gftool.fermi_fct_d1

gftool.fermi_fct_d1(eps, beta)[source]

Return the 1st derivative of the Fermi function.

\[f'(ϵ) = -β\exp(βϵ)/{[\exp(βϵ)+1]}^2 = -βf(ϵ)[1-f(ϵ)]\]

Parameters:

epsfloat or float np.ndarray: The energy at which the Fermi function is evaluated.
betafloat: The inverse temperature \(beta = 1/k_B T\).

Returns:

float or float np.ndarray: The Fermi function, same type as eps.

See also

fermi_fct

Examples

>>> eps = np.linspace(-15, 15, num=501)
>>> fermi_d1 = gt.fermi_fct_d1(eps, beta=1.0)

>>> import matplotlib.pyplot as plt
>>> _ = plt.plot(eps, fermi_d1)
>>> _ = plt.xlabel(r"$\epsilon/\beta$")
>>> _ = plt.axvline(0, color='black', linewidth=0.8)
>>> _ = plt.xlim(left=eps.min(), right=eps.max())
>>> _ = plt.ylim(top=0)
>>> plt.show()

(png, pdf)