THRHTableDataImport1a=Import["/Users/richarddudley/Dropbox/BH/BEC/nofxcofxvofx/CorrectCVN/2020Files/Potentialvariations/RawData/M4p17THRHTableDatap1.mx"];
THRHTableDataImport2a=Import["/Users/richarddudley/Dropbox/BH/BEC/nofxcofxvofx/CorrectCVN/2020Files/Potentialvariations/RawData/M4p17THRHTableDatap2.mx"];
THRHTableDataImport3a=Import["/Users/richarddudley/Dropbox/BH/BEC/nofxcofxvofx/CorrectCVN/2020Files/Potentialvariations/RawData/M4p17THRHTableDatap3.mx"];
THRHTableDataImport4a=Import["/Users/richarddudley/Dropbox/BH/BEC/nofxcofxvofx/CorrectCVN/2020Files/Potentialvariations/RawData/M4p17THRHTableDatap4.mx"];
THRHTableDataImport5a=Import["/Users/richarddudley/Dropbox/BH/BEC/nofxcofxvofx/CorrectCVN/2020Files/Potentialvariations/RawData/M4p17THRHTableDatap5.mx"];
THRHTableDataImport6a=Import["/Users/richarddudley/Dropbox/BH/BEC/nofxcofxvofx/CorrectCVN/2020Files/Potentialvariations/RawData/M4p17THRHTableDatap6.mx"];

TIRITableDataImport1=Import["/Users/richarddudley/Dropbox/BH/BEC/nofxcofxvofx/CorrectCVN/2020Files/Potentialvariations/RawData/M4p17TIRITableData50p1.mx"];
TIRITableDataImport2=Import["/Users/richarddudley/Dropbox/BH/BEC/nofxcofxvofx/CorrectCVN/2020Files/Potentialvariations/RawData/M4p17TIRITableData50p2.mx"];
TIRITableDataImport3=Import["/Users/richarddudley/Dropbox/BH/BEC/nofxcofxvofx/CorrectCVN/2020Files/Potentialvariations/RawData/M4p17TIRITableData50p3.mx"];
TIRITableDataImport4=Import["/Users/richarddudley/Dropbox/BH/BEC/nofxcofxvofx/CorrectCVN/2020Files/Potentialvariations/RawData/M4p17TIRITableData50p4.mx"];
TIRITableDataImport5=Import["/Users/richarddudley/Dropbox/BH/BEC/nofxcofxvofx/CorrectCVN/2020Files/Potentialvariations/RawData/M4p17TIRITableData50p5.mx"];
TIRITableDataImport6=Import["/Users/richarddudley/Dropbox/BH/BEC/nofxcofxvofx/CorrectCVN/2020Files/Potentialvariations/RawData/M4p17TIRITableData50p6.mx"];

alphabetaTableDataImport11=Import["/Users/richarddudley/Dropbox/BH/BEC/nofxcofxvofx/CorrectCVN/2020Files/Potentialvariations/RawData/M4p17alphabetaTableData50p1.mx"];
alphabetaTableDataImport11a=Table[Flatten[alphabetaTableDataImport11[[i, All]], 1], {i, 1, 50}];
alphabetaTableDataImport2=Import["/Users/richarddudley/Dropbox/BH/BEC/nofxcofxvofx/CorrectCVN/2020Files/Potentialvariations/RawData/M4p17alphabetaTableData50p2.mx"];
alphabetaTableDataImport2a=Table[Flatten[alphabetaTableDataImport2[[i, All]], 1], {i, 1, 20}];
alphabetaTableDataImport3=Import["/Users/richarddudley/Dropbox/BH/BEC/nofxcofxvofx/CorrectCVN/2020Files/Potentialvariations/RawData/M4p17alphabetaTableData50p3.mx"];
alphabetaTableDataImport3a=Table[Flatten[alphabetaTableDataImport3[[i, All]], 1], {i, 1, 10}];
alphabetaTableDataImport4=Import["/Users/richarddudley/Dropbox/BH/BEC/nofxcofxvofx/CorrectCVN/2020Files/Potentialvariations/RawData/M4p17alphabetaTableData50p4.mx"];
alphabetaTableDataImport4a=Table[Flatten[alphabetaTableDataImport4[[i, All]], 1], {i, 1, 10}];
alphabetaTableDataImport5=Import["/Users/richarddudley/Dropbox/BH/BEC/nofxcofxvofx/CorrectCVN/2020Files/Potentialvariations/RawData/M4p17alphabetaTableData50p5.mx"];
alphabetaTableDataImport5a=Table[Flatten[alphabetaTableDataImport5[[i, All]], 1], {i, 1, 10}];
alphabetaTableDataImport6=Import["/Users/richarddudley/Dropbox/BH/BEC/nofxcofxvofx/CorrectCVN/2020Files/Potentialvariations/RawData/M4p17alphabetaTableData50p6.mx"];
alphabetaTableDataImport6a=Table[Flatten[alphabetaTableDataImport6[[i, All]], 1], {i, 1, 10}];
THRHTableDataImport=Join[THRHTableDataImport1a, THRHTableDataImport2a, THRHTableDataImport3a, THRHTableDataImport4a, THRHTableDataImport5a, THRHTableDataImport6a];

