response_convolution() [1/4]

template<typename T >

void cntr::response_convolution	(	int	tstp,
		std::complex< T > &	cc,
		herm_matrix< T > &	W,
		int	a1,
		int	a2,
		function< T > &	f,
		int	b1,
		int	b2,
		int	kt,
		T	beta,
		T	h
	)

Evaluate the convolution between a two-time contour function ( \(W\)) and a real-time function ( \(f\)) at the time step ( \(t\)); \( c(t) = \int_C dt' W_{a1,a2}(t,t') f_{b1,b2}(t') \).

Purpose

This function evaluates the convolution between a two-time contour function ( \(W\)) and a real-time function ( \(f\)) at the time step ( \(t\)); \( c(t) = \int_C dt' W_{a1,a2}(t,t') f_{b1,b2}(t') \). It can be used, for example, to evaluate a lineaer response by using a response function as \(W\) and an external field as \(f\).

Parameters

tstp	Time step.
cc	Value of the conovlution at the time step; \( c(t) = \int_C dt' W_{a1,a2}(t,t') f_{b1,b2}(t') \).
W	Two-time contour object in the Matrix form with the hermitian symmetry.
a1	First index of the matrix \(W\).
a2	Second index of the matrix \(W\).
f	Function in the Matrix from on the real-time axis.
b1	First index of the matrix \(f\).
b2	Second index of the matrix \(f\).
kt	Integration order
beta	Inversed temperature
h	time step interval