극저온 방사광 X-선 나노회절 기반 기타에프 양자 스핀 액체(alpha-RuCl3) 마요라나 페르미온 열 홀 전도도 능동 서보 아키텍처 (.NET 9 C# SIMD)

using System;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
using System.Runtime.Intrinsics;
using System.Runtime.Intrinsics.X86;

namespace ZeliDesk.Quantum.KitaevSpinLiquid
{
    /// <summary>
    /// 기타에프 양자 스핀 액체(alpha-RuCl3) 마요라나 열 홀 전도도 능동 서보
    /// GC 제로 할당 ref struct 및 AVX-256 SIMD 가속화
    /// </summary>
    public ref struct KitaevQslMajoranaServo
    {
        private readonly ReadOnlySpan<float> _measuredThermalVoltages; // 횡방향 열기전력 V_xy (uV)
        private readonly ReadOnlySpan<float> _sampleTemperatures;      // 극저온 시편 온도 T (K)
        private readonly Span<float> _thermalConductivityRatios;      // 연산된 kappa_xy / T
        private readonly Span<float> _magneticFieldAdjustments;       // 자장 미세 튜닝 지령 (mT)

        private readonly float _halfQuantumLimit; // 0.5 * pi^2 * kB^2 / (3h) ~ 0.5 * 0.945e-12 W/K^2
        private readonly float _fieldFeedbackGain;// 자장 피드백 게인
        private readonly float _voltageFactor;    // 열기전력 -> 열전도도 환산 계수

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public KitaevQslMajoranaServo(
            ReadOnlySpan<float> measuredThermalVoltages,
            ReadOnlySpan<float> sampleTemperatures,
            Span<float> thermalConductivityRatios,
            Span<float> magneticFieldAdjustments,
            float halfQuantumLimit = 0.5f,
            float fieldFeedbackGain = 180.0f,
            float voltageFactor = 0.22f)
        {
            _measuredThermalVoltages = measuredThermalVoltages;
            _sampleTemperatures = sampleTemperatures;
            _thermalConductivityRatios = thermalConductivityRatios;
            _magneticFieldAdjustments = magneticFieldAdjustments;
            _halfQuantumLimit = halfQuantumLimit;
            _fieldFeedbackGain = fieldFeedbackGain;
            _voltageFactor = voltageFactor;
        }

        /// <summary>
        /// 8채널 열 홀 전도도 측정값을 SIMD 병렬 분석하여 반정수 양자화 자장 제어
        /// </summary>
        [MethodImpl(MethodImplOptions.AggressiveOptimization)]
        public void ProcessMajoranaQuantizationLoop()
        {
            int length = _measuredThermalVoltages.Length;
            int simdLength = length - (length % 8);

            Vector256<float> vQuantLimit = Vector256.Create(_halfQuantumLimit);
            Vector256<float> vGain = Vector256.Create(_fieldFeedbackGain);
            Vector256<float> vFactor = Vector256.Create(_voltageFactor);
            Vector256<float> vSmallT = Vector256.Create(1e-4f);

            int i = 0;
            if (Avx2.IsSupported)
            {
                for (; i < simdLength; i += 8)
                {
                    Vector256<float> vV = Vector256.Create(MemoryMarshal.Cast<float, Vector256<float>>(_measuredThermalVoltages.Slice(i, 8))[0]);
                    Vector256<float> vT = Vector256.Create(MemoryMarshal.Cast<float, Vector256<float>>(_sampleTemperatures.Slice(i, 8))[0]);

                    // kappa_xy / T = (Factor * V_xy) / (T^2 + eps)
                    Vector256<float> vTSq = Avx.Multiply(vT, vT);
                    Vector256<float> vSafeTSq = Avx.Add(vTSq, vSmallT);
                    Vector256<float> vRatio = Avx.Divide(Avx.Multiply(vFactor, vV), vSafeTSq);

                    // 양자화 오차 Error = Ratio - HalfQuantumLimit
                    Vector256<float> vErr = Avx.Subtract(vRatio, vQuantLimit);

                    // 자장 보정 명령 = -Gain * Error
                    Vector256<float> vDeltaB = Avx.Multiply(Avx.Subtract(Vector256<float>.Zero, vErr), vGain);

                    vRatio.CopyTo(_thermalConductivityRatios.Slice(i, 8));
                    vDeltaB.CopyTo(_magneticFieldAdjustments.Slice(i, 8));
                }
            }

            for (; i < length; i++)
            {
                float tSq = _sampleTemperatures[i] * _sampleTemperatures[i] + 1e-4f;
                float ratio = (_voltageFactor * _measuredThermalVoltages[i]) / tSq;
                float err = ratio - _halfQuantumLimit;
                _thermalConductivityRatios[i] = ratio;
                _magneticFieldAdjustments[i] = -_fieldFeedbackGain * err;
            }
        }
    }
}