TIRITableDataImport=Join[TIRITableDataImport1, TIRITableDataImport2, TIRITableDataImport3, TIRITableDataImport4, TIRITableDataImport5, TIRITableDataImport6];

alphabetaTableDataImport=Join[alphabetaTableDataImport11a,alphabetaTableDataImport2a ,alphabetaTableDataImport3a,alphabetaTableDataImport4a,alphabetaTableDataImport5a,alphabetaTableDataImport6a];

Length[THRHTableDataImport]
Length[TIRITableDataImport]
Length[alphabetaTableDataImport]

c1=Sqrt[(1/2)^2+1/2*((1)^2-(1/2)^2)*(1+(2/Pi)*ArcTan[(x+(8*Tan[(Pi/((1)^2-(1/2)^2))*((3/4)^2-1/2*((1/2)^2+1^2))]))/(8)])];

kappa=437.27939024018158198816096720906240310868354576448923082842892460361517999703211`50.

Length[alphabetaTableDataImport]

Omega1Veff2=Flatten[TIRITableDataImport[[All, 1]]];
TI1Veff2=Flatten[TIRITableDataImport[[All, 2]]];
RI1Veff2=Flatten[TIRITableDataImport[[All, 3]]];
TH1Veff2=Flatten[THRHTableDataImport[[All, 2]]];
RH1Veff2=Flatten[THRHTableDataImport[[All, 3]]];
alpha1Veff2=Flatten[alphabetaTableDataImport[[All, 2]]];
beta1Veff2=Flatten[alphabetaTableDataImport[[All, 3]]];

Alphacheck=Table[1+1/(Omega1Veff2[[i]]*100),{i,1, 110}];

Watefall2016alphavomegasquared=Abs[(TH1Veff2*alpha1Veff2)^2];
Watefall2016Bomegasquared=Abs[(beta1Veff2*TH1Veff2)^2];
Watefall2016Aomegasquared=Abs[(RI1Veff2)^2];


WaterfallData1=Transpose[{Omega1Veff2,Watefall2016alphavomegasquared}];
WaterfallData2=Transpose[{Omega1Veff2,Watefall2016Bomegasquared}];
WaterfallData3=Transpose[{Omega1Veff2,Watefall2016Aomegasquared}];

ListLogLogPlot[{WaterfallData1,WaterfallData2, WaterfallData3}, PlotRange->{0, 10}, PlotLabel->"|T_I|", ImageSize->Full, PlotLegends->Placed[{"α^2","B^2","A^2"}, Above]]

dataTIVeff2=Transpose[{Omega1Veff2, TI1Veff2}];
dataRIVeff=Transpose[{Omega1Veff2, RI1Veff2}];

dataTHVeff2=Transpose[{Omega1Veff2, TH1Veff2}];
dataRHVeff=Transpose[{Omega1Veff2, RH1Veff2}];

dataalphaVeff2=Transpose[{Omega1Veff2, alpha1Veff2}];
databetaVeff=Transpose[{Omega1Veff2, beta1Veff2}];

Length[Omega1Veff2]

Length[alpha1Veff2]

Data01=Transpose[{Omega1Veff2,Map[Abs,TI1Veff2]}];
Data01aa=Transpose[{Omega1Veff2,Map[Abs,RI1Veff2]}];
DataH01=Transpose[{Omega1Veff2,Map[Abs,TH1Veff2]}];
DataH01aa=Transpose[{Omega1Veff2,Map[Abs,RH1Veff2]}];

ListLogLinearPlot[{Data01,Data01aa}, PlotRange->All, PlotLabel->"|T_I|", ImageSize->Large]

Data02=Transpose[{Omega1Veff2,Map[Abs,RH1Veff2]}];

Thplot=ListLogLinearPlot[Data02, PlotRange->All, PlotLabel->"|T_H|", ImageSize->Large,GridLines->{{{1/30,Red},{1/700,Red} },None}]

