Pomerol::TwoParticleGFPart::ResonantTerm Struct Reference

A resonant term in the Lehmann representation of TwoParticleGF. More...

#include <TwoParticleGFPart.hpp>

Data Structures
struct	Hash
	Hasher for resonant terms. More...
struct	IsNegligible
	Predicate: Does a term have a negligible residue? More...
struct	KeyEqual
	Similarity predicate for resonant terms. More...

Public Member Functions
	ResonantTerm ()=default
	ResonantTerm (ComplexType ResCoeff, ComplexType NonResCoeff, RealType P1, RealType P2, RealType P3, bool isz1z2)
ComplexType	operator() (ComplexType z1, ComplexType z2, ComplexType z3, RealType DeltaTolerance=1e-16) const
ResonantTerm &	operator+= (ResonantTerm const &AnotherTerm)

Static Public Member Functions
static MPI_Datatype	mpi_datatype ()
	Create and commit an MPI datatype for ResonantTerm. More...

Data Fields
ComplexType	ResCoeff = 0
	Coefficient \(R\). More...
ComplexType	NonResCoeff = 0
	Coefficient \(N\). More...
std::array< RealType, 3 >	Poles = {{0, 0, 0}}
	Poles \(P_1\), \(P_2\), \(P_3\). More...
bool	isz1z2 = false
long	Weight = 0

Detailed Description

A resonant term in the Lehmann representation of TwoParticleGF.

It is parametrized by two complex coefficients \(R\) and \(N\), and positions of real poles \(P_1, P_2, P_3\). Depending on the value of the isz1z2 flag, an explicit expression for the term reads

• \( \frac{1}{(z_1-P_1)(z_3-P_3)} \left( R \delta(z_1+z_2-P_1-P_2) + N \frac{1 - \delta(z_1+z_2-P_1-P_2)}{z_1+z_2-P_1-P_2} \right) \) for isz1z2 == true,
• \( \frac{1}{(z_1-P_1)(z_3-P_3)} \left( R \delta(z_2+z_3-P_2-P_3) + N \frac{1 - \delta(z_2+z_3-P_2-P_3)}{z_2+z_3-P_2-P_3} \right) \) for isz1z2 == false.

Definition at line 189 of file TwoParticleGFPart.hpp.

Constructor & Destructor Documentation

ResonantTerm() [1/2]

Pomerol::TwoParticleGFPart::ResonantTerm::ResonantTerm ( )

default

ResonantTerm() [2/2]

Pomerol::TwoParticleGFPart::ResonantTerm::ResonantTerm ( ComplexType  ResCoeff, ComplexType  NonResCoeff, RealType  P1, RealType  P2, RealType  P3, bool  isz1z2  )

inline

Constructor.

Parameters

[in]	ResCoeff	Numerator of the term for the resonant case, \(R\).
[in]	NonResCoeff	Numerator of the term for the non-resonant case, \(N\).
[in]	P1	Pole \(P_1\).
[in]	P2	Pole \(P_2\).
[in]	P3	Pole \(P_3\).
[in]	isz1z2	Are we using the \(\delta(z_1+z_2-P_1-P_2)\) resonance condition?

Definition at line 279 of file TwoParticleGFPart.hpp.

Member Function Documentation

mpi_datatype()

static MPI_Datatype Pomerol::TwoParticleGFPart::ResonantTerm::mpi_datatype ( )

static

Create and commit an MPI datatype for ResonantTerm.

operator()()

ComplexType Pomerol::TwoParticleGFPart::ResonantTerm::operator() ( ComplexType  z1, ComplexType  z2, ComplexType  z3, RealType  DeltaTolerance = 1e-16  ) const

inline

Substitute complex frequencies \(z_1, z_2, z_3\) into this term.

Parameters

[in]	z1	Complex frequency \(z_1\).
[in]	z2	Complex frequency \(z_2\).
[in]	z3	Complex frequency \(z_3\).
[in]	DeltaTolerance	Tolerance for the resonance detection.

Definition at line 481 of file TwoParticleGFPart.hpp.

operator+=()

ResonantTerm& Pomerol::TwoParticleGFPart::ResonantTerm::operator+=

(

ResonantTerm const &

AnotherTerm

)

Add a resonant term to this term.

This operator does not check similarity of the terms! Parameters of this term are updated as follows.

• ResCoeff += AnotherTerm.ResCoeff
• NonResCoeff += AnotherTerm.NonResCoeff
• Poles[i] = (Poles[i] * Weight + AnotherTerm.Poles[i] * AnotherTerm.Weight) / (Weight + AnotherTerm.Weight)
• Weight += AnotherTerm.Weight

  Parameters

  [in]

  AnotherTerm

  Term to add.

Field Documentation

isz1z2

bool Pomerol::TwoParticleGFPart::ResonantTerm::isz1z2 = false

Are we using \( \delta(z_1+z_2-P_1-P_2) \) resonance condition? If not, we are using \( \delta(z_2+z_3-P_2-P_3) \).

Definition at line 201 of file TwoParticleGFPart.hpp.

NonResCoeff

ComplexType Pomerol::TwoParticleGFPart::ResonantTerm::NonResCoeff = 0

Coefficient \(N\).

Definition at line 194 of file TwoParticleGFPart.hpp.

Poles

std::array<RealType, 3> Pomerol::TwoParticleGFPart::ResonantTerm::Poles = {{0, 0, 0}}

Poles \(P_1\), \(P_2\), \(P_3\).

Definition at line 197 of file TwoParticleGFPart.hpp.

ResCoeff

ComplexType Pomerol::TwoParticleGFPart::ResonantTerm::ResCoeff = 0

Coefficient \(R\).

Definition at line 192 of file TwoParticleGFPart.hpp.

Weight

long Pomerol::TwoParticleGFPart::ResonantTerm::Weight = 0

Weight \(W\) used in addition of terms with different poles.

See also

operator+=()

Definition at line 205 of file TwoParticleGFPart.hpp.

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The documentation for this struct was generated from the following file:

• pomerol/TwoParticleGFPart.hpp