gftool.fourier¶
Fourier transformations of Green’s functions.
Fourier transformation between imaginary time and Matsubara frequencies. The function in this module should be used after explicitly treating the high-frequency behavior, as this is not yet implemented. Typically, transformation from τ-space to Matsubara frequency are unproblematic.
The Fourier transforms are defined in the following way:
Definitions¶
imaginary time → Matsubara frequencies¶
The Fourier integral for the Matsubara Green’s function is defined as:
\[G(iw_n) = 0.5 ∫_{-β}^{β}dτ G(τ) \exp(iw_n τ)\]
with \(iw_n = iπn/β\). For fermionic Green’s functions only odd frequencies are non-vanishing, for bosonic Green’s functions only even.
The recommended high-level function to perform this Fourier transform is:
Glossary¶
- dft
- <discrete Foruier transform>
- ft
- <Fourier transformation> In contrast to dft, this is used for Fourier integration of continous variables without discretization.
Previously defined:
API¶
Functions
iw2tau (gf_iw, beta[, moments, fourier]) |
Discrete Fourier transform of the Hermitian Green’s function gf_iw. |
iw2tau_dft (gf_iw, beta) |
Discrete Fourier transform of the Hermitian Green’s function gf_iw. |
iw2tau_dft_soft (gf_iw, beta) |
Discrete Fourier transform of the Hermitian Green’s function gf_iw. |
pole_gf_from_moments (moments) |
Find pole Green’s function matching given moments. |
pole_gf_from_tau (gf_tau, n_pole, beta[, moments]) |
Find pole Green’s function fitting gf_tau. |
tau2iv (gf_tau, beta[, fourier]) |
Fourier transformation of the real Green’s function gf_tau. |
tau2iv_dft (gf_tau, beta) |
Discrete Fourier transform of the real Green’s function gf_tau. |
tau2iv_ft_lin (gf_tau, beta) |
Fourier integration of the real Green’s function gf_tau. |
tau2iw (gf_tau, beta[, n_pole, moments, fourier]) |
Fourier transform of the real Green’s function gf_tau. |
tau2iw_dft (gf_tau, beta) |
Discrete Fourier transform of the real Green’s function gf_tau. |
tau2iw_ft_lin (gf_tau, beta) |
Fourier integration of the real Green’s function gf_tau. |
Classes
PoleGf (resids, poles) |