Rhplot=ListLogLinearPlot[Data02, PlotRange->All, PlotLabel->Subscript["R","H"], ImageSize->Large,GridLines->{{{25,Red},{750,Red} },None}]

(*Export["/Users/richarddudley/Dropbox/Correlator/PlotProducers/M4p17Rhplot.pdf",Rhplot,ImageResolution->200]

Data03=Transpose[{Omega1Veff2,Map[Abs,alpha1Veff2]}];

Data03b=Transpose[{Omega1Veff2,Map[Abs,beta1Veff2]}];

alphaplot=ListLogLinearPlot[Data03, PlotRange->All, PlotLabel->"|α|", ImageSize->Large,GridLines->{{{25,Red},{750,Red} },None}]

(*Export["/Users/richarddudley/Dropbox/Correlator/PlotProducers/M4p17alphaplot.pdf",alphaplot,ImageResolution->200]

betaplot=ListLogLinearPlot[Data03b, PlotRange->All, PlotLabel->"|β|", ImageSize->Large,GridLines->{{{1/30,Red},{1/700,Red} },None}]

(*Export["/Users/richarddudley/Dropbox/BH/BEC/nofxcofxvofx/CorrectCVN/2020Files/Potentialvariations/Plots/M4p17betaplot.pdf",betaplot,ImageResolution->200]

Data03a=Transpose[{Omega1Veff2,Alphacheck}];

ListPlot[{Data03,Data03a}, PlotLabel->"|α|", ImageSize->Large, PlotRange->{1, 1.03}]

ListPlot[{Data03,Data03a}, PlotLabel->"|α|", ImageSize->Large, PlotRange->{0.8, 1.05}]

Data04=Transpose[{Omega1Veff2,Map[Abs,RH1Veff2]}];

Rhplot=ListLogLinearPlot[Data04, PlotRange->All, PlotLabel->"|R_H|", ImageSize->Large, GridLines->{{{1/30,Red},{1/700,Red} },None}]

(*Export["/Users/richarddudley/Dropbox/BH/BEC/nofxcofxvofx/CorrectCVN/2020Files/Potentialvariations/Plots/M4p17Rhplot.pdf",Rhplot,ImageResolution->200]

Stipulation1=Abs[RI1Veff2]^2+Abs[TI1Veff2]^2;

Data1=Transpose[{Omega1Veff2,Stipulation1-1}];

ListLogLinearPlot[Data1, PlotRange->All, PlotLabel->"|T_H|^2+|R_H|^2-1", ImageSize->Large]

Stipulation2=Abs[TH1Veff2]^2+Abs[RH1Veff2]^2;
Data2=Transpose[{Omega1Veff2,Stipulation2-1}];
ListLogLinearPlot[Data2, PlotRange->All, PlotLabel->"|T_I|^2+|R_I|^2-1", ImageSize->Large]

Stipulation3=Abs[alpha1Veff2]^2-Abs[beta1Veff2]^2;
Data3=Transpose[{Omega1Veff2,Stipulation3-1}];
ListLogLinearPlot[Data3, PlotLabel->"|α|^2-|β|^2-1", ImageSize->Large]

Stipulation4=Abs[TH1Veff2]^2-Abs[TI1Veff2]^2;
Data4=Transpose[{Omega1Veff2,Stipulation4}];
ListLogLinearPlot[Data4, PlotRange->All, PlotLabel->"|T_H|^2-|T_I|^2", ImageSize->Large]

Stipulation5=Abs[RH1Veff2]^2-Abs[RI1Veff2]^2;
Data5=Transpose[{Omega1Veff2,Stipulation5}];
ListLogLinearPlot[Data5, PlotRange->All, PlotLabel->"|R_H|^2+|R_I|^2", ImageSize->Large]

Stipulation6=TH1Veff2*Conjugate[RH1Veff2]+RI1Veff2*Conjugate[TH1Veff2];
Data6=Transpose[{Omega1Veff2,Stipulation6}];
ListLogLinearPlot[Re[Data6], PlotRange->All, PlotLabel->"(T_H)(R_H)^*+(R_I)(T_H)^*", ImageSize->Large]

VariousChecks50=ListLogLinearPlot[{Data1,Data2,Data3, Data4, Data5, Data6}, PlotRange->All, PlotLabel->"Various Numerical Checks",PlotLegends->{"|T_H|^2+|R_H|^2-1","|T_I|^2+|R_I|^2-1","|α|^2-|β|^2-1","|T_H|^2-|T_I|^2","|R_H|^2+|R_I|^2","(T_H)(R_H)^*+(R_I)(T_H)^*"},PlotStyle->{PointSize[0.01]}, ImageSize->Full]

