triqs.mesh.matsubara_freq.MatsubaraFreq

class triqs.mesh.matsubara_freq.MatsubaraFreq(n, beta, statistic='Fermion')

Bases: object

A single Matsubara frequency \(i\omega_n\).

Castable to complex via complex(freq); arithmetic with scalars is implemented by casting to complex, while arithmetic between two MatsubaraFreq instances returns a new MatsubaraFreq whose statistic follows from the usual selection rules (fermion + fermion = boson, fermion + boson = fermion, etc.).

The associated complex value is

\[i\omega_n = i\, \frac{(2n + \mathrm{is\_fermion})\,\pi}{\beta},\]

so fermionic frequencies are odd multiples of \(\pi/\beta\) and bosonic frequencies are even multiples.

Parameters:

nint

The Matsubara index \(n\).

betafloat

Inverse temperature \(\beta > 0\).

statisticstr, optional

Particle statistic, either 'Fermion' or 'Boson'. Default 'Fermion'.

Attributes

index	Matsubara index \(n\) (alias of n).
value	Complex value \(i\omega_n\) of this Matsubara frequency.
real	Real part of \(i\omega_n\), identically zero.
imag	Imaginary part of \(i\omega_n\).

n	(int) The Matsubara index \(n\).
beta	(float) Inverse temperature \(\beta\).
statistic	(str) Particle statistic, 'Fermion' or 'Boson'.
is_fermion	(bool) True for a fermionic frequency, False for a bosonic one.