cold

sisl.physics.cold(E, kT=0.1, mu=0.0)

Cold smearing function, see 1

\[\begin{split}C(E,k_BT,\mu) = \frac12 &+ \mathrm{erf}\Big(-\frac{E-\mu}{k_BT}-\frac1{\sqrt2}\Big) \\ &+ \frac1{\sqrt{2\pi}} \exp\Bigg\{-\Big[\frac{E-\mu}{k_BT}+\frac1{\sqrt2}\Big]^2\Bigg\}\end{split}\]

Parameters

• E (array_like) – energy evaluation points

• kT (float, optional) – temperature broadening

• mu (float, optional) – chemical potential

References

1

N. Marzari, D. Vanderbilt, A. de Vita, M.C. Payne “Thermal Contraction and Disordering of the Al(110) Surface”, PRL **82**, 16 (1999)

Returns

the Cold smearing distribution function, same length as E

Return type

numpy.ndarray