Class implementing the HRG model in the canonical ensemble. More...

#include <ThermalModelCanonical.h>

Inheritance diagram for thermalfist::ThermalModelCanonical:

Public Member Functions
	ThermalModelCanonical (ThermalParticleSystem *TPS, const ThermalModelParameters &params=ThermalModelParameters())
	Construct a new ThermalModelCanonical object.

virtual	~ThermalModelCanonical (void)
	Destroy the ThermalModelCanonical object.

virtual void	CalculateQuantumNumbersRange (bool computeFluctuations=false)
	Calculates the range of quantum numbers values for which it is necessary to compute the canonical partition functions.

virtual void	CalculatePartitionFunctions (double Vc=-1.)
	Calculates all necessary canonical partition functions.

virtual bool	IsParticleCanonical (const ThermalParticle &part)
	Determines whether the specified ThermalParticle is treat canonically or grand-canonically in the present setup.

virtual void	ConserveBaryonCharge (bool conserve=true)
	Specifies whether the baryon number is treated canonically.

virtual void	ConserveElectricCharge (bool conserve=true)
	Specifies whether the electric charge is treated canonically.

virtual void	ConserveStrangeness (bool conserve=true)
	Specifies whether the strangeness charge is treated canonically.

virtual void	ConserveCharm (bool conserve=true)
	Specifies whether the charm charge is treated canonically.

virtual bool	IsConservedChargeCanonical (ConservedCharge::Name charge) const

virtual double	GetGCEDensity (int i) const
	Density of particle species i in the grand-canonical ensemble.

int	IntegrationIterationsMultiplier () const
	The multiplier of the number of iterations in the numerical integration.

void	SetIntegrationIterationsMultiplier (int multiplier)
	Assigns the multiplier of the number of iterations in the numerical integration.

CanonicalMethod	Method () const
	Returns the method used for computing the canonical partition functions.

void	SetMethod (CanonicalMethod method)
	Sets the method for computing the canonical partition functions.

void	SetModelGCE (ThermalModelBase *model)
	Sets an external GCE model to use in the saddle-point approach.

virtual void	ResetCalculatedFlags ()

void	ResetPartialZCalculated ()

bool	IsPartialZCalculated () const

bool	IsPartialZCalculatedFlucts () const

void	ChangeTPS (ThermalParticleSystem *TPS)
	Change the particle list.

virtual void	SetStatistics (bool stats)

virtual void	FixParameters ()
	Method which actually implements ConstrainChemicalPotentials() (for backward compatibility).

virtual void	FixParametersNoReset ()
	Method which actually implements ConstrainChemicalPotentialsNoReset() (for backward compatibility).

void	SolveChemicalPotentialsGCE (bool resetInitialValues)

virtual void	CalculatePrimordialDensities ()
	Calculates the primordial densities of all species.

virtual void	ValidateCalculation ()
	Checks whether issues have occured during the calculation of particle densities in the CalculateDensities() method.

virtual double	ParticleScaledVariance (int part)

virtual void	CalculateTwoParticleCorrelations ()
	Computes the fluctuations and correlations of the primordial particle numbers.

virtual void	CalculateFluctuations ()
	Computes the fluctuation observables.

virtual double	CalculateEnergyDensity ()

virtual double	CalculatePressure ()

virtual double	CalculateEntropyDensity ()

virtual double	CalculateEnergyDensityDerivativeT ()

virtual double	CalculateEntropyDensityDerivativeT ()

virtual double	ParticleScalarDensity (int)
	Returns the scalar density of a particle species.

Public Member Functions inherited from thermalfist::ThermalModelBase
	ThermalModelBase (ThermalParticleSystem *TPS, const ThermalModelParameters &params=ThermalModelParameters())
	Construct a new ThermalModelBase object.

virtual	~ThermalModelBase (void)

int	ComponentsNumber () const
	Number of different particle species in the list.

virtual void	FillVirial (const std::vector< double > &ri=std::vector< double >(0))
	Fills the excluded volume coefficients \( \tilde{b}_{ij} \) based on the provided radii parameters for all species.

bool	UseWidth () const
	Whether finite resonance widths are considered.

void	SetUseWidth (bool useWidth)
	Sets whether finite resonance widths are used. Deprecated.

void	SetUseWidth (ThermalParticle::ResonanceWidthIntegration type)
	Sets the finite resonance widths scheme to use.

void	SetNormBratio (bool normBratio)
	Whether branching ratios are renormalized to 100%.

bool	NormBratio () const

void	SetOMP (bool openMP)
	OpenMP support. Currently not used.

virtual void	SetParameters (const ThermalModelParameters &params)
	The thermal parameters.

const ThermalModelParameters &	Parameters () const

void	UpdateParameters ()
	Calls SetParameters() with current m_Parameters.

virtual void	SetTemperature (double T)
	Set the temperature.

virtual void	SetBaryonChemicalPotential (double muB)
	Set the baryon chemical potential.

virtual void	SetElectricChemicalPotential (double muQ)
	Set the electric chemical potential.

virtual void	SetStrangenessChemicalPotential (double muS)
	Set the strangeness chemical potential.

virtual void	SetCharmChemicalPotential (double muC)
	Set the charm chemical potential.

virtual void	SetGammaq (double gammaq)
	Set the light quark fugacity factor.

virtual void	SetGammaS (double gammaS)
	Set the strange quark fugacity factor.

virtual void	SetGammaC (double gammaC)
	Set the charm quark fugacity factor.

virtual void	SetBaryonCharge (int B)
	Set the total baryon number (for canonical ensemble only)

virtual void	SetElectricCharge (int Q)
	Set the total electric charge (for canonical ensemble only)

virtual void	SetStrangeness (int S)
	Set the total strangeness (for canonical ensemble only)

virtual void	SetCharm (int C)
	Set the total charm (for canonical ensemble only)

virtual void	SetRadius (double)
	Set the same excluded volume radius parameter for all species.