(*Export["/Users/richarddudley/Dropbox/BH/BEC/nofxcofxvofx/CorrectCVN/2020Files/Potentialvariations/Plots/M4p17VariousChecks50v2.pdf",VariousChecks50]

Particleproduction1=Table[{Omega1Veff2[[i]], Abs[TH1Veff2[[i]]]^2*Abs[(Exp[Pi*Omega1Veff2[[i]]/kappa]*alpha1Veff2[[i]]+Conjugate[RH1Veff2[[i]]*beta1Veff2[[i]]])/(Exp[Pi*Omega1Veff2[[i]]/kappa]-1)]^2, N[Abs[(Exp[Pi*Omega1Veff2[[i]]/kappa])/(Exp[Pi*Omega1Veff2[[i]]/kappa]-1)]^2, 10]}, {i, 1,110}];

ListLogLinearPlot[Particleproduction1[[All, 2]], PlotRange->All,PlotLabel->"|<a_u^Ra_u^L|^2 [Eq.(27)]", ImageSize->Full]

Particleproduction2=Table[{Omega1Veff2[[i]]/kappa,Omega1Veff2[[i]]^2*Abs[TH1Veff2[[i]]]^2*Abs[(Exp[Pi*Omega1Veff2[[i]]/kappa]*alpha1Veff2[[i]]+Conjugate[RH1Veff2[[i]]*beta1Veff2[[i]]])/(Exp[2*Pi*Omega1Veff2[[i]]/kappa]-1)]^2}, {i, 1,110}];

Particleproduction3=Table[{Omega1Veff2[[i]]/kappa, Omega1Veff2[[i]]^2*N[Abs[(Exp[Pi*Omega1Veff2[[i]]/kappa])/(Exp[2*Pi*Omega1Veff2[[i]]/kappa]-1)]^2, 50]}, {i, 1,110}];
Particleproduction2Comparev1=ListLogLinearPlot[{ Particleproduction2, Particleproduction3},   ImageSize-> Full,PlotStyle->{{Blue, Thick},{Orange, Thick}  },FrameLabel->{Style[ ω, 14],Style[ Superscript["ω","2"]HoldForm[ Superscript["HPC","2"]], 14]  },FrameTicksStyle->Directive["Label", 12],Frame->True]

Particleproduction2Compare=ListLogLinearPlot[{ Particleproduction2, Particleproduction3},   ImageSize-> Full,PlotMarkers->{{Graphics[{Disk[]}],1/80},{Graphics[{Rectangle[]}],1/80}},PlotStyle->{{Blue, Thick},{Orange, Thick}  },FrameLabel->{Style[ ω/κ, 14],Style[ HoldForm[Superscript["ω", "2"] "|⟨"(Subscript[OverHat[a], up]^ext)(Subscript[OverHat[a], up]^int)"⟩((|)^2)"], 16] },FrameTicksStyle->Directive["Label", 12],FrameTicks->{{Table[{2*k*10^(3), 2*k * Superscript["x 10", 3]},{k,0,4}], None},{ Table[{10^(3*k),Superscript[10,3*k]},{k,-3,0}] ,None}},Frame->True]

Export["/Users/richarddudley/Dropbox/Correlator/PlotProducers/M4p17uRuLv2.pdf",Particleproduction2Compare]

Particleproduction2v2=Table[{Omega1Veff2[[i]],Omega1Veff2[[i]]^2*Abs[TH1Veff2[[i]]]^2*Abs[(Exp[Pi*Omega1Veff2[[i]]/kappa]*alpha1Veff2[[i]]+Conjugate[RH1Veff2[[i]]*beta1Veff2[[i]]])/(Exp[2*Pi*Omega1Veff2[[i]]/kappa]-1)]^2}, {i, 1,90}];

Particleproduction3v2=Table[{Omega1Veff2[[i]], Omega1Veff2[[i]]^2*N[Abs[(Exp[Pi*Omega1Veff2[[i]]/kappa])/(Exp[2*Pi*Omega1Veff2[[i]]/kappa]-1)]^2, 50]}, {i, 1,90}];

Particleproduction2Comparev2=ListPlot[{ Particleproduction2v2, Particleproduction3v2}, PlotLabel->Superscript["ω","2"] Superscript["|<a_u^Ra_u^L>|","2"], PlotLegends->{"With "Subscript["V","Eff"],Subscript["V","Eff"]"0="}, PlotRange->All, ImageSize->Full, AxesLabel->{ω}]

