dyson()

template<typename T >

void cntr::dyson	(	herm_matrix< T > &	G,
		T	mu,
		function< T > &	H,
		herm_matrix< T > &	Sigma,
		T	beta,
		T	h,
		const int	SolveOrder,
		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<T>] solution
mu	[T] chemical potential
&H	[function<T>] time-dependent function
&Sigma	[herm_matrix<T>] self-energy
beta	[double] inverse temperature
h	[double] time interval
SolveOrder	[int] integrator order
matsubara_method	[int] Solution method on the Matsubara axis with 0: Fourier, 1: steep, 2: fixpoint
force_hermitian	[bool] force hermitian solution

Definition at line 1725 of file cntr_dyson_impl.hpp.

References cntr::herm_matrix< T >::nt().

                                       {
    int n, nt = G.nt();
    dyson_mat(G, mu, H, Sigma, beta, SolveOrder, matsubara_method, force_hermitian);
    if (nt >= 0)
        dyson_start(G, mu, H, Sigma, beta, h, SolveOrder);
    for (n = SolveOrder + 1; n <= nt; n++)
        dyson_timestep(n, G, mu, H, Sigma, beta, h, SolveOrder);
}

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