virtual void	SetRadius (int, double)
	Set the radius parameter for particle species i.

virtual void	SetVirial (int, int, double)
	Set the excluded volume coefficient \( \tilde{b}_{ij} \).

virtual void	SetRepulsion (int i, int j, double b)
	Same as SetVirial() but with a more clear name on what is actually does.

virtual void	SetAttraction (int, int, double)
	Set the vdW mean field attraction coefficient \( a_{ij} \).

virtual void	DisableMesonMesonVirial ()

void	DisableMesonMesonRepulsion ()

virtual void	DisableMesonMesonAttraction ()

virtual void	DisableMesonBaryonVirial ()

void	DisableMesonBaryonRepulsion ()

virtual void	DisableMesonBaryonAttraction ()

virtual void	DisableBaryonBaryonVirial ()

void	DisableBaryonBaryonRepulsion ()

virtual void	DisableBaryonBaryonAttraction ()

virtual void	DisableBaryonAntiBaryonVirial ()

void	DisableBaryonAntiBaryonRepulsion ()

virtual void	DisableBaryonAntiBaryonAttraction ()

virtual void	ReadInteractionParameters (const std::string &)
	Reads the QvdW interaction parameters from a file.

virtual void	WriteInteractionParameters (const std::string &)
	Write the QvdW interaction parameters to a file.

virtual double	VirialCoefficient (int, int) const
	Excluded volume coefficient \( \tilde{b}_{ij} = 0 \).

double	RepulsionCoefficient (int i, int j) const

virtual double	AttractionCoefficient (int, int) const
	QvdW mean field attraction coefficient \( a_{ij} \).

bool	QuantumStatistics () const

virtual void	SetCalculationType (IdealGasFunctions::QStatsCalculationType type)
	Sets the CalculationType() method to evaluate quantum statistics. Calls the corresponding method in TPS().

virtual void	SetClusterExpansionOrder (int order)
	Set the number of terms in the cluster expansion method. Calls the corresponding method in TPS().

void	SetResonanceWidthShape (ThermalParticle::ResonanceWidthShape shape)
	Set the ThermalParticle::ResonanceWidthShape for all particles. Calls the corresponding method in TPS().

void	SetResonanceWidthIntegrationType (ThermalParticle::ResonanceWidthIntegration type)
	Set the ThermalParticle::ResonanceWidthIntegration scheme for all particles. Calls the corresponding method in TPS().

virtual void	FillChemicalPotentials ()
	Sets the chemical potentials of all particles.

virtual void	SetChemicalPotentials (const std::vector< double > &chem=std::vector< double >(0))
	Sets the chemical potentials of all particles.

const std::vector< double > &	ChemicalPotentials () const
	A vector of chemical potentials of all particles.

double	ChemicalPotential (int i) const
	Chemical potential of particle species i.

virtual void	SetChemicalPotential (int i, double chem)
	Sets the chemical potential of particle species i.

virtual double	FullIdealChemicalPotential (int i) const
	Chemical potential entering the ideal gas expressions of particle species i.

bool	ConstrainMuB () const

void	ConstrainMuB (bool constrain)

bool	ConstrainMuQ () const

void	ConstrainMuQ (bool constrain)

bool	ConstrainMuS () const

void	ConstrainMuS (bool constrain)

bool	ConstrainMuC () const

void	ConstrainMuC (bool constrain)

bool	ConstrainGammaC () const

void	ConstrainGammaC (bool constrain)
	Sets whether gammaC is constrained from target Nccbar.

void	SetNccbar (double Nccbar)
	The target number of cc-bar pairs to be used to constrain gammaC.

double	NccbarGoal () const

void	UsePartialChemicalEquilibrium (bool usePCE)
	Sets whether partial chemical equilibrium with additional chemical potentials is used.

bool	UsePartialChemicalEquilibrium ()
	Whether partial chemical equilibrium with additional chemical potentials is used.

void	SetSoverB (double SB)
	The entropy per baryon ratio to be used to constrain the baryon chemical potential.

double	SoverB () const

void	SetQoverB (double QB)
	The electric-to-baryon charge ratio to be used to constrain the electric chemical potential.

double	QoverB () const

void	SetVolume (double Volume)
	Sets the system volume.

double	Volume () const
	System volume (fm \(^3\))

void	SetVolumeRadius (double R)
	Sets the system radius.

double	CanonicalVolume () const
	The canonical correlation volume V \(_c\) (fm \(^3\))

void	SetCanonicalVolume (double Volume)
	Set the canonical correlation volume V \(_c\).

void	SetCanonicalVolumeRadius (double Rc)
	Set the canonical correlation system radius.

void	ConstrainChemicalPotentials (bool resetInitialValues=true)
	Constrains the chemical potentials \( \mu_B,\,\mu_Q,\,\mu_S,\,\mu_C \) by the conservation laws imposed.

virtual bool	SolveChemicalPotentials (double totB=0., double totQ=0., double totS=0., double totC=0., double muBinit=0., double muQinit=0., double muSinit=0., double muCinit=0., bool ConstrMuB=true, bool ConstrMuQ=true, bool ConstrMuS=true, bool ConstrMuC=true)
	The procedure which calculates the chemical potentials \( \mu_B,\,\mu_Q,\,\mu_S,\,\mu_C \) which reproduce the specified total baryon, electric, strangeness, and charm charges of the system.

virtual bool	FixChemicalPotentialsThroughDensities (double rhoB=0., double rhoQ=0., double rhoS=0., double rhoC=0., double muBinit=0., double muQinit=0., double muSinit=0., double muCinit=0., bool ConstrMuB=true, bool ConstrMuQ=true, bool ConstrMuS=true, bool ConstrMuC=true)
	The procedure which calculates the chemical potentials \( \mu_B,\,\mu_Q,\,\mu_S,\,\mu_C \) which reproduce the specified baryon, electric, strangeness, and charm densities.

virtual void	CalculateDensities ()
	Calculates the primordial and total (after decays) densities of all species.