Particleproduction4=Table[{Omega1Veff2[[i]]/kappa,(Omega1Veff2[[i]]^2*Abs[TH1Veff2[[i]]]^2*Abs[(Exp[Pi*Omega1Veff2[[i]]/kappa]*alpha1Veff2[[i]]+Conjugate[RH1Veff2[[i]]*beta1Veff2[[i]]])/(Exp[2*Pi*Omega1Veff2[[i]]/kappa]-1)]^2)/(Omega1Veff2[[i]]^2*N[Abs[(Exp[Pi*Omega1Veff2[[i]]/kappa])/(Exp[2*Pi*Omega1Veff2[[i]]/kappa]-1)]^2, 14])}, {i, 1,110}];

Particleproduction4Compare=ListLogLinearPlot[Particleproduction4,  ImageSize-> Full, FrameLabel->{Style[ ω/κ, 14],None  },FrameTicksStyle->Directive["Label", 12],FrameTicks->{{Automatic, None},{ Table[{10^(3*k),Superscript[10,3*k]},{k,-3,0}] ,None}},Frame->True]

Export["/Users/richarddudley/Dropbox/Correlator/PlotProducers/M4p17uRuLRatiov2.pdf",Particleproduction4Compare]

Particleproduction4v2=Table[{Omega1Veff2[[i]],(Omega1Veff2[[i]]^2*Abs[TH1Veff2[[i]]]^2*Abs[(Exp[Pi*Omega1Veff2[[i]]/kappa]*alpha1Veff2[[i]]+Conjugate[RH1Veff2[[i]]*beta1Veff2[[i]]])/(Exp[2*Pi*Omega1Veff2[[i]]/kappa]-1)]^2)/(Omega1Veff2[[i]]^2*N[Abs[(Exp[Pi*Omega1Veff2[[i]]/kappa])/(Exp[2*Pi*Omega1Veff2[[i]]/kappa]-1)]^2, 14])}, {i, 1,90}];
Particleproduction4Comparev2=ListPlot[Particleproduction4v2,  PlotLabel->" V_Eff/(V_Eff=0) for "Superscript["|<a_u^Ra_u^L>|","2"], ImageSize->Full, AxesLabel->{ω}]

ParticleproductionRR1=Table[{Omega1Veff2[[i]],Omega1Veff2[[i]]^2*Abs[TH1Veff2[[i]]]^4*(1/(Exp[2*Pi*Omega1Veff2[[i]]/kappa]-1))^2}, {i, 1, 90}];

ParticleproductionRR2=Table[{Omega1Veff2[[i]],Omega1Veff2[[i]]^2*Abs[1]^4*(1/(Exp[2*Pi*Omega1Veff2[[i]]/kappa]-1))^2}, {i, 1, 110}];

Particleproduction2CompareRR12=ListLogLinearPlot[{ ParticleproductionRR1, ParticleproductionRR2}, PlotLabel->Superscript["ω","2"]HoldForm[ Superscript["("Superscript["n","u, R "]")","2"]], PlotLegends->{"With "Subscript["V","Eff"],Subscript["V","Eff"]"0="}, ImageSize->Full, AxesLabel->{ω}, PlotRange->All]

(*Export["/Users/richarddudley/Dropbox/BH/BEC/nofxcofxvofx/CorrectCVN/2020Files/Potentialvariations/Plots/M4p17nuRSquaredv2.pdf",Particleproduction2CompareRR12]

ParticleproductionLL1=Table[{Omega1Veff2[[i]]/kappa,Omega1Veff2[[i]]^2*(Abs[alpha1Veff2[[i]]+Conjugate[RH1Veff2[[i]]*beta1Veff2[[i]]]*Exp[Pi*Omega1Veff2[[i]]/kappa]]^2/(Exp[2*Pi*Omega1Veff2[[i]]/kappa]-1)+Abs[beta1Veff2[[i]]*TH1Veff2[[i]]]^2)^2}, {i, 1, 110}];
ParticleproductionLL2=Table[{Omega1Veff2[[i]]/kappa,Omega1Veff2[[i]]^2*Abs[Abs[1+Conjugate[0*0]*Exp[Pi*Omega1Veff2[[i]]/kappa]]^2/(Exp[2*Pi*Omega1Veff2[[i]]/kappa]-1)+Abs[0*1]]^2}, {i, 1,110}];

