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documentation:basics:resonant_spectra [2016/10/06 20:36] – created Maurits W. Haverkortdocumentation:basics:resonant_spectra [2016/10/10 09:40] (current) – external edit 127.0.0.1
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 +{{indexmenu_n>7}}
 +====== 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()//
 +<code Quanty 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)
 +</code>
 +###
 +
 +===== Index =====
 +  - [[documentation:basics:basis|]]
 +  - [[documentation:basics:operators|]]
 +  - [[documentation:basics:wave_functions|]]
 +  - [[documentation:basics:expectation_values|]]
 +  - [[documentation:basics:eigen_states|]]
 +  - [[documentation:basics:spectra|]]
 +  - Resonant spectra
 +  - [[documentation:basics:fluorescence_yield|]]

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