std::string	ValidityCheckLog () const
	All messaged which occured during the validation procedure in the ValidateCalculation() method.

virtual void	CalculateDensitiesGCE ()
	Calculates the particle densities in a grand-canonical ensemble.

virtual void	CalculateFeeddown ()
	Calculates the total densities which include feeddown contributions.

virtual void	CalculateTemperatureDerivatives ()
	Computes the temperature derivatives of densities, shifted chemical potentials, and primordial hadron number susceptibilities.

virtual void	CalculateTwoParticleFluctuationsDecays ()
	Computes particle number correlations and fluctuations for all final-state particles which are marked stable.

virtual void	ApplyBaryonAnnihilation (double gammaBbar)
	[EXPERIMENTAL] Applies a baryon annihilation toy model to baryon yields and susceptibilities with the given gammaBbar.

virtual double	TwoParticleSusceptibilityPrimordial (int i, int j) const
	Returns the computed primordial particle number (cross-)susceptibility \( \frac{1}{VT^3} \, \langle \Delta N_i \Delta N_j \rangle \) for particles with ids i and j. CalculateFluctuations() must be called beforehand.

virtual double	TwoParticleSusceptibilityPrimordialByPdg (long long id1, long long id2)
	Returns the computed primordial particle number (cross-)susceptibility \( \frac{1}{VT^3} \, \langle \Delta N_i \Delta N_j \rangle \) for particles with pdg codes id1 and id2. CalculateFluctuations() must be called beforehand.

virtual double	TwoParticleSusceptibilityTemperatureDerivativePrimordial (int i, int j) const
	Returns the computed temperature derivative of the primordial particle number (cross-)susceptibility \( \frac{\partial}{\partial T} \frac{1}{VT^3} \, \langle \Delta N_i \Delta N_j \rangle \) for particles with ids i and j. CalculateFluctuations() must be called beforehand.

virtual double	TwoParticleSusceptibilityTemperatureDerivativePrimordialByPdg (long long id1, long long id2)
	Returns the computed temperature derivative of the primordial particle number (cross-)susceptibility \( \frac{\partial}{\partial T} \frac{1}{VT^3} \, \langle \Delta N_i \Delta N_j \rangle \) for particles with pdg codes id1 and id2. CalculateFluctuations() must be called beforehand.

virtual double	NetParticleSusceptibilityPrimordialByPdg (long long id1, long long id2)
	Returns the computed (cross-)susceptibility \( \frac{1}{VT^3} \, \langle \Delta N_i \Delta N_j \rangle \) between primordial net-particle numbers for pdg codes id1 and id2. CalculateFluctuations() must be called beforehand.

virtual double	TwoParticleSusceptibilityFinal (int i, int j) const
	Returns the computed final particle number (cross-)susceptibility \( \frac{1}{VT^3} \, \langle \Delta N_i \Delta N_j \rangle \) for particles with ids i and j. CalculateFluctuations() must be called beforehand. Both particle species must be those marked stable.

virtual double	TwoParticleSusceptibilityFinalByPdg (long long id1, long long id2)
	Returns the computed final particle number (cross-)susceptibility \( \frac{1}{VT^3} \, \langle \Delta N_i \Delta N_j \rangle \) for particles with pdg codes id1 and id2. CalculateFluctuations() must be called beforehand. Both particle species must be those marked stable.

virtual double	NetParticleSusceptibilityFinalByPdg (long long id1, long long id2)
	Returns the computed (cross-)susceptibility \( \frac{1}{VT^3} \, \langle \Delta N_i \Delta N_j \rangle \) between final net-particle numbers for pdg codes id1 and id2. CalculateFluctuations() must be called beforehand.

virtual double	PrimordialParticleChargeSusceptibility (int i, ConservedCharge::Name chg) const
	Returns the computed primordial particle vs conserved charge (cross-)susceptibility \( \frac{1}{VT^3} \, \langle \Delta N_i \Delta N_chg \rangle \) for particle with id i and conserved charge chg. CalculateFluctuations() must be called beforehand.

virtual double	PrimordialParticleChargeSusceptibilityByPdg (long long id1, ConservedCharge::Name chg)
	Returns the computed primordial particle vs conserved charge (cross-)susceptibility \( \frac{1}{VT^3} \, \langle \Delta N_i \Delta N_chg \rangle \) for particle with pdg code id1 and conserved charge chg. CalculateFluctuations() must be called beforehand.

virtual double	PrimordialNetParticleChargeSusceptibilityByPdg (long long id1, ConservedCharge::Name chg)
	Returns the computed primordial net particle vs conserved charge (cross-)susceptibility \( \frac{1}{VT^3} \, \langle \Delta N_i \Delta N_chg \rangle \) for particle with pdg code id1 and conserved charge chg. CalculateFluctuations() must be called beforehand.

virtual double	FinalParticleChargeSusceptibility (int i, ConservedCharge::Name chg) const
	Returns the computed final (after decays) particle vs conserved charge (cross-)susceptibility \( \frac{1}{VT^3} \, \langle \Delta N_i \Delta N_chg \rangle \) for particle with id i and conserved charge chg. CalculateFluctuations() must be called beforehand.

virtual double	FinalParticleChargeSusceptibilityByPdg (long long id1, ConservedCharge::Name chg)
	Returns the computed final (after decays) particle vs conserved charge (cross-)susceptibility \( \frac{1}{VT^3} \, \langle \Delta N_i \Delta N_chg \rangle \) for particle with pdg code id1 and conserved charge chg. CalculateFluctuations() must be called beforehand.

virtual double	FinalNetParticleChargeSusceptibilityByPdg (long long id1, ConservedCharge::Name chg)
	Returns the computed final (after decays) net particle vs conserved charge (cross-)susceptibility \( \frac{1}{VT^3} \, \langle \Delta N_i \Delta N_chg \rangle \) for particle with pdg code id1 and conserved charge chg. CalculateFluctuations() must be called beforehand.

virtual double	SusceptibilityDimensionfull (ConservedCharge::Name i, ConservedCharge::Name j) const
	A 2nd order susceptibility of conserved charges.

virtual void	CalculateSusceptibilityMatrix ()
	Calculates the conserved charges susceptibility matrix.

virtual void	CalculateProxySusceptibilityMatrix ()
	Calculates the susceptibility matrix of conserved charges proxies.

virtual void	CalculateParticleChargeCorrelationMatrix ()
	Calculates the matrix of correlators between primordial (and also final) particle numbers and conserved charges.

virtual std::vector< double >	CalculateChargeFluctuations (const std::vector< double > &chgs, int order=4, bool dimensionfull=false)
	Calculates fluctuations (diagonal susceptibilities) of an arbitrary "conserved" charge.

