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]

nuRZeroPotential=1/(Exp[2*Pi*omega/kappa]-1);
nuLZeroPotential=1/(4*omega^2)*Abs[Exp[Pi*omega/kappa](0)/(2*I*omega+0)+(2*I*omega)]^2*1/(Exp[2*Pi*omega/kappa]-1)+0^2/(4*omega^2+0^2);
nvLZeroPotential=1/(4*omega^2)*Abs[0(2*I*omega-0)/(2*I*omega-0)-0*Exp[Pi*omega/kappa]]^2*1/(Exp[2*Pi*omega/kappa]-1);
LogLinearPlot[omega*nuRZeroPotential,{omega,1/1000000,2},PlotStyle->Automatic, ImageSize->Large, WorkingPrecision->30, PlotLabel->" No potential ", AxesLabel->{ ω,Superscript["ω n","u,R"] }]

LogLinearPlot[omega*nuLZeroPotential,{omega,1/1000000,2},PlotStyle->Automatic, ImageSize->Large, WorkingPrecision->30, PlotLabel->" No potential ", AxesLabel->{ ω,Superscript["ω n","u,L"] }]

LogLinearPlot[omega*nvLZeroPotential,{omega,1/1000000,2},PlotStyle->Automatic, ImageSize->Large, WorkingPrecision->30, PlotLabel->" No potential ", AxesLabel->{ ω,Superscript["ω n","v,L"] }]

Massive Case

m=4*10^-2;
kR=Sqrt[omega^2-mR^2];
kL=Sqrt[omega^2+mL^2];

nuRmassiveGeneric=HeavisideTheta[omega-mR]*(4*kR*omega/(omega+kR)^2*1/(Exp[2*Pi*omega/kappa]-1));
nuLmassiveGeneric=1/(4*omega*kL)*Abs[Exp[Pi*omega/kappa]*(omega-kR)/(omega+kR)*(kL-omega)+(kL+omega)]^2*1/(Exp[2*Pi*omega/kappa]-1)+HeavisideTheta[omega-mR]*kR/kL*(kL-omega)^2/(kR+omega)^2;
nvLmassiveGeneric=1/(4*omega*kL)*Abs[(omega-kR)/(omega+kR)*(kL+omega)+Exp[Pi*omega/kappa]*(kL-omega)]^2*1/(Exp[2*Pi*omega/kappa]-1);

nuRmassive=nuRmassiveGeneric/.{mR-> Sqrt[7/16]*m,mL->Sqrt[5/16]*m};
nuLmassive=nuLmassiveGeneric/.{mR-> Sqrt[7/16]*m,mL->Sqrt[5/16]*m};
nvLmassive=nvLmassiveGeneric/.{mR-> Sqrt[7/16]*m,mL->Sqrt[5/16]*m};
uRuRMassive=LogLinearPlot[omega*nuRmassive,{omega,2/100,1/10},PlotStyle->{Orange, Thick}, ImageSize-> Full,  PlotLabel->" Massive Case" , PlotRange->All, AxesLabel->{ ω,Superscript["ω n","u,R"] }]
uLuLMassive=LogLinearPlot[omega*nuLmassive,{omega,1/100000,1/10},PlotStyle->{Orange, Thick}, ImageSize-> Full,  PlotLabel->" Massive Case" , PlotRange->All, AxesLabel->{ ω,Superscript["ω n","u,L"] }]
vLvLMassive=LogLinearPlot[omega*nvLmassive,{omega,1/100000,1/10},PlotStyle->{Orange, Thick}, ImageSize-> Full,  PlotLabel->" Massive Case" , PlotRange->All, AxesLabel->{ ω,Superscript["ω n","v,L"] }]

uRuRMassiveRatio=LogLinearPlot[nuRmassive/nuRZeroPotential,{omega,2/100,1/10},PlotStyle->{Orange, Thick}, ImageSize-> Full,  PlotLabel->" Massive Case Ratio" , PlotRange->All, AxesLabel->{ ω,Ratio  Superscript[" n","u,R"] }]
uLuLMassiveRatio=LogLinearPlot[nuLmassive/nuLZeroPotential,{omega,1/100000,1/10},PlotStyle->{Orange, Thick}, ImageSize-> Full,  PlotLabel->" Massive Case Ratio" , PlotRange->All, AxesLabel->{ ω,Ratio Superscript["ω n","u,L"] }]

