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,
beta,
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