dmft.utils

Tools to calculate quantities out of spectral functions

Functions

dmft.utils.bubble(A1, A2, nf)

Calculates the Polarization Bubble convolution given 2 Spectral functions

It follows the formula

\Pi(w') &= \int dw A_1(w) A_2(w+w') (n_f(w)-n_f(w+w')) \\ &= \int dw A_1^+(w) A_2(w+w')-A_1(w) A_2^+(w+w')

Parameters:
  • A1 (1D ndarrays, only information in w) – Correspond to the spectral functions
  • A2 (1D ndarrays, only information in w) – Correspond to the spectral functions
  • nf (ndarray) – Fermi function
dmft.utils.dc_conductivity(lat_A1, lat_A2, dnf, w, dosde)
dmft.utils.differential_weight(grid)

For the grid array calculate the half-way differentials

Examples using dmft.utils.differential_weight

dmft.utils.optical_conductivity(lat_A1, lat_A2, nf, w, dosde)

Calculates the optical conductivity from lattice spectral functions

\sigma(w) = \int dE \rho(E) \Pi (E,w) / w

Parameters:
  • lat_A1 (2D ndarrays) – lattice Spectral functions A(E,w)
  • lat_A2 (2D ndarrays) – lattice Spectral functions A(E,w)
  • nf (1D ndarray) – fermi function
  • w (1D ndarray) – real frequency array
  • dosde (1D ndarray) – differentially weighted density of states dE ρ(E)
Returns:

  • Re σ(w) (1D ndarray)
  • Real part of optical conductivity. Posterior scaling required

See also

bubble()

Examples using dmft.utils.optical_conductivity

dmft.utils.trapz(y, x=None, dx=1.0, axis=-1)

Integrate along the given axis using the composite trapezoidal rule.

Integrate y (x) along given axis.

Parameters:
  • y (array_like) – Input array to integrate.
  • x (array_like, optional) – The sample points corresponding to the y values. If x is None, the sample points are assumed to be evenly spaced dx apart. The default is None.
  • dx (scalar, optional) – The spacing between sample points when x is None. The default is 1.
  • axis (int, optional) – The axis along which to integrate.
Returns:

trapz – Definite integral as approximated by trapezoidal rule.
Return type:

float

See also

sum(), cumsum()

Notes

Image [2] illustrates trapezoidal rule – y-axis locations of points will be taken from y array, by default x-axis distances between points will be 1.0, alternatively they can be provided with x array or with dx scalar. Return value will be equal to combined area under the red lines.

References

[1]Wikipedia page: http://en.wikipedia.org/wiki/Trapezoidal_rule
[2]Illustration image: http://en.wikipedia.org/wiki/File:Composite_trapezoidal_rule_illustration.png

Examples

>>> np.trapz([1,2,3])
4.0
>>> np.trapz([1,2,3], x=[4,6,8])
8.0
>>> np.trapz([1,2,3], dx=2)
8.0
>>> a = np.arange(6).reshape(2, 3)
>>> a
array([[0, 1, 2],
       [3, 4, 5]])
>>> np.trapz(a, axis=0)
array([ 1.5,  2.5,  3.5])
>>> np.trapz(a, axis=1)
array([ 2.,  8.])