IdealGasFunctions.h

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/*
 * Thermal-FIST package
 * 
 * Copyright (c) 2017-2019 Volodymyr Vovchenko
 *
 * GNU General Public License (GPLv3 or later)
 */
#ifndef IDEALGASFUNCTIONS_H
#define IDEALGASFUNCTIONS_H

 
namespace thermalfist {

  namespace IdealGasFunctions {
    enum Quantity { ParticleDensity, EnergyDensity, EntropyDensity, Pressure, chi2, chi3, chi4, ScalarDensity, 
      chi2difull, chi3difull, chi4difull,
      dndT, d2ndT2, dedT, dedmu, dchi2dT
    };
    enum QStatsCalculationType { ClusterExpansion, Quadratures };

    extern bool calculationHadBECIssue;

    struct MagneticFieldConfiguration {
      double B;        
      int lmax;        
      double degSpin;  
      double Q;        
      MagneticFieldConfiguration(double in_B = 0.,
                                 int in_lmax = 100,
                                 double in_degSpin = 1.,
                                 double in_Q = 0.) :
                                 B(in_B), lmax(in_lmax), degSpin(in_degSpin), Q(in_Q)
                                 { }
      MagneticFieldConfiguration(double in_B = 0., {…}
    };
    struct MagneticFieldConfiguration {…};
 
 
 
    struct IdealGasFunctionsExtraConfig {
      MagneticFieldConfiguration MagneticField;  
      IdealGasFunctionsExtraConfig(const MagneticFieldConfiguration& in_MagneticField = MagneticFieldConfiguration()) :
                                   MagneticField(in_MagneticField)
                                   { }
      IdealGasFunctionsExtraConfig(const MagneticFieldConfiguration& in_MagneticField = MagneticFieldConfiguration()) : {…}
    };
    struct IdealGasFunctionsExtraConfig {…};

    double BoltzmannDensity(double T, double mu, double m, double deg,
                            const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double BoltzmannPressure(double T, double mu, double m, double deg,
                             const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double BoltzmannEnergyDensity(double T, double mu, double m, double deg,
                                  const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double BoltzmannEntropyDensity(double T, double mu, double m, double deg,
                                   const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double BoltzmannScalarDensity(double T, double mu, double m, double deg,
                                  const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());  // TODO: Check if the scalar density formula and implementation are correct
    
    double BoltzmannTdndmu(int N, double T, double mu, double m, double deg,
                           const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double BoltzmannChiN(int N, double T, double mu, double m, double deg,
                         const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double BoltzmannChiNDimensionfull(int N, double T, double mu, double m, double deg,
                                      const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double BoltzmannMagnetization(double T, double mu, double m, double deg,
                            const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double QuantumClusterExpansionDensity(int statistics, double T, double mu, double m, double deg, int order = 1,
                                          const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());
    
    double QuantumClusterExpansionPressure(int statistics, double T, double mu, double m, double deg, int order = 1,
                                           const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());
    
    double QuantumClusterExpansionEnergyDensity(int statistics, double T, double mu, double m, double deg, int order = 1,
                                                const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());  // TODO: Check for correctness
    
    double QuantumClusterExpansionEntropyDensity(int statistics, double T, double mu, double m, double deg, int order = 1,
                                                 const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());
    
    double QuantumClusterExpansionScalarDensity(int statistics, double T, double mu, double m, double deg, int order = 1,
                                                const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());   // TODO: Check for correctness
    
    double QuantumClusterExpansionTdndmu(int N, int statistics, double T, double mu, double m, double deg, int order = 1,
                                         const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());
    
    double QuantumClusterExpansionChiN(int N, int statistics, double T, double mu, double m, double deg, int order = 1,
                                       const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double QuantumClusterExpansionChiNDimensionfull(int N, int statistics, double T, double mu, double m, double deg, int order = 1,
                                                    const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());
 
 

    double QuantumClusterExpansionMagnetization(int statistics, double T, double mu, double m, double deg, int order = 1,
                                                const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double QuantumNumericalIntegrationDensity(int statistics, double T, double mu, double m, double deg,
                                              const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());
    
    double QuantumNumericalIntegrationPressure(int statistics, double T, double mu, double m, double deg,
                                               const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());
    
    double QuantumNumericalIntegrationEnergyDensity(int statistics, double T, double mu, double m, double deg,
                                                    const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());
    
    double QuantumNumericalIntegrationEntropyDensity(int statistics, double T, double mu, double m, double deg,
                                                     const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());
    
    double QuantumNumericalIntegrationScalarDensity(int statistics, double T, double mu, double m, double deg,
                                                    const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());  // TODO: Check for correctness

    double QuantumNumericalIntegrationMagnetization(int statistics, double T, double mu, double m, double deg,
                                                    const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());
 
    double QuantumNumericalIntegrationT1dn1dmu1(int statistics, double T, double mu, double m, double deg,
                                                const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());
    double QuantumNumericalIntegrationT2dn2dmu2(int statistics, double T, double mu, double m, double deg,
                                                const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());
    double QuantumNumericalIntegrationT3dn3dmu3(int statistics, double T, double mu, double m, double deg,
                                                const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());
    double QuantumNumericalIntegrationTdndmu(int N, int statistics, double T, double mu, double m, double deg,
                                             const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());
    
    double QuantumNumericalIntegrationChiN(int N, int statistics, double T, double mu, double m, double deg,
                                           const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double QuantumNumericalIntegrationChiNDimensionfull(int N, int statistics, double T, double mu, double m, double deg,
                                                        const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double psi(double x);

    double psi2(double x);

