(*THRHTableDataImport=Import["D:\\Dropbox\\BH\\BEC\\nofxcofxvofx\\Writeup\\6\\THRH2013TableData42v1.mx"];
TIRITableDataImport=Import["D:\\Dropbox\\BH\\BEC\\nofxcofxvofx\\Writeup\\6\\TIRI2013TableData42v1.mx"];
alphabetaTableDataImport=Import["D:\\Dropbox\\BH\\BEC\\nofxcofxvofx\\Writeup\\6\\alphabeta2013TableData42v1.mx"];*)


THRHTableDataImport=Import["/Users/richarddudley/Dropbox/BH/BEC/nofxcofxvofx/Writeup/6/THRH2013TableData42v1.mx"];
TIRITableDataImport=Import["/Users/richarddudley/Dropbox/BH/BEC/nofxcofxvofx/Writeup/6/TIRI2013TableData42v1.mx"];
alphabetaTableDataImport=Import["/Users/richarddudley/Dropbox/BH/BEC/nofxcofxvofx/Writeup/6/alphabeta2013TableData42v1.mx"];

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=N[D[c1,x]/.x->0,60]

Omega1Veff2=Flatten[THRHTableDataImport[[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]]];

dataTIVeff2=Transpose[{Omega1Veff2, TI1Veff2}];
dataRIVeff=Transpose[{Omega1Veff2, RI1Veff2}];
dataTHVeff2=Transpose[{Omega1Veff2, TH1Veff2}];
dataRHVeff=Transpose[{Omega1Veff2, RH1Veff2}];
dataalphaVeff2=Transpose[{Omega1Veff2, alpha1Veff2}];
databetaVeff=Transpose[{Omega1Veff2, beta1Veff2}];

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->Full]

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->Full]

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

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

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

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->Full]

RI1Veff2

RH1Veff2

TH1Veff2*Conjugate[RH1Veff2]

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/Correlator/PlotProducers/2013VariousChecks50v2.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, 25}];

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

Particleproduction2=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, 1,50}];

Particleproduction3=Table[{Omega1Veff2[[i]], Omega1Veff2[[i]]^2*N[Abs[(Exp[Pi*Omega1Veff2[[i]]/kappa])/(Exp[2*Pi*Omega1Veff2[[i]]/kappa]-1)]^2, 50]}, {i, 1,50}];

Particleproduction2Compare=ListLogLinearPlot[{ Particleproduction2, Particleproduction3}, PlotLabel->Superscript["ω","2"] Superscript["|<a_u^Ra_u^L>|","2"], PlotLegends->{"With "Subscript["V","Eff"],Subscript["V","Eff"]"0="}, PlotRange->All, ImageSize->Full]

Particleproduction2Compare2=ListPlot[{ Particleproduction2, Particleproduction3}, PlotLabel->Superscript["ω","2"] Superscript["|<a_u^Ra_u^L>|","2"], PlotLegends->{"With "Subscript["V","Eff"],Subscript["V","Eff"]"0="}, PlotRange->All, ImageSize->Full]

Particleproduction22=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, 49}];

Particleproduction32=Table[{Omega1Veff2[[i]]/kappa, Omega1Veff2[[i]]^2*N[Abs[(Exp[Pi*Omega1Veff2[[i]]/kappa])/(Exp[2*Pi*Omega1Veff2[[i]]/kappa]-1)]^2, 14]}, {i, 1, 49}];

Particleproduction2Compare22=ListLogLinearPlot[{ Particleproduction22, Particleproduction32},  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^(-6),2*k Superscript["x 10",-6]},{k,1,8}], None},{ Table[{10^(k),Superscript[10,k]},{k,-4,0}] ,None}},Frame->True]

Export["/Users/richarddudley/Dropbox/Correlator/PlotProducers/2013uRuLv2.pdf",Particleproduction2Compare22]

ParticleproductionRatio=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, 49}];

Particleproduction4Compare=ListLogLinearPlot[ParticleproductionRatio, ImageSize-> Full, FrameLabel->{Style[ ω/κ, 14],None  },FrameTicksStyle->Directive["Label", 12],FrameTicks->{{Automatic, None},{ Table[{10^(k),Superscript[10,k]},{k,-4,0}] ,None}},Frame->True]

Export["/Users/richarddudley/Dropbox/Correlator/PlotProducers/2013uRuLRatio.pdf",Particleproduction4Compare]

ParticleproductionRR1=Table[{Omega1Veff2[[i]],Omega1Veff2[[i]]^2*Abs[TH1Veff2[[i]]]^4*(1/(Exp[2*Pi*Omega1Veff2[[i]]/kappa]-1))^2}, {i, 1, 49}];

ParticleproductionRR2=Table[{Omega1Veff2[[i]],Omega1Veff2[[i]]^2*Abs[1]^4*(1/(Exp[2*Pi*Omega1Veff2[[i]]/kappa]-1))^2}, {i, 1, 49}];

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

(*Export["D:\\Dropbox\\BH\\BEC\\nofxcofxvofx\\Writeup\\2013andWaterfall\\2013nuR.pdf",Particleproduction2CompareRR12]*)

ParticleproductionLL1=Table[{Omega1Veff2[[i]]/kappa,Omega1Veff2[[i]]^2*Abs[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, 49}];
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, 49}];

Particleproduction2CompareLL12=ListLogLinearPlot[{ ParticleproductionLL1, ParticleproductionLL2},  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, up]^int)|","2"]], 16]  },FrameTicksStyle->Directive["Label", 12],FrameTicks->{{Table[{3*k*10^(-6),3*k Superscript["x 10",-6]},{k,0,8}], None},{ Table[{10^(k),Superscript[10,k]},{k,-4,0}] ,None}},Frame->True]

Export["/Users/richarddudley/Dropbox/Correlator/PlotProducers/2013nuLSquaredv2.pdf",Particleproduction2CompareLL12]

ParticleproductionLL1Ratio=Table[{Omega1Veff2[[i]],(Abs[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)/(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, 49}];

Particleproduction4CompareRatio=ListLogLinearPlot[ParticleproductionLL1Ratio,  PlotLabel->" V_Eff/(V_Eff=0) for "Superscript["n","u, l"], ImageSize->Full]

ParticleproductionLL12=Table[{Omega1Veff2[[i]],Omega1Veff2[[i]]^2*Abs[Abs[Sqrt[2]*Exp[Pi*Omega1Veff2[[i]]/kappa]+Conjugate[RH1Veff2[[i]]*2]]^2/(Exp[2*Pi*Omega1Veff2[[i]]/kappa]-1)+Abs[1*TH1Veff2[[i]]]]^2}, {i, 1, 49}];

Particleproduction2CompareRR12222=ListPlot[{ ParticleproductionLL12, ParticleproductionLL2}, PlotLabel->Superscript["ω","2"] Superscript["|<a_u^La_u^L>|","2"], PlotLegends->{"With α=(2)^1/2, β=1"}, PlotRange->All, ImageSize->Full]

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, 50}];
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, 50}];

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[{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]

Export["/Users/richarddudley/Dropbox/Correlator/PlotProducers/2013nvLSquaredv2.pdf",Particleproduction2ComparevLL12]

i98