Protected Attributes
std::vector< QuantumNumbers >	m_QNvec
	A set of QuantumNumbers combinations for which it is necessary to compute the canonical partition function.

std::map< QuantumNumbers, int >	m_QNMap
	Maps QuantumNumbers combinations to a 1-dimensional index.

std::vector< double >	m_Corr
	A vector of chemical factors.

std::vector< double >	m_PartialZ
	The computed canonical partition function.

int	m_IntegrationIterationsMultiplier
	A multiplier to increase the number of iterations during the numerical integration used to calculate the partition functions.

CanonicalMethod	m_Method
	Method for computing the canonical partition functions.

int	m_BMAX
	Maximum baryon number.

int	m_QMAX
	Maximum electric charge.

int	m_SMAX
	Maximum strangeness.

int	m_CMAX
	Maximum charm.

int	m_BMAX_list

int	m_QMAX_list

int	m_SMAX_list

int	m_CMAX_list

double	m_MultExp
	Exponential multiplier for canonical partition function calculations.

double	m_MultExpBanalyt
	Exponential multiplier for analytical baryon fugacity calculations.

ThermalModelBase *	m_modelgce

ThermalModelBase *	m_modelgce_default
	Default ideal-gas GCE model (owned, created once)

ThermalModelBase *	m_modelgce_ext
	External GCE model (not owned), set via SetModelGCE()

int	m_BCE
	Flag indicating if baryon charge is conserved canonically.

int	m_QCE
	Flag indicating if electric charge is conserved canonically.

int	m_SCE
	Flag indicating if strangeness is conserved canonically.

int	m_CCE
	Flag indicating if charm is conserved canonically.

bool	m_Banalyt
	Flag indicating whether the analytical calculation of baryon fugacity is used.

bool	m_PartialZCalculated

bool	m_PartialZCalculatedFlucts

int	m_SaddlePointDim
	Saddle-point approximation data (for SaddlePoint quadrature method)

std::vector< int >	m_SaddlePointChargeIndices
	Which of {B=0,Q=1,S=2,C=3} are canonical.

std::vector< double >	m_SaddlePointMu
	Saddle-point mu*_a/T for each conserved charge (size 4)

std::vector< double >	m_SaddlePointMuStar
	Per-particle full chemical potential at saddle point.

double	m_SaddlePointLogDetSigma
	log(det(Sigma))

std::vector< double >	m_W2
	Per-particle W^(2) = Vc * chi2 (for SaddlePointNLO)

double	m_NLOEnergyDensity
	ε = ε^GCE(μ) - (1/2) Σ_j E_j G_jj (LO: ε^GCE(μ))

double	m_NLOPressure
	P = p^GCE(μ) - d·T/(2·Vc) (LO: p^GCE(μ))

double	m_NLOEntropyDensity
	LO entropy: s^GCE(μ*) (used only by SaddlePointLO; NLO uses lnZ_SP)

Additional Inherited Members
Public Types inherited from thermalfist::ThermalModelBase
enum	ThermalModelEnsemble { GCE = 0 , CE = 1 , SCE = 2 , CCE = 3 }
	The list of statistical ensembles. More...

enum	ThermalModelInteraction { Ideal = 0 , DiagonalEV = 1 , CrosstermsEV = 2 , QvdW = 3 , RealGas = 4 , MeanField = 5 }
	Type of interactions included in the HRG model. More...

Detailed Description

Class implementing the HRG model in the canonical ensemble.

Computes particle densities and fluctuations with exact conservation of an arbitrary subset of {B, Q, S, C}. Several computational methods are available (see CanonicalMethod):

GaussLegendre / SaddlePoint: numerical integration or per-QN saddle-point evaluation; ideal gas only.
SaddlePointNLO: systematic 1/V expansion including O(1/V_c) corrections to means, covariances, and thermodynamics; ideal gas only.
SaddlePointLO: leading-order saddle-point; supports non-ideal equations of state via SetModelGCE().

Non-ideal interactions (SaddlePointLO only)

Provide a pre-configured GCE model via SetModelGCE():

auto* rg = new ThermalModelRealGas(&TPS, params);
rg->SetExcludedVolumeModel(...);
model.SetModelGCE(rg);    // borrow; caller retains ownership

LO covariance formula

The SaddlePointLO covariance is computed from the general formula

\[ \mathrm{cov}(N_l, N_m) = \chi^{\rm GCE}_{lm} - \sum_{a,b} v_{l,a}\,[\Sigma_\chi^{-1}]_{ab}\,v_{m,b} \]

where \(\chi^{\rm GCE}_{jk}\) is the GCE species-level susceptibility matrix (diagonal for ideal gas, full for interacting models), \(v_{l,a} = \sum_j q_{a,j}\,\chi^{\rm GCE}_{jl}\), and \(\Sigma_{ab} = \sum_{j,k} q_{a,j}\,q_{b,k}\,\chi^{\rm GCE}_{jk}\).

This is equivalent to the subensemble acceptance method (SAM) at full acceptance ( \(\alpha = 1\)), specifically Eq. (2.86) of V. Vovchenko, R.V. Poberezhnyuk, V. Koch, JHEP 10 (2020) 089 [arXiv:2007.03850]: \(\chi_{pp}^{\rm ce} = \det\tilde\chi / \det\chi\), via the Schur complement identity.

