Differences

This shows you the differences between two versions of the page.

Link to this comparison view

documentation:basics:resonant_spectra [2016/10/10 09:40] (current)
Line 1: Line 1:
 +{{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|]]
Print/export