AIDT 온디바이스 STEM 초저온 페르미 기체 페시바흐 공명(Feshbach Resonance) 및 BCS-BEC 교차 서보 엔진

using System;
using System.Runtime.CompilerServices;

namespace ZeliDesk.Stem.ColdAtoms
{
    public enum CrossoverRegime : byte
    {
        BcsSuperfluid = 0,
        UnitaryFermiGas = 1,
        BecMolecularCondensate = 2
    }

    public readonly ref struct FermiGasState
    {
        public readonly double MagneticFieldGauss;  // 인가 자기장 B (Gauss)
        public readonly double ScatteringLengthBohr; // 산란 길이 a (Bohr radius a0)
        public readonly double InverseInteraction;   // 1 / (k_F * a)
        public readonly double PairingGapJoules;     // 페어링 에너지 간극 Delta (J)
        public readonly double ChemicalPotentialJoules; // 화학 퍼텐셜 mu (J)
        public readonly CrossoverRegime Regime;

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public FermiGasState(double bField, double aBohr, double invKfa, double gap, double mu, CrossoverRegime regime)
        {
            MagneticFieldGauss = bField;
            ScatteringLengthBohr = aBohr;
            InverseInteraction = invKfa;
            PairingGapJoules = gap;
            ChemicalPotentialJoules = mu;
            Regime = regime;
        }
    }

    public ref struct FeshbachServoEngine
    {
        private const double A0 = 5.29177210903e-11; // Bohr radius (m)
        private const double HBar = 1.054571817e-34; // J*s
        private const double M_Li6 = 9.98834e-27;    // kg (Lithium-6 mass)

        private readonly double _b0Gauss;            // Feshbach 공명점 B0 (Gauss, Li-6 = 832.2 G)
        private readonly double _deltaBGauss;        // 공명 폭 (Gauss, Li-6 = -262.8 G)
        private readonly double _aBgMeters;          // 배경 산란 길이 (m, Li-6 = -1582 a0)
        private readonly double _kF;                 // Fermi wavevector (1/m)
        private readonly double _ef;                 // Fermi energy (J)

        private double _currentBField;               // 현재 자속 밀도 (Gauss)

        public FeshbachServoEngine(double atomicDensityPerM3, double b0 = 832.18, double deltaB = -262.8, double aBgBohr = -1582.0)
        {
            _b0Gauss = b0;
            _deltaBGauss = deltaB;
            _aBgMeters = aBgBohr * A0;

            _kF = Math.Cbrt(3.0 * Math.PI * Math.PI * atomicDensityPerM3);
            _ef = (HBar * HBar * _kF * _kF) / (2.0 * M_Li6);
            _currentBField = b0; // 시작점: 유니타리 공명
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public FermiGasState StepServo(double targetInverseKfa, double coilCurrentCorrectionGauss, double dtSec)
        {
            // 1. 자기장 제어 루프 갱신
            _currentBField += coilCurrentCorrectionGauss;

            // 2. 페시바흐 산란 길이 계산
            double detuning = _currentBField - _b0Gauss;
            if (Math.Abs(detuning) < 1e-4) detuning = (detuning >= 0 ? 1e-4 : -1e-4);

            double aMeters = _aBgMeters * (1.0 - (_deltaBGauss / detuning));
            double invKfa = 1.0 / (_kF * aMeters);

            // 3. 교차 영역 분류 및 간극/화학 퍼텐셜 보편 함수 근사
            CrossoverRegime regime;
            double pairingGap;
            double chemicalPotential;

            if (invKfa < -1.0)
            {
                regime = CrossoverRegime.BcsSuperfluid;
                pairingGap = (8.0 / (Math.E * Math.E)) * _ef * Math.Exp(-Math.PI / (2.0 * Math.Abs(_kF * aMeters)));
                chemicalPotential = _ef;
            }
            else if (invKfa > 1.0)
            {
                regime = CrossoverRegime.BecMolecularCondensate;
                double bindingEnergy = (HBar * HBar) / (M_Li6 * aMeters * aMeters);
                pairingGap = Math.Sqrt((16.0 / (3.0 * Math.PI)) * _ef * bindingEnergy);
                chemicalPotential = -0.5 * bindingEnergy;
            }
            else
            {
                regime = CrossoverRegime.UnitaryFermiGas;
                pairingGap = 0.50 * _ef;
                chemicalPotential = 0.37 * _ef; // Bertsch parameter xi approx 0.37
            }

            return new FermiGasState(
                bField: _currentBField,
                aBohr: aMeters / A0,
                invKfa: invKfa,
                gap: pairingGap,
                mu: chemicalPotential,
                regime: regime
            );
        }
    }
}