Massive Case 2

nuRmassive2=nuRmassiveGeneric/.{mR-> Sqrt[7/16]*m,mL->10*Sqrt[5/16]*m};
nuLmassive2=nuLmassiveGeneric/.{mR-> Sqrt[7/16]*m,mL->10*Sqrt[5/16]*m};
nvLmassive2=nvLmassiveGeneric/.{mR-> Sqrt[7/16]*m,mL->10*Sqrt[5/16]*m};
uRuRMassive2=LogLinearPlot[omega*nuRmassive2,{omega,2/100,1/10},PlotStyle->{Orange, Thick}, ImageSize-> Full,  PlotLabel->" Massive Case" , PlotRange->All, AxesLabel->{ ω,Superscript["ω n","u,R"] }]
uLuLMassive2=LogLinearPlot[omega*nuLmassive2,{omega,1/100000,1/10},PlotStyle->{Orange, Thick}, ImageSize-> Full,  PlotLabel->" Massive Case" , PlotRange->All, AxesLabel->{ ω,Superscript["ω n","u,L"] }]
vLvLMassive2=LogLinearPlot[omega*nvLmassive2,{omega,1/100000,1/10},PlotStyle->{Orange, Thick}, ImageSize-> Full,  PlotLabel->" Massive Case" , PlotRange->All, AxesLabel->{ ω,Superscript["ω n","v,L"] }]

Massive Case 3

nuRmassive3=nuRmassiveGeneric/.{mR-> Sqrt[7/16]*m,mL->1/10*Sqrt[5/16]*m};
nuLmassive3=nuLmassiveGeneric/.{mR-> Sqrt[7/16]*m,mL->1/10*Sqrt[5/16]*m};
nvLmassive3=nvLmassiveGeneric/.{mR-> Sqrt[7/16]*m,mL->1/10*Sqrt[5/16]*m};
uRuRMassive3=LogLinearPlot[omega*nuRmassive3,{omega,2/100,1/10},PlotStyle->{Orange, Thick}, ImageSize-> Full,  PlotLabel->" Massive Case" , PlotRange->All, AxesLabel->{ ω,Superscript["ω n","u,R"] }]
uLuLMassive3=LogLinearPlot[omega*nuLmassive3,{omega,1/100000,1/10},PlotStyle->{Orange, Thick}, ImageSize-> Full,  PlotLabel->" Massive Case" , PlotRange->All, AxesLabel->{ ω,Superscript["ω n","u,L"] }]
vLvLMassive3=LogLinearPlot[omega*nvLmassive3,{omega,1/100000,1/10},PlotStyle->{Orange, Thick}, ImageSize-> Full,  PlotLabel->" Massive Case" , PlotRange->All, AxesLabel->{ ω,Superscript["ω n","v,L"] }]

Massive Comparison

nuLmassiveMax=FindMaximum[omega*nuLmassive, {omega,2*10^-6,9/200}];
nuLmassive2Max=FindMaximum[omega*nuLmassive2, {omega,2*10^-6,9/200}];
nuLmassive3Max=FindMaximum[omega*nuLmassive3, {omega,2*10^-6,9/200}];
nvLmassiveMax=FindMaximum[omega*nvLmassive, {omega,2*10^-6,9/200}];
nvLmassive2Max=FindMaximum[omega*nvLmassive2, {omega,2*10^-6,9/200}];
nvLmassive3Max=FindMaximum[omega*nvLmassive3, {omega,2*10^-6,9/200}];

uLuLMassiveCompare123=LogLinearPlot[{(omega*nuLmassive3)/nuLmassive3Max[[1]],(omega*nuLmassive)/nuLmassiveMax[[1]],(omega*nuLmassive2)/nuLmassive2Max[[1]]},{omega,2*10^-6,9/200},PlotStyle->{{Blue, Thick, Dashed},{Green, Thick , Dotted},{Orange, Thick}  }, ImageSize-> Full, PlotLabel->"Massive Case Comparsion", PlotRange->All, PlotLegends->{"mL=1/10*Sqrt[5/16]*m","mL=Sqrt[5/16]*m","mL=10*Sqrt[5/16]*m"}, AxesLabel->{ ω,Superscript["C*ω n","u,L"] }]
vLvLMassiveCompare123=LogLinearPlot[{(omega*nvLmassive3)/nvLmassive3Max[[1]],(omega*nvLmassive)/nvLmassiveMax[[1]],(omega*nvLmassive2)/nvLmassive2Max[[1]]},{omega,2*10^-6,9/200},PlotStyle->{{Blue, Thick, Dashed},{Green, Thick , Dotted},{Orange, Thick} }, ImageSize-> Full, PlotLabel->"Massive Case Comparsion", PlotRange->All, PlotLegends->{"mL=1/10*Sqrt[5/16]*m","mL=Sqrt[5/16]*m","mL=10*Sqrt[5/16]*m"}, AxesLabel->{ ω,Superscript["C*ω n","v,L"] }]

uLuLMassiveCompare123=LogLinearPlot[{(omega*nuLmassive3),(omega*nuLmassive),(omega*nuLmassive2)/38},{omega,2*10^-6,9/200},PlotStyle->{{Blue, Thick},{Green, Thick},{Orange, Thick} }, ImageSize-> Full, PlotLabel->Superscript["ω","2"]HoldForm[ Superscript["("Superscript["n","u, L "]")","2"]], PlotRange->All, PlotLegends->{"VR/10=-VL/100=κ","VR=-VL/100=κ","3*VR/2=-VL/100=κ"}, AxesLabel->{ω}]