Particleproduction2CompareLL12=ListLogLinearPlot[{ ParticleproductionLL1, ParticleproductionLL2}, ImageSize-> Full,PlotStyle->{{Blue, Thick},{Orange, Thick}  },PlotMarkers->{{Graphics[{Disk[]}],1/80},{Graphics[{Rectangle[]}],1/80}},FrameLabel->{Style[ ω/κ, 14],Style[ HoldForm[ Superscript["|ω (Subscript[n, up]^int)|","2"]], 16] },FrameTicksStyle->Directive["Label", 12],FrameTicks->{{Table[{2*k*10^(3),2*k Superscript["x10",3]},{k,0,8}], None},{ Table[{10^(2*k),Superscript[10,2*k]},{k,-8,0}] ,None}},Frame->True]

Export["/Users/richarddudley/Dropbox/Correlator/PlotProducers/M4p17nuLSquaredv2.pdf",Particleproduction2CompareLL12]

"/Users/richarddudley/Dropbox/BH/BEC/nofxcofxvofx/CorrectCVN/2020Files/Potentialvariations/Plots/M4p17nuLSquaredv2.pdf"

Particleproduction2CompareLL12LogLog=ListLogLogPlot[{ ParticleproductionLL1, ParticleproductionLL2}, PlotLabel->Superscript["ω","2"] HoldForm[ Superscript["("Superscript["n","u, L "]")","2"]], PlotLegends->{"With "Subscript["V","Eff"],Subscript["V","Eff"]"0="}, PlotRange->All, ImageSize->Full, AxesLabel->{ω}]

(*Export["/Users/richarddudley/Dropbox/BH/BEC/nofxcofxvofx/CorrectCVN/2020Files/Potentialvariations/Plots/M4p17Particleproduction2CompareLL12LogLog.pdf",Particleproduction2CompareLL12LogLog]

ParticleproductionLL1Ratio=Table[{Omega1Veff2[[i]],(Omega1Veff2[[i]]^2*(Abs[alpha1Veff2[[i]]+Conjugate[RH1Veff2[[i]]*beta1Veff2[[i]]]*Exp[Pi*Omega1Veff2[[i]]/kappa]]^2/(Exp[2*Pi*Omega1Veff2[[i]]/kappa]-1)+Abs[beta1Veff2[[i]]*TH1Veff2[[i]]]^2)^2)/(Omega1Veff2[[i]]^2*Abs[Abs[1+Conjugate[0*0]*Exp[Pi*Omega1Veff2[[i]]/kappa]]^2/(Exp[2*Pi*Omega1Veff2[[i]]/kappa]-1)+Abs[0*1]]^2)}, {i, 1, 110}];

Particleproduction4CompareUL1=ListLogLinearPlot[ParticleproductionLL1Ratio,  PlotLabel->" V_Eff/(V_Eff=0) for "Superscript["n","u, L 2"], ImageSize->Full, AxesLabel->{ω}]

ParticleproductionLL1222=Table[{Omega1Veff2[[i]],Omega1Veff2[[i]]*(Abs[alpha1Veff2[[i]]+Conjugate[RH1Veff2[[i]]*beta1Veff2[[i]]]*Exp[Pi*Omega1Veff2[[i]]/kappa]]^2/(Exp[2*Pi*Omega1Veff2[[i]]/kappa]-1)+Abs[beta1Veff2[[i]]*TH1Veff2[[i]]]^2)}, {i, 1, 110}];
ParticleproductionLL2222=Table[{Omega1Veff2[[i]],Omega1Veff2[[i]]*Abs[Abs[1+Conjugate[0*0]*Exp[Pi*Omega1Veff2[[i]]/kappa]]^2/(Exp[2*Pi*Omega1Veff2[[i]]/kappa]-1)+Abs[0*1]]}, {i, 1,110}];

Particleproduction2CompareLL12222=ListLogLinearPlot[{ ParticleproductionLL1222, ParticleproductionLL2222}, PlotLabel->Superscript["ω",""] HoldForm[ Superscript["("Superscript["n","u, L "]")",""]], PlotLegends->{"With "Subscript["V","Eff"],Subscript["V","Eff"]"0="}, PlotRange->All, ImageSize->Full, AxesLabel->{ω}]

(*Export["/Users/richarddudley/Dropbox/BH/BEC/nofxcofxvofx/CorrectCVN/2020Files/Potentialvariations/Plots/M4p17nuLv2.pdf",Particleproduction2CompareLL12222]

