NESSi  v1.0.2
The NonEquilibrium Systems Simulation Library

◆ green_from_H() [6/6]

template<typename T >
void cntr::green_from_H ( int  tstp,
herm_matrix< T > &  G,
mu,
cntr::function< T > &  eps,
beta,
h,
bool  fixHam,
int  SolveOrder,
int  cf_order 
)

Propagator for time-dependent free Hamiltonian

Purpose

Calculate the free propagator G from time dependent quadratic Hamiltonian using high-order commutator-free exponential time-propagation, see https://doi.org/10.1016/j.jcp.2011.04.006 for the description. Currently implemented versions are the second order using one exponential CF2:1 (order=2) and fourth order using two exponentials CF4:2 (order=4), see also article for more details.

Parameters
tstp

the index of the time step

G

The output: a timestep of the Greens function set to time dependent free propagator

mu

chemical potential

eps

time dependent representation of quadratical hamiltonian

beta

inverse temperature

h

time step interval

fixHam

If True Hamiltonian is known for all times and no extrapolation is needed for the predictor/corrector

SolveOrder

Order of integrator used for extrapolation and interpolation

cf_order

Order of approximation for commutator-free exponential, currently implemented orders = 2,4

Definition at line 1394 of file cntr_equilibrium_impl.hpp.

References cntr::herm_matrix< T >::nt(), cntr::herm_matrix< T >::ntau(), cntr::herm_matrix< T >::set_timestep(), cntr::herm_matrix< T >::sig(), cntr::herm_matrix< T >::size1(), cntr::function< T >::size1_, and cntr::function< T >::size2_.

1394  {
1395  assert(tstp <= G.nt());
1396  assert(G.size1()==eps.size2_);
1397  assert(eps.size1_==eps.size2_);
1398  assert(SolveOrder <= MAX_SOLVE_ORDER);
1399  assert(cf_order == 2 || cf_order == 4);
1400  herm_matrix_timestep<T> Gstep(tstp,G.ntau(),G.size1(),G.sig());
1401 
1402  int size=G.size1();
1403  if(size==1) green_from_H_dispatch<T,1>(Gstep,mu,eps,beta,h,SolveOrder,cf_order,fixHam);
1404  else green_from_H_dispatch<T,LARGESIZE>(Gstep,mu,eps,beta,h,SolveOrder,cf_order,fixHam);
1405 
1406  G.set_timestep(tstp, Gstep);
1407 }
int size2_
Number of the rows in the Matrix form.
int size1_
Number of the colums in the Matrix form.
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