# Is the integral for current correct?

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1. Jul 7, 2017

### wondering12

Hi,
I am using Mathematica to calculate density of states and current of the Green's function times self energy in most simple form. I am not sure if I am getting current integral over energy implemented correctly. Shouldnt first current plot be a line with a slope? Below is my code:
Code (Text):

Remove["Global`*"];//Quiet
ClearAll
inputEta=0.6;inputHop=0.6;inputStep=0.1;inputAngle=1;inputCoup=0.5;inputDrange={0,2.5};inputCrange={0,0.1};range=10;\[Chi]range=4*Pi;

(* plotting density of states *)
greenF[\[Eta]_,t_,\[Theta]_]:=1/(e+I*\[Eta]-2*t*Cos[\[Theta]])
integral[eta_,hopping_,steps_,plotrange_]:=Module[{},ListPlot[Table[{e,-1/Pi*Im[NIntegrate[greenF[eta,hopping,angle],{angle,-Pi,Pi}]]},{e,-range,range,steps}],Joined->True,AxesLabel->{"E","DOS"},PlotRange->Automatic]]//Timing
integral[inputEta,inputHop,inputStep,inputDrange]

(* plotting current *)
(*selfEnergy1=1 ,   greenF1=greenF*selfEnergy1 *)
greenF1[\[Eta]_,t_,\[Theta]_,v_,e_]:=v/(e+I*\[Eta]-2*t*Cos[\[Theta]]);
integral[eta_,hopping_,angle_,coupling_,steps_,plotrange_]:=Module[{},ListPlot[Table[{\[Chi],1/(2*Pi)*Re[NIntegrate[greenF1[eta,hopping,angle,coupling,energy],{energy,-range,range}]]},{\[Chi],-\[Chi]range,\[Chi]range,steps}],Joined->True,AxesLabel->{"\[Chi]","I"},PlotRange->Automatic]]//Timing
integral[inputEta,inputHop,inputStep,inputAngle,inputCoup,inputCrange]

(*selfEnergy2=v*Cos[\[Chi]] ,   greenF1=greenF*selfEnergy1 *)
greenF2[\[Eta]_,t_,\[Theta]_,v_,e_]:=v*Cos[\[Chi]]/(e+I*\[Eta]-2*t*Cos[\[Theta]]);
integral[eta_,hopping_,angle_,coupling_,steps_,plotrange_]:=Module[{},ListPlot[Table[{\[Chi],1/(2*Pi)*Re[NIntegrate[greenF2[eta,hopping,angle,coupling,energy],{energy,-range,range}]]},{\[Chi],-\[Chi]range,\[Chi]range,steps}],Joined->True,AxesLabel->{"\[Chi]","I"},PlotRange->Automatic]]//Timing
integral[inputEta,inputHop,inputStep,inputAngle,inputCoup,inputCrange]

Last edited by a moderator: Jul 7, 2017
2. Jul 12, 2017

### PF_Help_Bot

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.

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