References

F. Becattini, U. Heinz, Z. Phys. C76, 269 (1997) hep-ph/9702274
Fluctuations via fictitious fugacities: nucl-th/0404056
SAM formalism: V. Vovchenko, R.V. Poberezhnyuk, V. Koch, JHEP 10 (2020) 089 arXiv:2007.03850

Definition at line 147 of file ThermalModelCanonical.h.

Constructor & Destructor Documentation

◆ ThermalModelCanonical()

thermalfist::ThermalModelCanonical::ThermalModelCanonical	(	ThermalParticleSystem *	TPS,
		const ThermalModelParameters &	params = ThermalModelParameters() )

Construct a new ThermalModelCanonical object.

Parameters

TPS	A pointer to the ThermalParticleSystem object containing the particle list
params	ThermalModelParameters object with current thermal parameters

Definition at line 41 of file ThermalModelCanonical.cpp.

◆ ~ThermalModelCanonical()

thermalfist::ThermalModelCanonical::~ThermalModelCanonical ( void )

virtual

Destroy the ThermalModelCanonical object.

Definition at line 73 of file ThermalModelCanonical.cpp.

Member Function Documentation

◆ CalculateEnergyDensity()

double thermalfist::ThermalModelCanonical::CalculateEnergyDensity ( )

virtual

Definition at line 943 of file ThermalModelCanonical.cpp.

◆ CalculateEnergyDensityDerivativeT()

virtual double thermalfist::ThermalModelCanonical::CalculateEnergyDensityDerivativeT ( )

inlinevirtual

Definition at line 356 of file ThermalModelCanonical.h.

◆ CalculateEntropyDensity()

double thermalfist::ThermalModelCanonical::CalculateEntropyDensity ( )

virtual

Definition at line 1020 of file ThermalModelCanonical.cpp.

◆ CalculateEntropyDensityDerivativeT()

virtual double thermalfist::ThermalModelCanonical::CalculateEntropyDensityDerivativeT ( )

inlinevirtual

Definition at line 358 of file ThermalModelCanonical.h.

◆ CalculateFluctuations()

void thermalfist::ThermalModelCanonical::CalculateFluctuations ( )

virtual

Computes the fluctuation observables.

Includes the matrix of 2nd order susceptibilities of conserved charges, as well as particle number correlations and fluctuations, both for primordial yields and after decays. Restricted to 2nd moments. TODO: Higher moments

Reimplemented from thermalfist::ThermalModelBase.

Definition at line 910 of file ThermalModelCanonical.cpp.

◆ CalculatePartitionFunctions()

void thermalfist::ThermalModelCanonical::CalculatePartitionFunctions ( double Vc = -1. )

virtual

Calculates all necessary canonical partition functions.

This corresponds to Eq. (8) in https://arxiv.org/pdf/hep-ph/9702274.pdf

Integrals are performed numerically using quadratures.

If multi-baryon states (light nuclei) are not included in the list, and quantum statistics for baryons is neglected, the integral over the baryon fugacity is performed analytically as described in (https://arxiv.org/pdf/nucl-th/0112021.pdf)[https://arxiv.org/pdf/nucl-th/0112021.pdf].

Parameters

Vc

Definition at line 428 of file ThermalModelCanonical.cpp.

◆ CalculatePressure()

double thermalfist::ThermalModelCanonical::CalculatePressure ( )

virtual

Definition at line 981 of file ThermalModelCanonical.cpp.

◆ CalculatePrimordialDensities()

void thermalfist::ThermalModelCanonical::CalculatePrimordialDensities ( )

virtual

Calculates the primordial densities of all species.

Implements thermalfist::ThermalModelBase.

Definition at line 261 of file ThermalModelCanonical.cpp.

◆ CalculateQuantumNumbersRange()

void thermalfist::ThermalModelCanonical::CalculateQuantumNumbersRange ( bool computeFluctuations = false )

virtual

Calculates the range of quantum numbers values for which it is necessary to compute the canonical partition functions.

Parameters

computeFluctuations Whether it will be necessary to compute fluctuations. If that is the case the range is doubled for every quantum number.

Definition at line 84 of file ThermalModelCanonical.cpp.

◆ CalculateTwoParticleCorrelations()

void thermalfist::ThermalModelCanonical::CalculateTwoParticleCorrelations ( )

virtual

Computes the fluctuations and correlations of the primordial particle numbers.

More specifically, computes the susceptibility matrix \( \frac{1}{VT^3} \, \langle \Delta N_i^* \Delta N_j^* \rangle \), where \( N_i^* \) is the primordial yield of species i.

Reimplemented from thermalfist::ThermalModelBase.

Definition at line 813 of file ThermalModelCanonical.cpp.

◆ ChangeTPS()

void thermalfist::ThermalModelCanonical::ChangeTPS ( ThermalParticleSystem * TPS )

virtual

Change the particle list.

Parameters

TPS	A pointer to new particle list.

Reimplemented from thermalfist::ThermalModelBase.

Definition at line 78 of file ThermalModelCanonical.cpp.

◆ ConserveBaryonCharge()

virtual void thermalfist::ThermalModelCanonical::ConserveBaryonCharge ( bool conserve = true )

inlinevirtual

Specifies whether the baryon number is treated canonically.

By default the baryon number is treated canonically.

Parameters

conserve true – canonically, false – grand-canonically

Definition at line 213 of file ThermalModelCanonical.h.

◆ ConserveCharm()

virtual void thermalfist::ThermalModelCanonical::ConserveCharm ( bool conserve = true )

inlinevirtual

Specifies whether the charm charge is treated canonically.

By default the charm charge is treated canonically.

Parameters

conserve true – canonically, false – grand-canonically

Definition at line 240 of file ThermalModelCanonical.h.

