Resonant spectra

Resonant spectra are implemented by calculating a third order Green's function or susceptibility ($\chi_3$): $$\begin{eqnarray} G^3(\omega_1,\omega_2) = \bigg\langle \psi_i \bigg| T_1^{\dagger} \frac{1}{\omega_1 - H_1 - \imath \Gamma/2} T_2^{\dagger} \quad\quad\quad\quad \\ \nonumber \frac{1}{\omega_2 - H_2 + \imath \Gamma/2} T_2 \frac{1}{\omega_1 - H_1 + \imath \Gamma/2} T_1 \bigg | \psi_i \bigg\rangle, \end{eqnarray}$$ For $2p$ core level resonant inelastic x-ray scattering measuring magnons or $d-d$ excitations $T_1$ would excite a $2p$ core electron into the $3d$ valence orbitals and $T_2$ would de-excite a $3d$ electron into the $2p$ core hole. For core-core excitations $T_2$ would de-excite for example a $3s$ core electron into the $2p$ core hole. Quanty can calculate resonant spectra with the function CreateResonantSpectra()

Example.Quanty

-- Creating a spectrum from a starting state psi
-- a transition operator, T1, T2,
-- and Hamiltonians H1, H2
G3 = CreateResonantSpectra(H1, H2, T1, T2, psi)

1. Basis
2. Operators
3. Wave functions
4. Expectation values
5. Eigen states
6. Spectra
7. Resonant spectra
8. Fluorescence yield