VR=1;
VL=-10;




nuLDelta=1/(4*omega^2)*Abs[Exp[Pi*omega/kappa](VR*VL)/(2*I*omega+VR)+(2*I*omega-VL)]^2*1/(Exp[2*Pi*omega/kappa]-1)+VL^2/(4*omega^2+VR^2);
nvLDelta=1/(4*omega^2)*Abs[VR(2*I*omega-VL)/(2*I*omega-VR)-VL*Exp[Pi*omega/kappa]]^2*1/(Exp[2*Pi*omega/kappa]-1);

LogLinearPlot[omega*nuRNoPotential,{omega,1/1000000,2},PlotStyle->Automatic, ImageSize->Large, WorkingPrecision->30, PlotLabel->" No potential ", AxesLabel->{ ω,Superscript["ω n","u,R"] }]

TR=(2*I*omega)/(2*I*omega-VR);
alphal=(2*I*omega-VL)/(2*I*omega);

LogLinearPlot[Abs[TR],{omega,1/1000000,2},PlotStyle->Automatic, ImageSize->Large, WorkingPrecision->30]

LogLinearPlot[Abs[alphal],{omega,1/1000000,1},PlotStyle->Automatic, ImageSize->Large, WorkingPrecision->30]

nuLnoPotential=Abs[Abs[1+Conjugate[0*0]*Exp[Pi*omega/kappa]]/(Exp[2*Pi*omega/kappa]-1)+Abs[0*1]];

m=4*10^-2;
mR=Sqrt[7/16]*m;
mL=Sqrt[5/16]*m;
kR=Sqrt[omega^2-mR^2];
kL=Sqrt[omega^2+mL^2];

nuRmassive=HeavisideTheta[omega-mR]*(4*kR*omega/(omega+kR)^2*1/(Exp[2*Pi*omega/kappa]-1));
nuLmassive=1/(4*omega*kL)*Abs[Exp[Pi*omega/kappa]*(omega-kR)/(omega+kR)*(kL-omega)+(kL+omega)]^2*1/(Exp[2*Pi*omega/kappa]-1)+HeavisideTheta[omega-mR]*kR/kL*(kL-omega)^2/(kR+omega)^2;
nvLmassive=1/(4*omega*kL)*Abs[(omega-kR)/(omega+kR)*(kL+omega)+Exp[Pi*omega/kappa]*(kL-omega)]^2*1/(Exp[2*Pi*omega/kappa]-1);

nuLmassive2=HeavisideTheta[omega-mR]*kR/kL*(kL-omega)^2/(kR+omega)^2;

TRmassive=(2*Sqrt[kR*omega])/(kR+omega);
alphalmassive=Sqrt[kL/omega]*(kL+omega)/(2*kL);

LogLinearPlot[Abs[TRmassive],{omega,1/1000000,2},PlotStyle->Automatic, ImageSize->Large, WorkingPrecision->30]

LogLinearPlot[Abs[alphalmassive],{omega,1/100000000000,2},PlotStyle->Automatic, ImageSize->Large, WorkingPrecision->30]

LogLinearPlot[omega/(Exp[2*Pi*omega/kappa]-1),{omega,1/1000000,1},PlotStyle->Automatic, ImageSize->Full, WorkingPrecision->30]

LogLinearPlot[omega^2/(Exp[2*Pi*omega/kappa]-1),{omega,1/1000000,1},PlotStyle->Automatic, ImageSize-> Full, WorkingPrecision->30]

LogLinearPlot[{nuRDelta,nuRmassive},{omega,1,100},PlotStyle->Automatic, ImageSize-> Full, PlotLegends->{"nuRDelta","nuRmassive"}, WorkingPrecision->30]

uRuRParticleproductionMassive=LogLinearPlot[nuRmassive,{omega,2/100,1/10},PlotStyle->{Orange, Thick}, ImageSize-> Full,  PlotLabel->" Massive "Superscript["n","u,R"] , PlotRange->All]

uRuRParticleproductionMassive2=Plot[nuRmassive,{omega,2/100,1/10},PlotStyle->{Orange, Thick}, ImageSize-> Full,  PlotLabel->" Massive "Superscript["n","u,R"] , PlotRange->All]

uRuRParticleproductionDelta=LogLinearPlot[nuRDelta,{omega,5*10^-5,5*1/100},PlotStyle-> {Blue, Thick}, ImageSize-> Full,  PlotLabel->" Delta Function potential "Superscript["n","u,R"] , PlotRange->All]

uRuRParticleproductionDelta2=Plot[nuRDelta,{omega,5*10^-5,5*1/100},PlotStyle-> {Blue, Thick}, ImageSize-> Full,  PlotLabel->" Delta Function potential "Superscript["n","u,R"] , PlotRange->All]