◆ ConserveElectricCharge()

virtual void thermalfist::ThermalModelCanonical::ConserveElectricCharge ( bool conserve = true )

inlinevirtual

Specifies whether the electric charge is treated canonically.

By default the electric charge is treated canonically.

Parameters

conserve true – canonically, false – grand-canonically

Definition at line 222 of file ThermalModelCanonical.h.

◆ ConserveStrangeness()

virtual void thermalfist::ThermalModelCanonical::ConserveStrangeness ( bool conserve = true )

inlinevirtual

Specifies whether the strangeness charge is treated canonically.

By default the strangeness charge is treated canonically.

Parameters

conserve true – canonically, false – grand-canonically

Definition at line 231 of file ThermalModelCanonical.h.

◆ FixParameters()

void thermalfist::ThermalModelCanonical::FixParameters ( )

virtual

Method which actually implements ConstrainChemicalPotentials() (for backward compatibility).

Reimplemented from thermalfist::ThermalModelBase.

Definition at line 215 of file ThermalModelCanonical.cpp.

◆ FixParametersNoReset()

void thermalfist::ThermalModelCanonical::FixParametersNoReset ( )

virtual

Method which actually implements ConstrainChemicalPotentialsNoReset() (for backward compatibility).

Reimplemented from thermalfist::ThermalModelBase.

Definition at line 242 of file ThermalModelCanonical.cpp.

◆ GetGCEDensity()

double thermalfist::ThermalModelCanonical::GetGCEDensity ( int i ) const

virtual

Density of particle species i in the grand-canonical ensemble.

Parameters

i	0-based index of particle species

Returns: double The grand-canonical density

Definition at line 1060 of file ThermalModelCanonical.cpp.

◆ IntegrationIterationsMultiplier()

int thermalfist::ThermalModelCanonical::IntegrationIterationsMultiplier ( ) const

inline

The multiplier of the number of iterations in the numerical integration.

Returns: The multiplier

Definition at line 257 of file ThermalModelCanonical.h.

◆ IsConservedChargeCanonical()

bool thermalfist::ThermalModelCanonical::IsConservedChargeCanonical ( ConservedCharge::Name charge ) const

virtual

Definition at line 1075 of file ThermalModelCanonical.cpp.

◆ IsPartialZCalculated()

bool thermalfist::ThermalModelCanonical::IsPartialZCalculated ( ) const

inline

Definition at line 313 of file ThermalModelCanonical.h.

◆ IsPartialZCalculatedFlucts()

bool thermalfist::ThermalModelCanonical::IsPartialZCalculatedFlucts ( ) const

inline

Definition at line 318 of file ThermalModelCanonical.h.

◆ IsParticleCanonical()

bool thermalfist::ThermalModelCanonical::IsParticleCanonical ( const ThermalParticle & part )

virtual

Determines whether the specified ThermalParticle is treat canonically or grand-canonically in the present setup.

This depends on whether the particle carries any of the exactly conserved charges.

Parameters

part	The particle species.

Returns: true Canonically.; false Grand-canonically.

Definition at line 1065 of file ThermalModelCanonical.cpp.

◆ Method()

CanonicalMethod thermalfist::ThermalModelCanonical::Method ( ) const

inline

Returns the method used for computing the canonical partition functions.

Definition at line 271 of file ThermalModelCanonical.h.

◆ ParticleScalarDensity()

virtual double thermalfist::ThermalModelCanonical::ParticleScalarDensity ( int )

inlinevirtual

Returns the scalar density of a particle species.

This method is not implemented for the canonical ensemble model, hence it returns a constant value of 0.0.

Returns: double The scalar density, which is 0.0 in this implementation.

Definition at line 368 of file ThermalModelCanonical.h.

◆ ParticleScaledVariance()

double thermalfist::ThermalModelCanonical::ParticleScaledVariance ( int part )

virtual

Definition at line 761 of file ThermalModelCanonical.cpp.

◆ ResetCalculatedFlags()

virtual void thermalfist::ThermalModelCanonical::ResetCalculatedFlags ( )

inlinevirtual

Definition at line 301 of file ThermalModelCanonical.h.

◆ ResetPartialZCalculated()

void thermalfist::ThermalModelCanonical::ResetPartialZCalculated ( )

inline

Definition at line 308 of file ThermalModelCanonical.h.

◆ SetIntegrationIterationsMultiplier()

void thermalfist::ThermalModelCanonical::SetIntegrationIterationsMultiplier ( int multiplier )

inline

Assigns the multiplier of the number of iterations in the numerical integration.

The minimum value of multiplier is 1. Increase to improve the numerical accuracy of the canonical ensemble calculations.

Parameters

multiplier The multiplier (clamped to a minimum of 1).

Definition at line 266 of file ThermalModelCanonical.h.

◆ SetMethod()

void thermalfist::ThermalModelCanonical::SetMethod ( CanonicalMethod method )

inline

Sets the method for computing the canonical partition functions.

Parameters

method GaussLegendre (default) or SaddlePoint

Definition at line 278 of file ThermalModelCanonical.h.

◆ SetModelGCE()

void thermalfist::ThermalModelCanonical::SetModelGCE ( ThermalModelBase * model )

Sets an external GCE model to use in the saddle-point approach.

This is the only way to use non-ideal interactions with the canonical ensemble (SaddlePointLO method only). The provided model is borrowed (not owned) by the canonical model. The caller retains ownership and must ensure the model remains valid during canonical calculations.

The model's thermal parameters and chemical potentials will be overwritten during the saddle-point solve. The interaction parameters (virial, attraction, etc.) are preserved.

Pass nullptr to revert to the default ideal gas.

Parameters

model Pointer to a pre-configured GCE model, or nullptr to clear

Definition at line 1139 of file ThermalModelCanonical.cpp.

◆ SetStatistics()

void thermalfist::ThermalModelCanonical::SetStatistics ( bool stats )

virtual

Set whether quantum statistics is used, 0 - Boltzmann, 1 - Quantum

Reimplemented from thermalfist::ThermalModelBase.