ParticleproductionLL1555Ratio=Table[{Omega1Veff2[[i]],(Omega1Veff2[[i]]^2*(Abs[alpha1Veff2[[i]]+Conjugate[RH1Veff2[[i]]*beta1Veff2[[i]]]*Exp[Pi*Omega1Veff2[[i]]/(kappa*10)]]^2/(Exp[2*Pi*Omega1Veff2[[i]]/(kappa*10)]-1)+Abs[beta1Veff2[[i]]*TH1Veff2[[i]]]^2)^2)/(Omega1Veff2[[i]]^2*(Abs[1+Conjugate[0*0]*Exp[Pi*Omega1Veff2[[i]]/(kappa*10)]]^2/(Exp[2*Pi*Omega1Veff2[[i]]/(kappa*10)]-1)+Abs[0*1]^2)^2)}, {i, 1, 110}];

Particleproduction4CompareUL=ListLogLinearPlot[ParticleproductionLL1555Ratio,  PlotLabel->" V_Eff/(V_Eff=0) for "Superscript["n","u, L 2"], ImageSize->Full, AxesLabel->{ω}, PlotRange->All]

Particleproduction4Ratio=Table[{Omega1Veff2[[i]],(Omega1Veff2[[i]]^2*Abs[TH1Veff2[[i]]]^2*Abs[(Exp[Pi*Omega1Veff2[[i]]/(10*kappa)]*alpha1Veff2[[i]]+Conjugate[RH1Veff2[[i]]*beta1Veff2[[i]]])/(Exp[2*Pi*Omega1Veff2[[i]]/(10*kappa)]-1)]^2)/(Omega1Veff2[[i]]^2*N[1/(Exp[2*Pi*Omega1Veff2[[i]]/(10*kappa)]-1)^2, 14])}, {i, 1,110}];

Particleproduction4CompareUL=ListLogLinearPlot[Particleproduction4Ratio,  PlotLabel->" V_Eff/(V_Eff=0) for "Superscript["n","u, L 2"], ImageSize->Full, AxesLabel->{ω}]

ParticleproductionvLL12020=Table[{Omega1Veff2[[i]],Omega1Veff2[[i]]^2*(Abs[RH1Veff2[[i]]*alpha1Veff2[[i]]+Conjugate[beta1Veff2[[i]]*Exp[Pi*Omega1Veff2[[i]]/kappa]]]^2/(Exp[2*Pi*Omega1Veff2[[i]]/kappa]-1))^2}, {i, 1, 110}];

ParticleproductionLL1555Ratio=Table[{Omega1Veff2[[i]],((Abs[alpha1Veff2[[i]]+Conjugate[RH1Veff2[[i]]*beta1Veff2[[i]]]*Exp[Pi*Omega1Veff2[[i]]/(kappa*10)]]^2)/(Exp[2*Pi*Omega1Veff2[[i]]/(kappa*10)]-1)+Abs[beta1Veff2[[i]]*TH1Veff2[[i]]]^2)^2/(Abs[Abs[1+Conjugate[0*0]*Exp[Pi*Omega1Veff2[[i]]/(kappa*10)]]^2/(Exp[2*Pi*Omega1Veff2[[i]]/(kappa*10)]-1)+Abs[0*1]]^2)}, {i, 1, 110}];

ParticleproductionLL15556=Table[{Omega1Veff2[[i]]/kappa,Omega1Veff2[[i]]^2*(Abs[alpha1Veff2[[i]]+Conjugate[RH1Veff2[[i]]*beta1Veff2[[i]]]*Exp[Pi*Omega1Veff2[[i]]/(kappa*1000000)]]^2/(Exp[2*Pi*Omega1Veff2[[i]]/(kappa*1000000)]-1)+Abs[beta1Veff2[[i]]*TH1Veff2[[i]]]^2)^2}, {i, 1, 110}];
ParticleproductionLL25556=Table[{Omega1Veff2[[i]]/kappa,Omega1Veff2[[i]]^2*Abs[Abs[1+Conjugate[0*0]*Exp[Pi*Omega1Veff2[[i]]/(kappa*1000000)]]^2/(Exp[2*Pi*Omega1Veff2[[i]]/(kappa*1000000)]-1)+Abs[0*1]]^2}, {i, 1,110}];

Particleproduction2CompareLL155556=ListLogLinearPlot[{ ParticleproductionLL15556, ParticleproductionLL25556}, ImageSize-> Full,PlotMarkers->{{Graphics[{Disk[]}],1/80},{Graphics[{Rectangle[]}],1/80}},PlotStyle->{{Blue, Thick},{Orange, Thick}  },FrameLabel->{Style[ ω/κ, 14],Style[ HoldForm[ Superscript["(ω*(Subscript[n, ds]^int)|","2"]], 14]  },FrameTicksStyle->Directive["Label", 12],FrameTicks->{{Table[{5*k*10^(-8),5*k Superscript["x 10",-8]},{k,0,8}], None},{ Table[{10^(k),Superscript[10,k]},{k,-4,0}] ,None}},Frame->True]