Export["D:\\Dropbox\\BH\\BEC\\nofxcofxvofx\\Writeup\\MassiveandDelta\\New\\uRuRMassive.pdf",uRuRParticleproductionMassive ]

Export["D:\\Dropbox\\BH\\BEC\\nofxcofxvofx\\Writeup\\MassiveandDelta\\New\\uRuRDelta.pdf",uRuRParticleproductionDelta]

uLuLParticleproductionMassive=LogLinearPlot[nuLmassive,{omega,10^-5,1},PlotStyle->{Orange, Thick}, ImageSize-> Full, PlotLabel->" Massive "Superscript["n","u,L"], PlotRange->All]

uLuLParticleproductionMassive2=LogLinearPlot[nuLmassive,{omega,2/100,4/100},PlotStyle->{Orange, Thick}, ImageSize-> Full, PlotLabel->" Massive "Superscript["n","u,L"], PlotRange->{0, 0.04}]

uLuLParticleproductionMassive3=Plot[nuLmassive,{omega,10^-5,1},PlotStyle->{Orange, Thick}, ImageSize-> Full, PlotLabel->" Massive "Superscript["n","u,L"], PlotRange->All]

uLuLParticleproductionDelta=LogLinearPlot[omega^2*nuLDelta^2,{omega,10^-5,1},PlotStyle->{Blue, Thick}, ImageSize-> Full, PlotLabel->" Delta Function potential "Superscript["ω","2"]Superscript["n","u,L"], PlotRange->All]

uLuLParticleproductionDelta=LogLinearPlot[omega^2*nuLDelta^2,{omega,10^-5,10},PlotStyle->{Blue, Thick}, ImageSize-> Full, PlotLabel->" Delta Function potential "Superscript["ω","2"]Superscript["n","u,L"], PlotRange->All]

uLuLParticleproductionDelta=LogLinearPlot[omega^2*nuLDelta2^2,{omega,10^-5,2},PlotStyle->{Blue, Thick}, ImageSize-> Full, PlotLabel->" Delta Function potential "Superscript["ω","2"]Superscript["n","u,L 2"],  PlotRange->All]

uLuLParticleproductionDelta=LogLinearPlot[omega^2*nuLDelta3^2,{omega,10^-7,1},PlotStyle->{Blue, Thick}, ImageSize-> Full, PlotLabel->" Delta Function potential "Superscript["ω","2"]Superscript["n","u,L"], PlotRange->All]

uLuLParticleproductionDelta=LogLinearPlot[omega^2*nuLDelta4^2,{omega,10^-7,1},PlotStyle->{Blue, Thick}, ImageSize-> Full, PlotLabel->" Delta Function potential "Superscript["ω","2"]Superscript["n","u,L"], PlotRange->All]

uLuLParticleproductionDelta=LogLinearPlot[omega^2*nuLDelta5^2,{omega,10^-9,1},PlotStyle->{Blue, Thick}, ImageSize-> Full, PlotLabel->" Delta Function potential "Superscript["ω","2"]Superscript["n","u,L"], PlotRange->All]

uLuLParticleproductionDelta2=Plot[omega^2*nuLDelta,{omega,10^-5,1},PlotStyle->{Blue, Thick}, ImageSize-> Full, PlotLabel->" Delta Function potential "Superscript["ω","2"]Superscript["n","u,L"], PlotRange->All]

uLuLParticleproductionDelta322line=LogLinearPlot[{ (omega*nuLDelta)^2},{omega,10^-5,1},PlotStyle->{Blue, Thick}, ImageSize-> Full, PlotLabel->" Delta Function potential "Superscript["ω",""]Superscript["n","u,L"], PlotRange->{5365, 5366}]

Export["D:\\Dropbox\\BH\\BEC\\nofxcofxvofx\\Writeup\\MassiveandDelta\\New\\uRuRDelta.pdf",uLuLParticleproductionDelta322line]

10^1.2

uLuLParticleproductionDeltaCompare123=LogLinearPlot[{(omega*nuLDelta)^2,(omega*nuLDelta2)^2,(omega*nuLDelta3)^2},{omega,2*10^-6,9/200},PlotStyle->{{Blue, Thick},{Green, Thick},{Orange, Thick} }, ImageSize-> Full, PlotLabel->Superscript["ω","2"]HoldForm[ Superscript["("Superscript["n","u, L "]")","2"]], PlotRange->All, PlotLegends->{"VR/10=-VL/100=κ","VR=-VL/100=κ","3*VR/2=-VL/100=κ"}, AxesLabel->{ω}]

