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documentation:language_reference:functions:createresonantspectra [2016/10/10 09:41] – external edit 127.0.0.1 | documentation:language_reference:functions:createresonantspectra [2017/09/26 21:38] – Maurits W. Haverkort |
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//CreateResonantSpectra($O_1$,$O_2$,$O_3$,$O_4$,$\psi$)// calculates | //CreateResonantSpectra($O_1$,$O_2$,$O_3$,$O_4$,$\psi$)// calculates |
\begin{equation} | \begin{equation} |
\langle \psi | O_3^{\dagger} \frac{1}{(\omega_1 - \mathrm{i} \Gamma_1/2 + E_0 - O_1^{\dagger})} O_4^{\dagger} \frac{1}{(\omega_2 + \mathrm{i} \Gamma_2/2 + E_0 - O_2)} O_4\frac{1}{(\omega_1 + \mathrm{i} \Gamma_1/2 + E_0 - O_1)} O_3 | \psi \rangle, | \langle \psi | O_3^{\dagger} \frac{1}{(\omega_1 - \mathrm{i} \Gamma_1/2 + E_0^{(1)} - O_1^{\dagger})} O_4^{\dagger} \frac{1}{(\omega_2 + \mathrm{i} \Gamma_2/2 + E_0^{(2)} - O_2)} O_4\frac{1}{(\omega_1 + \mathrm{i} \Gamma_1/2 + E_0^{(1)} - O_1)} O_3 | \psi \rangle, |
\end{equation} | \end{equation} |
with $E_0 = \langle \psi | O_1 | \psi \rangle$. The spectrum is returned as a spectrum object. | with $E_0^{(i)} = \langle \psi | O_i | \psi \rangle$. The spectrum is returned as a spectrum object. |
### | ### |
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===== Output ===== | ===== Output ===== |
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* //G// : Spectrum object | * //G// : Spectrum object. |
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| In the case that $O_3$ ($\{O_3^a, O_3^b\}$) , $O_4$ ($\{O_4^{\alpha}, O_4^{\beta}, O_4^{\gamma}\}$) and $\psi$ ($\{\psi_1,\psi_2,\psi_3\}$) are given as tables the order of spectra returned is: |
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| $\{$ |
| $I_1^{a,\alpha}(E_0)$, $I_1^{a,\alpha}(E_1)$, $\dots$, $I_1^{a,\alpha}(E_{N_E})$, |
| $I_1^{a,\beta}(E_0)$, $I_1^{a,\beta}(E_1)$, $\dots$, $I_1^{a,\beta}(E_{N_E})$, |
| $I_1^{a,\gamma}(E_0)$, $I_1^{a,\gamma}(E_1)$, $\dots$, $I_1^{a,\gamma}(E_{N_E})$, |
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| $I_1^{b,\alpha}(E_0)$, $I_1^{b,\alpha}(E_1)$, $\dots$, $I_1^{b,\alpha}(E_{N_E})$, |
| $I_1^{b,\beta}(E_0)$, $I_1^{b,\beta}(E_1)$, $\dots$, $I_1^{b,\beta}(E_{N_E})$, |
| $I_1^{b,\gamma}(E_0)$, $I_1^{b,\gamma}(E_1)$, $\dots$, $I_1^{b,\gamma}(E_{N_E})$, |
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| $I_2^{a,\alpha}(E_0)$, $I_2^{a,\alpha}(E_1)$, $\dots$, $I_2^{a,\alpha}(E_{N_E})$, |
| $I_2^{a,\beta}(E_0)$, $I_2^{a,\beta}(E_1)$, $\dots$, $I_2^{a,\beta}(E_{N_E})$, |
| $I_2^{a,\gamma}(E_0)$, $I_2^{a,\gamma}(E_1)$, $\dots$, $I_2^{a,\gamma}(E_{N_E})$, |
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| $I_2^{b,\alpha}(E_0)$, $I_2^{b,\alpha}(E_1)$, $\dots$, $I_2^{b,\alpha}(E_{N_E})$, |
| $I_2^{b,\beta}(E_0)$, $I_2^{b,\beta}(E_1)$, $\dots$, $I_2^{b,\beta}(E_{N_E})$, |
| $I_2^{b,\gamma}(E_0)$, $I_2^{b,\gamma}(E_1)$, $\dots$, $I_2^{b,\gamma}(E_{N_E})$, |
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| $I_3^{a,\alpha}(E_0)$, $I_3^{a,\alpha}(E_1)$, $\dots$, $I_3^{a,\alpha}(E_{N_E})$, |
| $I_3^{a,\beta}(E_0)$, $I_3^{a,\beta}(E_1)$, $\dots$, $I_3^{a,\beta}(E_{N_E})$, |
| $I_3^{a,\gamma}(E_0)$, $I_3^{a,\gamma}(E_1)$, $\dots$, $I_3^{a,\gamma}(E_{N_E})$, |
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| $I_3^{b,\alpha}(E_0)$, $I_3^{b,\alpha}(E_1)$, $\dots$, $I_3^{b,\alpha}(E_{N_E})$, |
| $I_3^{b,\beta}(E_0)$, $I_3^{b,\beta}(E_1)$, $\dots$, $I_3^{b,\beta}(E_{N_E})$, |
| $I_3^{b,\gamma}(E_0)$, $I_3^{b,\gamma}(E_1)$, $\dots$, $I_3^{b,\gamma}(E_{N_E})$ $\}$ |
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| where the alphabetic, greek and numeral indices refer to $O_3$, $O_4$ and $\psi$. |
===== Example ===== | ===== Example ===== |
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### | ### |
description text | Calculates the resonant spectra for some toy Hamiltonian and transition operators. |
### | ### |
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