    double FermiNumericalIntegrationLargeMuDensity(double T, double mu, double m, double deg,
                                                   const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());
    
    double FermiNumericalIntegrationLargeMuPressure(double T, double mu, double m, double deg,
                                                    const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());
    
    double FermiNumericalIntegrationLargeMuEnergyDensity(double T, double mu, double m, double deg,
                                                         const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());
    
    double FermiNumericalIntegrationLargeMuEntropyDensity(double T, double mu, double m, double deg,
                                                          const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());
    
    double FermiNumericalIntegrationLargeMuScalarDensity(double T, double mu, double m, double deg,
                                                         const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());  // TODO: Check for correctness
 
 
    double FermiNumericalIntegrationLargeMuMagnetization(double T, double mu, double m, double deg,
                                                         const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());  // TODO: Check for correctness
 
    double FermiNumericalIntegrationLargeMuT1dn1dmu1(double T, double mu, double m, double deg,
                                                     const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());
    double FermiNumericalIntegrationLargeMuT2dn2dmu2(double T, double mu, double m, double deg,
                                                     const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());
    double FermiNumericalIntegrationLargeMuT3dn3dmu3(double T, double mu, double m, double deg,
                                                     const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());
    double FermiNumericalIntegrationLargeMuTdndmu(int N, double T, double mu, double m, double deg,
                                                  const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());
    
    double FermiNumericalIntegrationLargeMuChiN(int N, double T, double mu, double m, double deg,
                                                const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double FermiNumericalIntegrationLargeMuChiNDimensionfull(int N, double T, double mu, double m, double deg,
                                                             const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());
 

    double FermiZeroTDensity(double mu, double m, double deg,
                             const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double FermiZeroTPressure(double mu, double m, double deg,
                              const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double FermiZeroTEnergyDensity(double mu, double m, double deg,
                                   const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double FermiZeroTEntropyDensity(double mu, double m, double deg,
                                    const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double FermiZeroTScalarDensity(double mu, double m, double deg,
                                   const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());  // TODO: Check for correctness
 
    double FermiZeroTMagnetization(double mu, double m, double deg,
                                   const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());  // TODO: Check for correctness
 
 
    double FermiZeroTdn1dmu1(double mu, double m, double deg,
                             const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());
    double FermiZeroTdn2dmu2(double mu, double m, double deg,
                             const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());
    double FermiZeroTdn3dmu3(double mu, double m, double deg,
                             const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());
    double FermiZeroTdndmu(int N, double mu, double m, double deg,
                           const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double FermiZeroTChiN(int N, double mu, double m, double deg,
                          const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double FermiZeroTChiNDimensionfull(int N, double mu, double m, double deg,
                                       const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double IdealGasQuantity(Quantity quantity, QStatsCalculationType calctype, int statistics, double T, double mu, double m, double deg, int order = 1,
                            const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());


    double BoltzmanndndT(double T, double mu, double m, double deg,
                         const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double Boltzmannd2ndT2(double T, double mu, double m, double deg,
                           const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double BoltzmanndedT(double T, double mu, double m, double deg,
                         const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double Boltzmanndedmu(double T, double mu, double m, double deg,
                          const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double Boltzmanndchi2dT(double T, double mu, double m, double deg,
                            const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());
 
    // Cluster expansion
    double QuantumClusterExpansiondndT(int statistics, double T, double mu, double m, double deg, int order = 1,
                                       const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double QuantumClusterExpansiond2ndT2(int statistics, double T, double mu, double m, double deg, int order = 1,
                                         const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double QuantumClusterExpansiondedT(int statistics, double T, double mu, double m, double deg, int order = 1,
                                       const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double QuantumClusterExpansiondedmu(int statistics, double T, double mu, double m, double deg, int order = 1,
                                        const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double QuantumClusterExpansiondchi2dT(int statistics, double T, double mu, double m, double deg, int order = 1,
                                         const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());
 

    double QuantumNumericalIntegrationdndT(int statistics, double T, double mu, double m, double deg,
                         const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double QuantumNumericalIntegrationd2ndT2(int statistics, double T, double mu, double m, double deg,
                           const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double QuantumNumericalIntegrationdedT(int statistics, double T, double mu, double m, double deg,
                         const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double QuantumNumericalIntegrationdedmu(int statistics, double T, double mu, double m, double deg,
                          const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double QuantumNumericalIntegrationdchi2dT(int statistics, double T, double mu, double m, double deg,
                            const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double FermiNumericalIntegrationLargeMudndT(double T, double mu, double m, double deg,
                                           const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double FermiNumericalIntegrationLargeMud2ndT2(double T, double mu, double m, double deg,
                                                const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double FermiNumericalIntegrationLargeMudedT(double T, double mu, double m, double deg,
                                           const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double FermiNumericalIntegrationLargeMudedmu(double T, double mu, double m, double deg,
                                            const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());

    double FermiNumericalIntegrationLargeMudchi2dT(double T, double mu, double m, double deg,
                                              const IdealGasFunctionsExtraConfig& extraConfig = IdealGasFunctionsExtraConfig());
  }
  namespace IdealGasFunctions {…}

  class GeneralizedDensity {
  public:
    GeneralizedDensity() {}
    virtual ~GeneralizedDensity() {}
 
    virtual double Quantity(IdealGasFunctions::Quantity quantity, double T, double mu) = 0;
    virtual double EffectiveMass() const { return -1.; }
    virtual bool   IsBECPhase() const { return false; }
    virtual double BECFraction() const { return 0.; }
  };
  class GeneralizedDensity {…};
 
} // namespace thermalfist
 
#endif // IDEALGASFUNCTIONS_H