Export["D:\\Dropbox\\BH\\BEC\\nofxcofxvofx\\Writeup\\MassiveandDelta\\New\\uLuLParticleproductionDeltaCompare123.pdf",uLuLParticleproductionDeltaCompare123]

uLuLParticleproductionDeltaCompare123ZeroPotential=LogLogPlot[{(nuLDelta/nuLDeltaZeroPotential),(nuLDelta2/nuLDeltaZeroPotential),(nuLDelta3/nuLDeltaZeroPotential)},{omega,2*10^-6,9/200},PlotStyle->{{Blue, Thick},{Green, Thick},{Orange, Thick} }, ImageSize-> Full, PlotLabel->"Veff/Veff=0 for "HoldForm[ Superscript["("Superscript["n","u, L "]")",""]], PlotRange->All, PlotLegends->{"VR/10=-VL/100=κ","VR=-VL/100=κ","3*VR/2=-VL/100=κ"}, AxesLabel->{ω}]

Export["D:\\Dropbox\\BH\\BEC\\nofxcofxvofx\\Writeup\\MassiveandDelta\\New\\uLuLParticleproductionDeltaCompare123ZeroPotential.pdf",uLuLParticleproductionDeltaCompare123ZeroPotential]

nuLDeltaSymmetric=1/(4*omega^2)*Abs[Exp[Pi*omega/kappa](VR*(-VR))/(2*I*omega+VR)+(2*I*omega-(-VR))]^2*1/(Exp[2*Pi*omega/kappa]-1)+(-VR)^2/(4*omega^2+VR^2);
nvLDeltaSymmetric=1/(4*omega^2)*Abs[VR(2*I*omega-(-VR))/(2*I*omega-VR)-(-VR)*Exp[Pi*omega/kappa]]^2*1/(Exp[2*Pi*omega/kappa]-1);

uLuLParticleproductionDeltaCompare123ZeroPotential=LogLogPlot[(nuLDeltaSymmetric/nuLDeltaZeroPotential),{omega,2*10^-6,9/200},PlotStyle->{{Blue, Thick},{Green, Thick},{Orange, Thick} }, ImageSize-> Full, PlotLabel->{"Veff/Veff=0"}, PlotRange->All, PlotLegends->{"VR/10=-VL/100=κ","VR=-VL/100=κ","3*VR/2=-VL/100=κ"}, AxesLabel->{ω}]

Export["D:\\Dropbox\\BH\\BEC\\nofxcofxvofx\\Writeup\\MassiveandDelta\\New\\uLuLParticleproductionDeltaCompare123ZeroPotential.pdf",uLuLParticleproductionDeltaCompare123ZeroPotential]

vLvLParticleproductionDeltaCompare123=LogLinearPlot[{(omega*nvLDelta)^2},{omega,10^-5,1},PlotStyle->{{Blue, Thick},{Green, Thick},{Orange, Thick} }, ImageSize-> Full, PlotLabel->Superscript["ω","2"]HoldForm[ Superscript["("Superscript["n","v, L "]")","2"]], PlotRange->All, PlotLegends->{"VR/10=-VL/100=κ","VR=-VL/100=κ","3*VR/2=-VL/100=κ"}, AxesLabel->{ω}]

uLuLParticleproductionDeltaCompare123v2=LogLinearPlot[{(omega*nuLDelta)^2,(omega*nuLDelta2)^2,(omega*nuLDelta3)^2},{omega,10^-5,1},PlotStyle->{{Blue, Thick},{Green, Thick},{Orange, Thick} }, ImageSize-> Full, PlotLabel->Superscript["ω","2"]HoldForm[ Superscript["("Superscript["n","u, L "]")","2"]], PlotRange->All, PlotLegends->{"VR/10=-VL/100=κ","VR=-VL/100=κ","3*VR/2=-VL/100=κ"}, AxesLabel->{ω}]

