양자 홀 효과(Quantum Hall Effect) 2DEG 란다우 준위 & 1,000Hz 0-Alloc C# 폰 클리칭 상수 양자 저항 표준기 계측 엔진

using System;
using System.Runtime.CompilerServices;

namespace ZeliDesk.QuantumMetrology
{
    /// <summary>
    /// 2차원 전자 기체(2DEG) 양자 홀 저항 표준기 상태 구조체
    /// </summary>
    public readonly ref struct QuantumHallState
    {
        public double MagneticFieldB { get; }       // 자기장 (Tesla)
        public double CarrierDensityNs { get; }     // 2DEG 전자 면밀도 (m^-2)
        public double TemperatureKelvin { get; }    // 시편 극저온도 (K)
        public double HallCurrentAmpere { get; }    // 측정 인가 전류 (A)
        public double HallVoltageVolt { get; }      // 측정된 홀 전압 (V)
        public double LongVoltageVolt { get; }      // 측정된 종방향 전압 (V)

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public QuantumHallState(double b, double ns, double temp, double i, double vh, double vl)
        {
            MagneticFieldB = b;
            CarrierDensityNs = ns;
            TemperatureKelvin = temp;
            HallCurrentAmpere = i;
            HallVoltageVolt = vh;
            LongVoltageVolt = vl;
        }
    }

    /// <summary>
    /// 1,000Hz 0-Alloc C# 폰 클리칭 양자 홀 저항 계측 및 록인 제어 엔진
    /// </summary>
    public ref struct QuantumHallBridgeEngine
    {
        // SI 2019 기본 물리 상수
        private const double PlanckConstant = 6.62607015e-34; // J*s (정의값)
        private const double ElementaryCharge = 1.602176634e-19; // C (정의값)
        public const double VonKlitzingConstant = PlanckConstant / (ElementaryCharge * ElementaryCharge); // ~25812.8074593045 Ohm

        private double _targetFillingFactor;
        private double _magnetCurrentCorrection;

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public QuantumHallBridgeEngine(int targetPlateauNu)
        {
            _targetFillingFactor = (double)targetPlateauNu;
            _magnetCurrentCorrection = 0.0;
        }

        /// <summary>
        /// 1,000Hz 실시간 란다우 준위 충진율 계산 및 양자화 편차 록인 루프
        /// </summary>
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public readonly void ProcessStep(
            in QuantumHallState state,
            out double fillingFactor,
            out double rxyMeasured,
            out double rxxMeasured,
            out double ppmDeviation,
            out double bFieldCompensationTesla)
        {
            // 1. 란다우 축퇴도 n_L = e*B / h
            double nL = (ElementaryCharge * state.MagneticFieldB) / PlanckConstant;

            // 2. 현재 충진율 nu = n_s / n_L
            fillingFactor = state.CarrierDensityNs / nL;

            // 3. 측정된 홀 저항 및 종방향 저항
            rxyMeasured = state.HallVoltageVolt / state.HallCurrentAmpere;
            rxxMeasured = state.LongVoltageVolt / state.HallCurrentAmpere;

            // 4. 이론적 양자화 저항 R_quant = R_K / nu
            double rTheoretical = VonKlitzingConstant / _targetFillingFactor;

            // 5. 상대 오차 (ppm, parts per million)
            ppmDeviation = ((rxyMeasured - rTheoretical) / rTheoretical) * 1e6;

            // 6. 란다우 플랫폼 중앙 정렬을 위한 자기장 보정값 (P-서보)
            // 충진율 편차 delta_nu = fillingFactor - targetNu
            double deltaNu = fillingFactor - _targetFillingFactor;
            // B_target = n_s * h / (targetNu * e)
            double bTarget = (state.CarrierDensityNs * PlanckConstant) / (_targetFillingFactor * ElementaryCharge);
            bFieldCompensationTesla = 0.85 * (bTarget - state.MagneticFieldB);
        }
    }
}