https://www.quanty.org/ 2026-04-30T18:07:08+00:00 https://www.quanty.org/ https://www.quanty.org/_media/wiki/dokuwiki.svg text/html 2025-11-20T03:20:25+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/responsefunction/operations/add?rev=1763608825&do=diff Add Response functions can be summed using “+” Example a1 = {0, -1,-0.5, 0 } b1 = { 0.1, 0.1, 0.1} G1 = ResponseFunction.New( {a1,b1,mu=0,type="ListOfPoles", name="G1"} ) a2 = {0, 0.5, 1, 1.5} b2 = { 0.1, 0.1, 0.1} G2 = ResponseFunction.New( {a2,b2,mu=0,type="ListOfPoles", name="G2"} ) G = G1 + G2 print("The response function of G is") print(G) omega = 1.1 Gamma = 0.001 print() print("Evaluated at omega =",omega," and Gamma =",Gamma," yields\nG (",G(omega,Gamma),") = G1 (",G1(omega,Ga… text/html 2025-11-20T03:20:25+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/responsefunction/operations/div?rev=1763608825&do=diff Div We can divide a response function by a double and scale the size of the response function, i.e. when $G2 = G1/2)$ then $G2(\omega,\Gamma) = (G1(\omega,\Gamma))/2$. For example Input a = {0, -1,-0.5, 0, 0.5, 1, 1.5} b = { 0.2, 0.4, 0.2, 0.4, 0.6, 0.2} G = ResponseFunction.New( {a,b,mu=0,type="ListOfPoles", name="G"} ) print(G/2) responsefunction index text/html 2025-11-20T03:20:26+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/responsefunction/operations/eq?rev=1763608826&do=diff Eq You can compare two response functions. Two response functions $G1(\omega,\Gamma)$ and $G2(\omega,\Gamma)$ are considered to be equal when $|G1(\omega,\Gamma) - G2(\omega,\Gamma)| < \epsilon$ for $\epsilon=10^{-11}$ at all values of $\omega$ and $\Gamma = \omega/10$. For example Input a1 = {0, -1,-0.5, 0, 0.5, 1, 1.5} b1 = { 0.2, 0.4, 0.2, 0.4, 0.6, 0.2} G1 = ResponseFunction.New( {a1,b1,mu=0,type="ListOfPoles", name="G1"} ) a2 = {0, -1,-0.5, 0, 0.5, 1, 1.5} b2 = { 0.2, 0.4, 0.… text/html 2025-11-20T03:20:25+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/responsefunction/operations/len?rev=1763608825&do=diff Len The length operator “#” returns the length of the table if the response function would have been transformed to a table. Note that the length for response functions in Tri-diagonal, Anderson, or ListOfPoles format is 2, for Natural impurity format the length is 1.responsefunction index text/html 2025-11-20T03:20:27+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/responsefunction/operations/mul?rev=1763608827&do=diff Mul We can divide a response function by a double and scale the size of the response function, i.e. when $G2 = G1*0.5)$ then $G2(\omega,\Gamma) = (G1(\omega,\Gamma))*0.5$. For example Input a = {0, -1,-0.5, 0, 0.5, 1, 1.5} b = { 0.2, 0.4, 0.2, 0.4, 0.6, 0.2} G = ResponseFunction.New( {a,b,mu=0,type="ListOfPoles", name="G"} ) print(G*0.5) responsefunction index text/html 2025-11-20T03:20:26+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/responsefunction/operations/start?rev=1763608826&do=diff Operations Quanty defines several operations like plus, minus, times, etc. Here you can find a list of the implemented operations Table of contents operations index text/html 2025-11-20T03:20:26+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/responsefunction/operations/sub?rev=1763608826&do=diff Sub We can subtract two response functions from each other. Note that the residue of a pole always needs to be positive. For $G = G_1 - G_2$ we start by setting $G=G_1$. For each pole in $G_2$ we look for the poles in $G_1$ at the same energy (a's). If this is present we subtract the residue of $G_2$$G$$G_2$$G_1$$G_2$$G_1$$G_2$$G_1$$G_2$$-0.5$$-1$$0$$G_1$$0.2/2=0.1$$G_2$$5.75$$5$$6$$G_1$$0.2 * (5.75 - 5) / (6-5) = 0.15$$6$$G_1$$0.2 * (6 - 5.75) / (6-5) = 0.05$$5$$G_1$responsefunction index