VR222=10^-3*kappa;
VL222=-VR*1000000;
VR333=10^-2*kappa;
VL333=-VR*10000;

nuLDelta222=1/(4*omega^2)*Abs[Exp[Pi*omega/kappa](VR222*VL222)/(2*I*omega+VR222)+(2*I*omega-VL222)]^2*1/(Exp[2*Pi*omega/kappa]-1)+VL222^2/(4*omega^2+VR222^2);
nvLDelta222=1/(4*omega^2)*Abs[VR222(2*I*omega-VL222)/(2*I*omega-VR222)-VL222*Exp[Pi*omega/kappa]]^2*1/(Exp[2*Pi*omega/kappa]-1);
nuLDelta333=1/(4*omega^2)*Abs[Exp[Pi*omega/kappa](VR333*VL333)/(2*I*omega+VR333)+(2*I*omega-VL333)]^2*1/(Exp[2*Pi*omega/kappa]-1)+VL333^2/(4*omega^2+VR333^2);
nvLDelta333=1/(4*omega^2)*Abs[VR333(2*I*omega-VL333)/(2*I*omega-VR333)-VL333*Exp[Pi*omega/kappa]]^2*1/(Exp[2*Pi*omega/kappa]-1);

uLuLParticleproductionDeltaCompare123=LogLinearPlot[{(omega*nuLDelta)^2,(omega*nuLDelta222)^2,(omega*nuLDelta3)^2},{omega,10^-8,1},PlotStyle->{{Blue, Thick},{Green, Thick},{Orange, Thick} }, ImageSize-> Full, PlotLabel->Superscript["ω","2"]HoldForm[ Superscript["("Superscript["n","u, L "]")","2"]], PlotRange->All, PlotLegends->{"VR/10=-VL/100=κ","VR=-VL/100=κ","3*VR/2=-VL/100=κ"}, AxesLabel->{ω}]

uLuLParticleproductionDeltaCompare145=LogLinearPlot[{(omega*nuLDelta)^2,(omega*nuLDelta4)^2,(omega*nuLDelta5)^2},{omega,10^-7,1}, ImageSize-> Full, PlotLabel->" Delta Function potential "Superscript["ω",""]Superscript["n","u,L"], PlotRange->All, PlotLegends->{"(omega*nuLDelta)^2","(omega*nuLDelta4)^2","(omega*nuLDelta5)^2"}]

uLuLParticleproductionDelta4=Plot[omega*nuLDelta,{omega,10^-5,1},PlotStyle->{Blue, Thick}, ImageSize-> Full, PlotLabel->" Delta Function potential "Superscript["ω",""]Superscript["n","u,L"], PlotRange->All]

Export["D:\\Dropbox\\BH\\BEC\\nofxcofxvofx\\Writeup\\MassiveandDelta\\New\\uLuLMassive.pdf",uLuLParticleproductionMassive]
Export["D:\\Dropbox\\BH\\BEC\\nofxcofxvofx\\Writeup\\MassiveandDelta\\New\\uLuLDelta.pdf",uLuLParticleproductionDelta3]

uLuLParticleproductionDelta2=LogLinearPlot[omega*nuLDelta/nuLmassive,{omega,10^-5,1/100},PlotStyle->{Green, Thick}, ImageSize-> Full, PlotLabel->" ω Delta Function potential/massive for "Superscript["n","u,L"], PlotRange->All]

vLvLParticleproductionMassive=LogLinearPlot[nvLmassive,{omega,10^-5,1},PlotStyle->{Orange, Thick}, ImageSize-> Full, PlotLabel->" Massive "Superscript["n","v,L"], PlotRange->All]

vLvLParticleproductionDelta=LogLinearPlot[omega^2*nvLDelta^2,{omega,10^-5,1},PlotStyle->{Blue, Thick}, ImageSize-> Full, PlotLabel->" Delta Function potential "Superscript["ω","2"]Superscript["n","v,L"], PlotRange->All]

vLvLParticleproductionDelta2=LogLinearPlot[omega^2*nvLDelta^2,{omega,10^-5,1},PlotStyle->{Blue, Thick}, ImageSize-> Full, PlotLabel->" Delta Function potential "Superscript["ω",""]Superscript["n","v,L"], PlotRange->All]

Export["D:\\Dropbox\\BH\\BEC\\nofxcofxvofx\\Writeup\\MassiveandDelta\\New\\vLvLMassive.pdf",vLvLParticleproductionMassive]
Export["D:\\Dropbox\\BH\\BEC\\nofxcofxvofx\\Writeup\\MassiveandDelta\\New\\vLvLDelta.pdf",vLvLParticleproductionDelta2]

nuLDelta2vRLarge=1/(4*omega^2)*Abs[Exp[Pi*omega/kappa]((VR*10^(1))*(VL*10^(-1)))/(2*I*omega+(VR*10^(1)))+(2*I*omega-(VL*10^(-1)))]^2*1/(Exp[2*Pi*omega/kappa]-1)+(VL*10^(-1))^2/(4*omega^2+(VR*10^(1))^2);

vLvLParticleproductionnuLDelta2vRLarge=LogLinearPlot[omega^2*nuLDelta2vRLarge^2,{omega,10^-5,10^-3},PlotStyle->{Blue, Thick}, ImageSize-> Full, PlotLabel->" Delta Function potential "Superscript["ω",""]Superscript["n","v,L"], PlotRange->{0.5364,0.5366}]

