Is the integral for current correct?

[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:

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]

 

[NateD]

The current plots should indeed be a line with a slope, but you have not implemented the integral over energy correctly. The integral should be over the energy variable, not the angle variable. Try changing the following lines: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]]//Timingto: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,energy,coupling,angle],{energy,-range,range}]]},{\[Chi],-\[Chi]range,\[Chi]range,steps}],Joined->True,AxesLabel->{"\[Chi]","I"},PlotRange->Automatic]]//TimingThis should give you the expected result. Hope this helps!