Enumerations
enum class	RealTimeTransport::Eta : int { Minus = 0 , Plus = 1 , _count }
	Particle-hole $ \eta $ index. More...

enum class	RealTimeTransport::Keldysh : int { Minus = 0 , Plus = 1 , _count }
	Keldysh index $ p $. More...

Functions
BlockMatrix	RealTimeTransport::computeSuperfermion (Keldysh p, Eta eta, int l, const std::unique_ptr< Model > &model)
	Computes a superfermion for a given model.

std::vector< BlockMatrix >	RealTimeTransport::computeAllSuperfermions (Keldysh p, const std::unique_ptr< Model > &model)
	Computes all creation or annihilation superfermions (for p=+,- respectively) for a given model.

SciCore::Complex	RealTimeTransport::computeGamma (Eta eta, int r, int l1, int l2, const std::unique_ptr< Model > &model)
	Convenience function to compute $ \Gamma_{η r l_1 l_2} $.

BlockDiagonalMatrix	RealTimeTransport::computeLiouvillian (const std::unique_ptr< Model > &model)
	Returns $ -i L $ for a given specific model, where $ L = [H, \bullet] $ denotes the bare Liouvillian.

BlockDiagonalMatrix	RealTimeTransport::computeSigmaInfty (const std::vector< BlockMatrix > &superfermion, const std::vector< BlockMatrix > &superfermionAnnihilation, const std::unique_ptr< Model > &model)
	Returns the $ \delta $-singular part $ -i \Sigma_\infty $ of the infinite temperature memory kernel for a given fermionic wideband model.

Model::SuperRowVectorType	RealTimeTransport::computeSigmaInftyCurrent (int r, const std::vector< BlockMatrix > &superfermionAnnihilation, const std::unique_ptr< Model > &model)
	Returns the $ \delta $-singular part of the current kernel, $ -i \Sigma^{(I_r)}_{\infty} $, for a given fermionic wideband model.

int	RealTimeTransport::singleToMultiIndex (Eta eta, int l, const std::unique_ptr< Model > &model)
	Converts multiple single indices into a multiindex.

Indices	RealTimeTransport::multiToSingleIndices (int i, const std::unique_ptr< Model > &model)
	Converts a multiindex into multiple single indices.

Enumeration Type Documentation

◆ Eta

enum class RealTimeTransport::Eta : int

strong

Enumerator
Minus	$ \eta=- $
Plus	$ \eta=+ $

◆ Keldysh

enum class RealTimeTransport::Keldysh : int

strong

Enumerator
Minus	$ p=- $
Plus	$ p=+ $

Function Documentation

◆ computeSuperfermion()

BlockMatrix RealTimeTransport::computeSuperfermion	(	Keldysh	p,
		Eta	eta,
		int	l,
		const std::unique_ptr< Model > &	model )

This function computes superfermionic creation/annihilation operators for given models. The superfermions are superoperators defined as $$ D^p_{\eta l} \bullet = \frac{1}{\sqrt{2}} ( d_{\eta l} \bullet + p (-\mathbb{1})^n \bullet (-\mathbb{1})^n d_{\eta l} ) $$ where $ \bullet $ denotes some operator argument.

Parameters

model	The model for which the superfermion is computed.
p	Represents creation or annihilation.
eta	Either "-" or "+".
l	Index for internal degrees of freedom (always $ \geq 0 $ !).

◆ multiToSingleIndices()

Indices RealTimeTransport::multiToSingleIndices	(	int	i,
		const std::unique_ptr< Model > &	model )

Transforms the multiindex $i$ into two single indices $\eta$ and $l$ which are returned as a tuple. The function can be used as

const auto [eta, l] = multiToSingleIndices(model, i);