nuRuL=Abs[T]^2*Abs[(Exp[Pi*omega/kappa]*alpha+Conjugate[RH*beta])/(Exp[2*Pi*omega/kappa]-1)]^2;

nuRuLMassive=nuRuL/.{T->HeavisideTheta[omega-mR]*2*Sqrt[kR*omega]/(omega+kR), alpha->Sqrt[kL/omega]*(kL+omega)/(2*kL), RH*beta->Sqrt[kL/omega]*(omega-kR)/(omega+kR)*(kL-omega)/(2*kL)};

nuRuLDelta=nuRuL/.{T->(2*I*omega)/(2*I*omega-VR), alpha->(2*I*omega-VL)/(2*I*omega), RH*beta->(VL)/(2*I*omega)*(VR)/(2*I*omega-VR)};

uRuLParticleproductionMassive=LogLinearPlot[nuRuLMassive,{omega,2*10^-2,1/10},PlotStyle->{Orange, Thick},PlotRange->All, ImageSize-> Full, PlotLabel->" Massive correlator for "HoldForm[Superscript[Superscript["|<a","u,R"]Superscript[a, "u,L"]">|",2] ]]

uRuLParticleproductionDelta=LogLinearPlot[nuRuLDelta,{omega,10^-5,1/10},PlotStyle->{Blue, Thick},PlotRange->All, ImageSize-> Full, PlotLabel->" Delta function correlator for "HoldForm[Superscript[Superscript["|<a","u,R"]Superscript[a, "u,L"]">|",2] ]]

Export["D:\\Dropbox\\BH\\BEC\\nofxcofxvofx\\Writeup\\MassiveandDelta\\New\\uLuRMassive.pdf",uRuLParticleproductionMassive]
Export["D:\\Dropbox\\BH\\BEC\\nofxcofxvofx\\Writeup\\MassiveandDelta\\New\\uLuRDelta.pdf",uRuLParticleproductionDelta]

LogLinearPlot[{omega*nuLDelta, omega*nvLDelta},{omega,10^-5,10},PlotStyle->{Blue, Thick},PlotRange->All, ImageSize-> Full]

RatioMassive=Simplify[nuLmassive/ (nvLmassive)-1];

Ratio1=Simplify[nuLDelta/ (nvLDelta)]-1;

nuLvsnvLMassive=LogLinearPlot[RatioMassive,{omega,1/100,1/5},PlotStyle->{Red, Thick},PlotRange->All, ImageSize-> Full, WorkingPrecision->30, PlotPoints->1000,PlotLabel->" Massive "HoldForm[Superscript["n","u,L"]"/" Superscript["n","v,L"]"-1"]]

nuLvsnvLDelta=LogLinearPlot[Ratio1,{omega,10^-5,10},PlotStyle->{Green, Thick},PlotRange->All, ImageSize-> Full, WorkingPrecision->30, PlotPoints->1000,PlotLabel->" Delta Function potential "HoldForm[Superscript["n","u,L"]"/" Superscript["n","v,L"]"-1"]]

Export["D:\\Dropbox\\BH\\BEC\\nofxcofxvofx\\Writeup\\MassiveandDelta\\New\\nuLvsnvLMassive.pdf",nuLvsnvLMassive]
Export["D:\\Dropbox\\BH\\BEC\\nofxcofxvofx\\Writeup\\MassiveandDelta\\New\\nLvsnvLDelta.pdf",nuLvsnvLDelta]

VR2=1;
VL2=-10*VR;
nuRDelta2=4*omega^2/(4*omega^2+VR2^2)*1/(Exp[2*Pi*omega/kappa]-1);
nuLDelta22=1/(4*omega^2)*Abs[Exp[Pi*omega/kappa](VR2*VL2)/(2*I*omega+VR2)+(2*I*omega-VL2)]^2*1/(Exp[2*Pi*omega/kappa]-1)+VL2^2/(4*omega^2+VR2^2);
nvLDelta2=1/(4*omega^2)*Abs[VR2(2*I*omega-VL2)/(2*I*omega-VR2)-VL2*Exp[Pi*omega/kappa]]^2*1/(Exp[2*Pi*omega/kappa]-1);

