NESSI  v1.1.2 The NonEquilibrium Systems SImulation Library

## ◆ dyson()

template<typename T >
 void cntr::dyson ( herm_matrix< T > & G, T mu, function< T > & H, herm_matrix< T > & Sigma, integration::Integrator< T > & I, T beta, T h, const int matsubara_method, const bool force_hermitian )

Solver of the Dyson equation in the integral-differential form for a Green's function $$G$$

Purpose

One solves the Dyson equation of the following form: $$[ id/dt + \mu - H(t) ] G(t,t^\prime) - [\Sigma*G](t,t^\prime) = \delta(t,t^\prime)$$ for a hermitian matrix $$G(t, t^\prime)$$ with given $$\Sigma(t, t^\prime)$$, $$\mu$$, and $$H(t)$$. Here, one calls the routines 'dyson_mat()', 'dyson_start()', 'dyson_timestep'.

Parameters
 &G [herm_matrix] solution mu [T] chemical potential &H [function] time-dependent function &Sigma [herm_matrix] self-energy I [Integrator] integrator class beta [double] inverse temperature h [double] time interval matsubara_method [const] Solution method on the Matsubara axis with 0: Fourier, 1: steep, 2: fixpoint force_hermitian [const bool] force hermitian solution

Definition at line 1437 of file cntr_dyson_impl.hpp.

1439  {
1440  int n, k = I.k(), nt = G.nt();
1441  dyson_mat(G, Sigma, mu, H, I, beta, matsubara_method, force_hermitian);
1442  if (nt >= 0)
1443  dyson_start(G, mu, H, Sigma, I, beta, h);
1444  for (n = k + 1; n <= nt; n++)
1445  dyson_timestep(n, G, mu, H, Sigma, I, beta, h);
1446 }
void dyson_start(herm_matrix< T > &G, T mu, function< T > &H, herm_matrix< T > &Sigma, integration::Integrator< T > &I, T beta, T h)
Start-up procedure for solving the Dyson equation of the integral-differential form for a Green&#39;s fu...
void dyson_mat(herm_matrix< T > &G, herm_matrix< T > &Sigma, T mu, function< T > &H, integration::Integrator< T > &I, T beta, const int method=CNTR_MAT_FIXPOINT, const bool force_hermitian=true)
Dyson solver (integral-differential form) for a Green&#39;s function
Integrator< T > & I(int k)
void dyson_timestep(int n, herm_matrix< T > &G, T mu, function< T > &H, herm_matrix< T > &Sigma, integration::Integrator< T > &I, T beta, T h)
One step Dyson solver (integral-differential form) for a Green&#39;s function
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