Differences

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

--- documentation:language_reference:functions:createresonantspectra [2016/10/10 09:41] – external edit 127.0.0.1
+++ documentation:language_reference:functions:createresonantspectra [2022/05/18 17:01] (current) – Corrected NTri1/2 standard values. Yi Lu
@@ Line 4: / Line 4: @@
 //CreateResonantSpectra( $O_1$ , $O_2$ , $O_3$ , $O_4$ , $\psi$ )// calculates
 \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}
-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.
 ###
@@ Line 17: / Line 17: @@
   *  $\psi$  : Wavefunction
   * Possible options are:
-    * "NTri1" Positive integer specifying the number of states in the Krylov basis of  $O_1$ . (Standard value 200)
+    * "NTri1" Positive integer specifying the number of states in the Krylov basis of  $O_1$ . (Standard value 100)
-    * "NTri2" Positive integer specifying the number of states in the Krylov basis of  $O_2$ . (Standard value 200)
+    * "NTri2" Positive integer specifying the number of states in the Krylov basis of  $O_2$ . (Standard value 100)
     * "epsilon" Positive real defining the smallest absolute value considered different than zero. (Standard value 1.49E-8)
     * "restrictions1" A list of restrictions defining restrictions on configurations and occupations included for  $O_1$  . Allows one to do restricted active space calculations. Note that the action of  $O_3$  and  $O_4$  are not restricted and all excitations they can make are included.
@@ Line 33: / Line 33: @@
 ===== Output =====
-  * //G// : Spectrum object
+  * //G// : Spectrum object.
+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:
+ $\{$
+ $I_1^{a,\alpha}(E_0)$ ,  $I_1^{a,\alpha}(E_1)$ ,  $\dots$ ,  $I_1^{a,\alpha}(E_{N_E})$ ,
+ $I_1^{a,\beta}(E_0)$ ,   $I_1^{a,\beta}(E_1)$ ,   $\dots$ ,  $I_1^{a,\beta}(E_{N_E})$ ,
+ $I_1^{a,\gamma}(E_0)$ ,  $I_1^{a,\gamma}(E_1)$ ,  $\dots$ ,  $I_1^{a,\gamma}(E_{N_E})$ ,
+ $I_1^{b,\alpha}(E_0)$ ,  $I_1^{b,\alpha}(E_1)$ ,  $\dots$ ,  $I_1^{b,\alpha}(E_{N_E})$ ,
+ $I_1^{b,\beta}(E_0)$ ,   $I_1^{b,\beta}(E_1)$ ,   $\dots$ ,  $I_1^{b,\beta}(E_{N_E})$ ,
+ $I_1^{b,\gamma}(E_0)$ ,  $I_1^{b,\gamma}(E_1)$ ,  $\dots$ ,  $I_1^{b,\gamma}(E_{N_E})$ ,
+ $I_2^{a,\alpha}(E_0)$ ,  $I_2^{a,\alpha}(E_1)$ ,  $\dots$ ,  $I_2^{a,\alpha}(E_{N_E})$ ,
+ $I_2^{a,\beta}(E_0)$ ,   $I_2^{a,\beta}(E_1)$ ,   $\dots$ ,  $I_2^{a,\beta}(E_{N_E})$ ,
+ $I_2^{a,\gamma}(E_0)$ ,  $I_2^{a,\gamma}(E_1)$ ,  $\dots$ ,  $I_2^{a,\gamma}(E_{N_E})$ ,
+ $I_2^{b,\alpha}(E_0)$ ,  $I_2^{b,\alpha}(E_1)$ ,  $\dots$ ,  $I_2^{b,\alpha}(E_{N_E})$ ,
+ $I_2^{b,\beta}(E_0)$ ,   $I_2^{b,\beta}(E_1)$ ,   $\dots$ ,  $I_2^{b,\beta}(E_{N_E})$ ,
+ $I_2^{b,\gamma}(E_0)$ ,  $I_2^{b,\gamma}(E_1)$ ,  $\dots$ ,  $I_2^{b,\gamma}(E_{N_E})$ ,
+ $I_3^{a,\alpha}(E_0)$ ,  $I_3^{a,\alpha}(E_1)$ ,  $\dots$ ,  $I_3^{a,\alpha}(E_{N_E})$ ,
+ $I_3^{a,\beta}(E_0)$ ,   $I_3^{a,\beta}(E_1)$ ,   $\dots$ ,  $I_3^{a,\beta}(E_{N_E})$ ,
+ $I_3^{a,\gamma}(E_0)$ ,  $I_3^{a,\gamma}(E_1)$ ,  $\dots$ ,  $I_3^{a,\gamma}(E_{N_E})$ ,
+ $I_3^{b,\alpha}(E_0)$ ,  $I_3^{b,\alpha}(E_1)$ ,  $\dots$ ,  $I_3^{b,\alpha}(E_{N_E})$ ,
+ $I_3^{b,\beta}(E_0)$ ,   $I_3^{b,\beta}(E_1)$ ,   $\dots$ ,  $I_3^{b,\beta}(E_{N_E})$ ,
+ $I_3^{b,\gamma}(E_0)$ ,  $I_3^{b,\gamma}(E_1)$ ,  $\dots$ ,  $I_3^{b,\gamma}(E_{N_E})$   $\}$
+where the alphabetic, greek and numeral indices refer to  $O_3$ ,  $O_4$  and  $\psi$ .
 ===== Example =====
 ###
-description text
+Calculates the resonant spectra for some toy Hamiltonian and transition operators.
 ###

You are here: Quanty - a quantum many body script language » Documentation » Language Reference » Functions » CreateResonantSpectra

Differences

Search

Navigation

Print/export

Tools