Definition at line 154 of file ThermalModelCanonical.cpp.

◆ SolveChemicalPotentialsGCE()

void thermalfist::ThermalModelCanonical::SolveChemicalPotentialsGCE ( bool resetInitialValues )

Solve non-canonical chemical potentials using a temporary GCE model, avoiding the expensive canonical partition function computation.

Definition at line 170 of file ThermalModelCanonical.cpp.

◆ ValidateCalculation()

void thermalfist::ThermalModelCanonical::ValidateCalculation ( )

virtual

Checks whether issues have occured during the calculation of particle densities in the CalculateDensities() method.

Reimplemented from thermalfist::ThermalModelBase.

Definition at line 342 of file ThermalModelCanonical.cpp.

Member Data Documentation

◆ m_Banalyt

bool thermalfist::ThermalModelCanonical::m_Banalyt

protected

Flag indicating whether the analytical calculation of baryon fugacity is used.

Definition at line 508 of file ThermalModelCanonical.h.

◆ m_BCE

int thermalfist::ThermalModelCanonical::m_BCE

protected

Flag indicating if baryon charge is conserved canonically.

Definition at line 500 of file ThermalModelCanonical.h.

◆ m_BMAX

int thermalfist::ThermalModelCanonical::m_BMAX

protected

Maximum baryon number.

Definition at line 485 of file ThermalModelCanonical.h.

◆ m_BMAX_list

int thermalfist::ThermalModelCanonical::m_BMAX_list

protected

Definition at line 489 of file ThermalModelCanonical.h.

◆ m_CCE

int thermalfist::ThermalModelCanonical::m_CCE

protected

Flag indicating if charm is conserved canonically.

Definition at line 503 of file ThermalModelCanonical.h.

◆ m_CMAX

int thermalfist::ThermalModelCanonical::m_CMAX

protected

Maximum charm.

Definition at line 488 of file ThermalModelCanonical.h.

◆ m_CMAX_list

int thermalfist::ThermalModelCanonical::m_CMAX_list

protected

Definition at line 489 of file ThermalModelCanonical.h.

◆ m_Corr

std::vector<double> thermalfist::ThermalModelCanonical::m_Corr

protected

A vector of chemical factors.

Chemical factors define the canonical corrections to the grand canonical thermodynamic functions.

Definition at line 462 of file ThermalModelCanonical.h.

◆ m_IntegrationIterationsMultiplier

int thermalfist::ThermalModelCanonical::m_IntegrationIterationsMultiplier

protected

A multiplier to increase the number of iterations during the numerical integration used to calculate the partition functions.

Set with SetIntegrationIterationsMultiplier()

Definition at line 481 of file ThermalModelCanonical.h.

◆ m_Method

CanonicalMethod thermalfist::ThermalModelCanonical::m_Method

protected

Method for computing the canonical partition functions.

Definition at line 483 of file ThermalModelCanonical.h.

◆ m_modelgce

ThermalModelBase* thermalfist::ThermalModelCanonical::m_modelgce

protected

Active GCE model pointer (set by PrepareModelGCE, cleared by CleanModelGCE). Points to either m_modelgce_default or m_modelgce_ext; never owned.

Definition at line 496 of file ThermalModelCanonical.h.

◆ m_modelgce_default

ThermalModelBase* thermalfist::ThermalModelCanonical::m_modelgce_default

protected

Default ideal-gas GCE model (owned, created once)

Definition at line 497 of file ThermalModelCanonical.h.

◆ m_modelgce_ext

ThermalModelBase* thermalfist::ThermalModelCanonical::m_modelgce_ext

protected

External GCE model (not owned), set via SetModelGCE()

Definition at line 498 of file ThermalModelCanonical.h.

◆ m_MultExp

double thermalfist::ThermalModelCanonical::m_MultExp

protected

Exponential multiplier for canonical partition function calculations.

Definition at line 491 of file ThermalModelCanonical.h.

◆ m_MultExpBanalyt

double thermalfist::ThermalModelCanonical::m_MultExpBanalyt

protected

Exponential multiplier for analytical baryon fugacity calculations.

Definition at line 492 of file ThermalModelCanonical.h.

◆ m_NLOEnergyDensity

double thermalfist::ThermalModelCanonical::m_NLOEnergyDensity

protected

ε = ε^GCE(μ*) - (1/2) Σ_j E_j G_jj (LO: ε^GCE(μ*))

NLO thermodynamic quantities computed by ComputeAnalyticCumulants(). These are exact at O(1/Vc) including quantum statistics (cluster expansion).

Definition at line 524 of file ThermalModelCanonical.h.

◆ m_NLOEntropyDensity

double thermalfist::ThermalModelCanonical::m_NLOEntropyDensity

protected

LO entropy: s^GCE(μ*) (used only by SaddlePointLO; NLO uses lnZ_SP)

Definition at line 526 of file ThermalModelCanonical.h.

◆ m_NLOPressure

double thermalfist::ThermalModelCanonical::m_NLOPressure

protected

P = p^GCE(μ*) - d·T/(2·Vc) (LO: p^GCE(μ*))

Definition at line 525 of file ThermalModelCanonical.h.

◆ m_PartialZ

std::vector<double> thermalfist::ThermalModelCanonical::m_PartialZ

protected

The computed canonical partition function.

The partition functions are computed up to a factor which does not depend of the quantum numbers since only ratios of the partition functions – the chemical factors – are of relevance.

Definition at line 473 of file ThermalModelCanonical.h.

◆ m_PartialZCalculated

bool thermalfist::ThermalModelCanonical::m_PartialZCalculated

protected

Definition at line 510 of file ThermalModelCanonical.h.

◆ m_PartialZCalculatedFlucts

bool thermalfist::ThermalModelCanonical::m_PartialZCalculatedFlucts

protected

Definition at line 511 of file ThermalModelCanonical.h.

