dyson_timestep()

template<typename T >

void cntr::dyson_timestep	(	int	n,
		herm_matrix< T > &	G,
		T	mu,
		function< T > &	H,
		herm_matrix< T > &	Sigma,
		T	beta,
		T	h,
		const int	SolveOrder
	)

One step Dyson solver (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 \(G(t, t^\prime)\) at a given timestep 'n', i.e., G^ret(nh,t'<=nh), G^les(t<=nh,nh), G^tv(nt,tau=0..beta). Timestep must be >k, where k is the Integration order 'I'. The timesteps n=0..k must be computed seperately, using the routine "_start", which assumes that the Matsubara component of \(G\) and \(\Sigma(t,t^\prime)\) for \(t,t^\prime\)<=k are given. Here, are given: \(\Sigma(t, t^\prime)\), \(\mu\), and \(H(t)\).

Parameters

n	[int] time step
&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

Definition at line 1618 of file cntr_dyson_impl.hpp.

References cntr::herm_matrix< T >::nt(), cntr::herm_matrix< T >::ntau(), cntr::function< T >::ptr(), and cntr::herm_matrix< T >::size1().

                                                       {
    int size1 = G.size1();
    assert(G.size1() == Sigma.size1());
    assert(G.ntau() == Sigma.ntau());
    assert(G.nt() >= n);
    assert(Sigma.nt() >= n);
    assert(n > SolveOrder);
    if (size1 == 1) {
        dyson_timestep_ret<T, herm_matrix<T>, 1>(n, G, mu, H.ptr(0), Sigma, integration::I<T>(SolveOrder), h);
        dyson_timestep_tv<T, herm_matrix<T>, 1>(n, G, mu, H.ptr(n), Sigma, integration::I<T>(SolveOrder), beta, h);
        dyson_timestep_les<T, herm_matrix<T>, 1>(n, G, mu, H.ptr(0), Sigma, integration::I<T>(SolveOrder), beta, h);
    } else {
        dyson_timestep_ret<T, herm_matrix<T>, LARGESIZE>(n, G, mu, H.ptr(0), Sigma, integration::I<T>(SolveOrder), h);
        dyson_timestep_tv<T, herm_matrix<T>, LARGESIZE>(n, G, mu, H.ptr(n), Sigma, integration::I<T>(SolveOrder), beta,
                                                        h);
        dyson_timestep_les<T, herm_matrix<T>, LARGESIZE>(n, G, mu, H.ptr(0), Sigma, integration::I<T>(SolveOrder), beta,
                                                         h);
    }
}

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