 NESSi  v1.0.2 The NonEquilibrium Systems Simulation Library

## ◆ response_convolution() [3/4]

template<typename T >
 void cntr::response_convolution ( int tstp, std::complex< T > & cc, herm_matrix_timestep< 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