ParticleproductionLL155567=Table[{Omega1Veff2[[i]],Omega1Veff2[[i]]^2*(Abs[alpha1Veff2[[i]]+Conjugate[RH1Veff2[[i]]*beta1Veff2[[i]]]*Exp[Pi*Omega1Veff2[[i]]/(kappa/10)]]^2/(Exp[2*Pi*Omega1Veff2[[i]]/(kappa/10)]-1)+Abs[beta1Veff2[[i]]*TH1Veff2[[i]]]^2)^2}, {i, 1, 110}];
ParticleproductionLL255567=Table[{Omega1Veff2[[i]],Omega1Veff2[[i]]^2*Abs[Abs[1+Conjugate[0*0]*Exp[Pi*Omega1Veff2[[i]]/(kappa/10)]]^2/(Exp[2*Pi*Omega1Veff2[[i]]/(kappa/10)]-1)+Abs[0*1]]^2}, {i, 1,110}];

Particleproduction2CompareLL1555567=ListLogLinearPlot[{ ParticleproductionLL155567, ParticleproductionLL255567}, PlotLabel->Superscript["ω",""] HoldForm[ Superscript["("Superscript["n","u, L "]")",""]], PlotLegends->{"With "Subscript["V","Eff"],Subscript["V","Eff"]"0="}, PlotRange->All, ImageSize->Full, AxesLabel->{ω}]

Particleproduction2CompareLL122=ListLogLinearPlot[ParticleproductionLL2, PlotLabel->Superscript["ω","2"] HoldForm[ Superscript["("Superscript["n","u, L "]")","2"]], PlotLegends->{"With "Subscript["V","Eff"],Subscript["V","Eff"]"0="}, PlotRange->All, ImageSize->Full]

(*Export["/Users/richarddudley/Dropbox/BH/BEC/nofxcofxvofx/CorrectCVN/2020Files/Potentialvariations/Plots/M4p17nuLSquaredv2.pdf",Particleproduction2CompareLL12]

ParticleproductionvLL1=Table[{Omega1Veff2[[i]]/kappa,Omega1Veff2[[i]]^2*(Abs[RH1Veff2[[i]]*alpha1Veff2[[i]]+Conjugate[beta1Veff2[[i]]*Exp[Pi*Omega1Veff2[[i]]/kappa]]]^2/(Exp[2*Pi*Omega1Veff2[[i]]/kappa]-1))^2}, {i, 1, 110}];
ParticleproductionvLL2=Table[{Omega1Veff2[[i]]/kappa,Omega1Veff2[[i]]^2*(Abs[Abs[0+Conjugate[0]*Exp[Pi*Omega1Veff2[[i]]/kappa]]^2/(Exp[2*Pi*Omega1Veff2[[i]]/kappa]-1)])}, {i, 1, 110}];

Particleproduction2ComparevLL12=ListLogLinearPlot[{ ParticleproductionvLL1, ParticleproductionvLL2},  ImageSize-> Full,PlotMarkers->{{Graphics[{Disk[]}],1/80},{Graphics[{Rectangle[]}],1/80}},PlotStyle->{{Blue, Thick},{Orange, Thick}  },FrameLabel->{Style[ ω/κ, 14],Style[ HoldForm[ Superscript["|ω (Subscript[n, ds]^int)|","2"]], 16] },FrameTicksStyle->Directive["Label", 12],FrameTicks->{{Table[{3*k*10^(2), 3*k Superscript["x10",2]},{k,0,8}], None},{ Table[{10^(2*k),Superscript[10,2*k]},{k,-4,0}] ,None}},Frame->True, PlotRange->All]

Export["/Users/richarddudley/Dropbox/Correlator/PlotProducers/M4p17nvLSquaredv2.pdf",Particleproduction2ComparevLL12]

(*Export["/Users/richarddudley/Dropbox/BH/BEC/nofxcofxvofx/CorrectCVN/2020Files/Potentialvariations/Plots/M4p17nvLSquaredv2.pdf",Particleproduction2ComparevLL12]

Particleproduction2ComparevLL12v2=ListLogLinearPlot[{ ParticleproductionvLL1, ParticleproductionvLL2}, PlotLabel->Superscript["ω","2"] HoldForm[ Superscript["("Superscript["n","v, L "]")","2"]], PlotLegends->{"With "Subscript["V","Eff"],Subscript["V","Eff"]"0="}, ImageSize->Full]