This file contains the non-equilibrium virial-velocity correlation function \(K(t)\) and the spectral heat current (SHC) \(J_q(\omega)\), in a given direction, for a group of atoms, as defined in Eq. (18) and the left part of Eq. (20) of [Fan2019]. It is generated when invoking the compute_shc keyword.

File format

For each run, there are 3 columns and 2*Nc-1 + num_omega rows. Here, Nc is the number of correlation steps and num_omega is the number of frequency points.

In the first 2*Nc-1 rows:

  • column 1: correlation time \(t\) from negative to positive, in units of ps

  • column 2: \(K^{\rm in}(t)\) in units of Å eV/ps

  • column 3: \(K^{\rm out}(t)\) in units of Å eV/ps

\(K^{\rm in}(t) + K^{\rm out}(t) = K(t)\) is exactly the expression in Eq. (18) of [Fan2019]. The in-out decomposition follows the definition in [Fan2017], which is useful for 2D materials but is not necessary for 3D materials.

In the next num_omega rows:

  • column 1: angular frequency \(\omega\) in units of THz

  • column 2: \(J_q^{\rm in}(\omega)\) in units of Å eV/ps/THz

  • column 3: \(J_q^{\rm out}(\omega)\) in units of Å eV/ps/THz

\(J_q^{\rm in}(\omega) + J_q^{\rm out}(\omega) = J_q(\omega)\) is exactly the left expression in Eq. (20) of [Fan2019].

Only the potential part of the heat current has been included.