◆ m_QCE

int thermalfist::ThermalModelCanonical::m_QCE

protected

Flag indicating if electric charge is conserved canonically.

Definition at line 501 of file ThermalModelCanonical.h.

◆ m_QMAX

int thermalfist::ThermalModelCanonical::m_QMAX

protected

Maximum electric charge.

Definition at line 486 of file ThermalModelCanonical.h.

◆ m_QMAX_list

int thermalfist::ThermalModelCanonical::m_QMAX_list

protected

Definition at line 489 of file ThermalModelCanonical.h.

◆ m_QNMap

std::map<QuantumNumbers, int> thermalfist::ThermalModelCanonical::m_QNMap

protected

Maps QuantumNumbers combinations to a 1-dimensional index.

Definition at line 453 of file ThermalModelCanonical.h.

◆ m_QNvec

std::vector<QuantumNumbers> thermalfist::ThermalModelCanonical::m_QNvec

protected

A set of QuantumNumbers combinations for which it is necessary to compute the canonical partition function.

Definition at line 446 of file ThermalModelCanonical.h.

◆ m_SaddlePointChargeIndices

std::vector<int> thermalfist::ThermalModelCanonical::m_SaddlePointChargeIndices

protected

Which of {B=0,Q=1,S=2,C=3} are canonical.

Definition at line 516 of file ThermalModelCanonical.h.

◆ m_SaddlePointDim

int thermalfist::ThermalModelCanonical::m_SaddlePointDim

protected

Saddle-point approximation data (for SaddlePoint quadrature method)

Number of canonically conserved charges (d <= 4)

Definition at line 515 of file ThermalModelCanonical.h.

◆ m_SaddlePointLogDetSigma

double thermalfist::ThermalModelCanonical::m_SaddlePointLogDetSigma

protected

log(det(Sigma))

Definition at line 519 of file ThermalModelCanonical.h.

◆ m_SaddlePointMu

std::vector<double> thermalfist::ThermalModelCanonical::m_SaddlePointMu

protected

Saddle-point mu*_a/T for each conserved charge (size 4)

Definition at line 517 of file ThermalModelCanonical.h.

◆ m_SaddlePointMuStar

std::vector<double> thermalfist::ThermalModelCanonical::m_SaddlePointMuStar

protected

Per-particle full chemical potential at saddle point.

Definition at line 518 of file ThermalModelCanonical.h.

◆ m_SCE

int thermalfist::ThermalModelCanonical::m_SCE

protected

Flag indicating if strangeness is conserved canonically.

Definition at line 502 of file ThermalModelCanonical.h.

◆ m_SMAX

int thermalfist::ThermalModelCanonical::m_SMAX

protected

Maximum strangeness.

Definition at line 487 of file ThermalModelCanonical.h.

◆ m_SMAX_list

int thermalfist::ThermalModelCanonical::m_SMAX_list

protected

Definition at line 489 of file ThermalModelCanonical.h.

◆ m_W2

std::vector<double> thermalfist::ThermalModelCanonical::m_W2

protected

Per-particle W^(2) = Vc * chi2 (for SaddlePointNLO)

Definition at line 520 of file ThermalModelCanonical.h.

The documentation for this class was generated from the following files:

include/HRGCanonical/ThermalModelCanonical.h
src/library/HRGCanonical/ThermalModelCanonical.cpp

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Non-ideal interactions (SaddlePointLO only)

LO covariance formula

References

Constructor & Destructor Documentation

◆ ThermalModelCanonical()

◆ ~ThermalModelCanonical()

Member Function Documentation

◆ CalculateEnergyDensity()

◆ CalculateEnergyDensityDerivativeT()

◆ CalculateEntropyDensity()

◆ CalculateEntropyDensityDerivativeT()

◆ CalculateFluctuations()

◆ CalculatePartitionFunctions()

◆ CalculatePressure()

◆ CalculatePrimordialDensities()

◆ CalculateQuantumNumbersRange()

◆ CalculateTwoParticleCorrelations()

◆ ChangeTPS()

◆ ConserveBaryonCharge()

◆ ConserveCharm()

◆ ConserveElectricCharge()

◆ ConserveStrangeness()

◆ FixParameters()

◆ FixParametersNoReset()

◆ GetGCEDensity()

◆ IntegrationIterationsMultiplier()

◆ IsConservedChargeCanonical()

◆ IsPartialZCalculated()

◆ IsPartialZCalculatedFlucts()

◆ IsParticleCanonical()

◆ Method()

◆ ParticleScalarDensity()

◆ ParticleScaledVariance()

◆ ResetCalculatedFlags()

◆ ResetPartialZCalculated()

◆ SetIntegrationIterationsMultiplier()

◆ SetMethod()

◆ SetModelGCE()

◆ SetStatistics()

◆ SolveChemicalPotentialsGCE()

◆ ValidateCalculation()

Member Data Documentation

◆ m_Banalyt

◆ m_BCE

◆ m_BMAX

◆ m_BMAX_list

◆ m_CCE

◆ m_CMAX

◆ m_CMAX_list

◆ m_Corr

◆ m_IntegrationIterationsMultiplier

◆ m_Method

◆ m_modelgce

◆ m_modelgce_default

◆ m_modelgce_ext

◆ m_MultExp

◆ m_MultExpBanalyt

◆ m_NLOEnergyDensity

◆ m_NLOEntropyDensity

◆ m_NLOPressure

◆ m_PartialZ

◆ m_PartialZCalculated

◆ m_PartialZCalculatedFlucts

◆ m_QCE

◆ m_QMAX

◆ m_QMAX_list

◆ m_QNMap

◆ m_QNvec

◆ m_SaddlePointChargeIndices

◆ m_SaddlePointDim

◆ m_SaddlePointLogDetSigma

◆ m_SaddlePointMu

◆ m_SaddlePointMuStar

◆ m_SCE

◆ m_SMAX

◆ m_SMAX_list