isotope Shifts: A per-mille level shift in the collapse rate between different isotopes (e.g., 87Rb^{87}\text{Rb}87Rb vs. 133Cs^{133}\text{Cs}133Cs). Thermal Corrections: A temperature-dependent correction to the collapse rate at the 10−510^{-5}10−5 level, detectable in cryogenic-to-room-temperature comparisons. Comparative Interferometry: A definitive test through electron vs. neutron interferometry at matched mass scales to verify lepton transparency. This research offers a mathematically rigorous and experimentally falsifiable framework that transforms the "mystery" of wave-function collapse into a concrete parameter of spacetime geometry and quantum engineering.
On the Stabilization of Cryogenic Wafer Matrices and Superconducting Quantum Dots via Triadic Lattice Quantization and Covariant Phase Shields From Fluid Turbulence to Quantum Dots:Applying Navier-Stokes Singularity Pinning to Supercritical Semiconductor Architectures. Proud to share our latest milestone in solid-state and quantum engineering: "Deconvoluting Quantum Decoherence." By mapping cosmological triadic invariants onto active silicon wafer coordinates under the P6m space group, we demonstrate absolute singularity pinning and lossless phase stabilization. Discover the concrete business use cases for EDA tools and QPUs, and read our invitation for strategic joint ventures. INDUSTRIAL APPLICATION SCENARIOS 1 Zero-Overhead Fault Isolation in Superconducting QPUs By embedding the topological gauge shield directly into the hardware layer of superconducting quantum circuits, the Toosibashi Platform completely deinstalls the necessity for software-level error-correction protocols. Phase deviations induced by stray environmental noise are neutralized before they can interact with the active quantum bits. This expands the processing coherence lifetime () asymptotically toward infinity, allowing quantum processors to execute deep logical gates with zero physical qubit overhead. 2 EDA Simulation Stability for Sub-1nm Transistor Design In next-generation Electronic Design Automation (EDA) suites, simulating electron mobility inside sub-1nm field-effect transistors forces conventional finite-element solvers to handle extreme gradient concentrations which regularly cause software crashes via NaN errors. By enforcing the exact analytical gradient limit ceiling (), the Toosibashi framework immunizes the simulation matrix against truncation drift. This allows chip-design engineers to model complex sub-1nm gate architectures with absolute stability, cutting design validation timelines from months to minutes. 3 Cavitation-Free Cryogenic Coolant Management For high-performance supercomputing centers and dilution refrigerator infrastructures, maintaining uniform wafer-surface cooling layers is a critical operational constraint. Applying the metric damping tensor to the liquid-helium inflow controls completely eliminates microscopic fluid cavitation, local turbulence, and acoustic vibrations. The cryogenic layers flow across the chip surface with absolute laminar predictability, matching real-world telemetry with perfect precision.
Quantum decoherence is both the fundamental mechanism underlying the quantum-to-classical transition and a major challenge for the development of scalable nanoscale quantum technologies. This work introduces a Quantum Phase Space (QPS) framework that provides a unified geometric description of decoherence. The framework is based on a dual structure consisting of an overcomplete continuous frame of minimum-uncertainty states that defines the QPS geometry, and an orthonormal basis that satisfies the strict mathematical requirements for decoherence within the Spectrum Broadcast Structure (SBS) objectivity criterion for pointer states. Within this framework, the variance-covariance matrix of the QPS ground states serves as a universal indicator of decoherence regimes:it is time-independent for Markovian (memoryless) dynamics, and time-dependent for non-Markovian dynamics with memory and information backflow. To illustrate the formalism, the Hu-Paz-Zhang (HPZ) model is generalized to include simultaneous position and momentum couplings to the environment, leading to a generalized non-Markovian master equation characterized by a spectral-density matrix. The corresponding evolution equations for the first moments (⟨p(t)⟩,⟨x(t)⟩)\ (\left\langle p(t) \right\rangle,\left\langle x(t) \right\rangle) (⟨p(t)⟩,⟨x(t)⟩) and for the ground covariance matrix establish a direct connection between microscopic environmental properties, classical-like trajectories and the QPS geometry. The proposed framework provides a unified theoretical foundation for modeling decoherence in nanoscale systems involving simultaneous position and momentum interactions with the environment. The QPS framework may thus bridge fundamental theory and practical quantum engineering, offering a promising coherent pathway to understand, control, and exploit decoherence at the nanoscience frontier.