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 — documentation:basics:resonant_spectra [2016/10/10 09:40] (current) 2016/10/06 20:36 Maurits W. Haverkort created 2016/10/06 20:36 Maurits W. Haverkort created 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()//​ + ​ + -- Creating a spectrum from a starting state psi + -- a transition operator, T1, T2, + -- and Hamiltonians H1, H2 + G3 = CreateResonantSpectra(H1,​ H2, T1, T2, psi) + ​ + ### + + ===== 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|]]