L=200;Ω=1;σ=5;λ=0.1;t[τ_]:=1/aSinh[aτ]x[τ_]:=1/a(Cosh[aτ]-1)(*Ensuremisnumerictoavoidsymbolicevaluations*)η0[a_]:=λNSum[NIntegrate[Exp[-τ^2/(2σ^2)]Exp[IΩτ+(2IPi)/L(Abs[m]t[τ]-mx[τ])]1/Sqrt[4PiAbs[m]],{τ,-100,100}],{m,1,100}]η1[a_]:=λNSum[NIntegrate[Exp[-τ^2/(2σ^2)]Exp[IΩτ-(2IPi)/L(Abs[m]t[τ]-mx[τ])]1/Sqrt[4PiAbs[m]],{τ,-100,100}],{m,1,100}]F[a_]:=-(η0[a]^2/(1+η0[a]^2))+1/(1+η1[a]^2)η0[0.21]
0.1NSumNIntegrate,{τ,-100,100},{m,1,100}
Exp-ExpΩτ+
2
τ
2
2
σ
(2π)(Abs[m]t[τ]-mx[τ])
L
4πAbs[m]