VR2=1;
VL3=-100*VR;
nuRDelta33=4*omega^2/(4*omega^2+VR2^2)*1/(Exp[2*Pi*omega/kappa]-1);
nuLDelta33=1/(4*omega^2)*Abs[Exp[Pi*omega/kappa](VR2*VL3)/(2*I*omega+VR2)+(2*I*omega-VL3)]^2*1/(Exp[2*Pi*omega/kappa]-1)+VL3^2/(4*omega^2+VR2^2);
nvLDelta3=1/(4*omega^2)*Abs[VR2(2*I*omega-VL3)/(2*I*omega-VR2)-VL3*Exp[Pi*omega/kappa]]^2*1/(Exp[2*Pi*omega/kappa]-1);

vLvLParticleproductionDelta22=LogLinearPlot[{omega*nvLDelta,omega*nvLDelta22},{omega,10^-5,1}, ImageSize-> Full, PlotLabel->" Delta Function potential "Superscript["ω",""]Superscript["n","v,L"], PlotRange->All]

vLvLParticleproductionDeltaCompare123=LogLinearPlot[(omega*nvLDelta3)^2,{omega,2*10^-6,9/200},PlotStyle->{{Blue, Thick},{Green, Thick},{Orange, Thick} }, ImageSize-> Full, PlotLabel->Superscript["ω","2"]HoldForm[ Superscript["("Superscript["n","v, L "]")","2"]], PlotRange->{53148200, 53148400}, PlotLegends->{"VR/10=-VL/100=κ","VR=-VL/100=κ","3*VR/2=-VL/100=κ"}, AxesLabel->{ω}]

vLvLParticleproductionDeltaCompare123=LogLinearPlot[(omega*nvLDelta)^2,{omega,2*10^-6,9/200},PlotStyle->{{Blue, Thick},{Green, Thick},{Orange, Thick} }, ImageSize-> Full, PlotLabel->Superscript["ω","2"]HoldForm[ Superscript["("Superscript["n","v, L "]")","2"]], PlotRange->{5000, 6000}, PlotLegends->{"VR/10=-VL/100=κ"}, AxesLabel->{ω}]

uLuLParticleproductionDelta32=LogLinearPlot[omega*nuLDelta22,{omega,10^-5,1},PlotStyle->{Blue, Thick}, ImageSize-> Full, PlotLabel->" Delta Function potential "Superscript["ω",""]Superscript["n","u,L"], PlotRange->All]

VR=1;
VL=-10;
kappa=1/2;

nuL2Delta=1/(4*omega^2)*Abs[Exp[Pi*omega/kappa](VR*VL)/(2*I*omega+VR)+(2*I*omega-VL)]^2*1/(Exp[2*Pi*omega/kappa]-1)+VL^2/(4*omega^2+VR^2);
nvL2Delta=1/(4*omega^2)*Abs[VR(2*I*omega-VL)/(2*I*omega-VR)-VL*Exp[Pi*omega/kappa]]^2*1/(Exp[2*Pi*omega/kappa]-1);

nuLuRnopotentialsquared=(omega^2)*(Exp[Pi*omega/kappa]/(Exp[2*Pi*omega/kappa]-1))^2;
nuLuRDeltasquared=(omega^2)*Abs[1/(1-VR/(2*I*omega))]*Abs[(Exp[Pi*omega/kappa]*(1-VL/(2*I*omega))+Conjugate[(VR/(2*I*omega))/(1-VR/(2*I*omega))*VL/(2*I*omega)])/(Exp[2*Pi*omega/kappa]-1)]^2;

LogLogPlot[{nuLuRDeltasquared,nuLuRnopotentialsquared},{omega, 10^-6, 2},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}]

LogLogPlot[{nuLuRDeltasquared/nuLuRnopotentialsquared},{omega, 10^-5, 100},PlotLabel->" V_Eff/(V_Eff=0) for "Superscript["|<a_u^Ra_u^L>|","2"],PlotRange->All,ImageSize->Full,AxesLabel->{ω}]

nuLuRDeltasquared=(omega^2)*Abs[1/(1-VR/(2*I*omega))]*Abs[(Exp[Pi*omega/kappa]*(1-VL/(2*I*omega))+Conjugate[(VR/(2*I*omega))/(1-VR/(2*I*omega))*VL/(2*I*omega)])/(Exp[2*Pi*omega/kappa]-1)]^2

alphaT2=(2*I*omega-VL)/(2*I*omega);
Tv2=(2*I*omega)/(2*I*omega-VR);
RH2=VR/(2*I*omega-VR);
beta2=VL/(2*I*omega);

nuLuRDeltasquaredv2=omega^2(Abs[Tv2]^2)*(Abs[(Exp[Pi*omega/kappa]*alphaT2+Conjugate[RH2*beta2])/(Exp[(2*Pi*omega)/kappa]-1)]^2)

LogLogPlot[{nuLuRDeltasquaredv2,nuLuRnopotentialsquared},{omega, 10^-6, 2},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}]

LogLogPlot[{nuLuRDeltasquaredv2/nuLuRnopotentialsquared},{omega, 10^-5, 100},PlotLabel->" V_Eff/(V_Eff=0) for "Superscript["|<a_u^Ra_u^L>|","2"],PlotRange->All,ImageSize->Full,AxesLabel->{ω}]