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MikeY
MikeY
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    A[\[Phi]_A[ϕ_, \[CapitalOmega]_Ω_, \[Gamma]_]γ_] = \[Sqrt]√(1 - 
    2 \[CapitalOmega]Ω Cos[\[Phi]]Cos[ϕ] + \[CapitalOmega]^2Ω^2 - \
\[Gamma]^2γ^2);(*= \[Sqrt]√(|1-\[CapitalOmega]Ω Exp[I \
\[Phi]]ϕ](|^2)-\[Gamma]^2γ^2)=\[Sqrt]=√(J^2-\[Gamma]^2γ^2). If J>\[Gamma]J>γ \
system is PT symmetric, otherwise its not.*)
alpha[\[Phi]_alpha[ϕ_, \[CapitalOmega]_Ω_, \[Gamma]_γ_, t_] = 
 Cos[A[\[Phi]Cos[A[ϕ, \[CapitalOmega]Ω, \[Gamma]]*γ]* t] - \[Gamma]γ/
   A[\[Phi]A[ϕ, \[CapitalOmega]Ω, \[Gamma]]γ] Sin[
    A[\[Phi]A[ϕ, \[CapitalOmega]Ω, \[Gamma]]γ] *t]; 
beta[\[Phi]_beta[ϕ_, \[CapitalOmega]_Ω_, \[Gamma]_γ_, t_] = -I (
   1 - \[CapitalOmega]*Ω* Exp[-I \[Phi]]ϕ])/
   A[\[Phi]A[ϕ, \[CapitalOmega]Ω, \[Gamma]]γ] Sin[
    A[\[Phi]A[ϕ, \[CapitalOmega]Ω, \[Gamma]]*γ]* t];

rho[\[Phi]_rho[ϕ_, \[CapitalOmega]_Ω_, \[Gamma]_γ_, 
   t_] = (1/(
    Abs[alpha[\[Phi]Abs[alpha[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2 + 
     Abs[beta[\[Phi]Abs[beta[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2) ) {{Abs[
      alpha[\[Phi]alpha[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2, 
     alpha[\[Phi]alpha[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]*
      Conjugate[
       beta[\[Phi]beta[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, 
        t]]}, {beta[\[Phi]beta[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]*
      Conjugate[alpha[\[Phi]Conjugate[alpha[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]], 
     Abs[beta[\[Phi]Abs[beta[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2}};
p[\[Phi]_p[ϕ_, \[CapitalOmega]_Ω_, \[Gamma]_γ_, t_] = 
  rho[\[Phi]rho[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t][[2]][[2]];
x[\[Phi]_x[ϕ_, \[CapitalOmega]_Ω_, \[Gamma]_γ_, t_] = 
  rho[\[Phi]rho[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t][[1]][[2]];

myfun[\[Phi]_myfun[ϕ_, \[CapitalOmega]_Ω_, \[Gamma]_γ_, 
   t_] = -(((-1 + 
          p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, 
           t]) ((-1 + 
             p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, 
              t]) p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t] + 
          Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2) Log[((-1 + 
            p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, 
             t]) ((-1 + 
               p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, 
                t]) p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t] + 
            Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2))/(
         2 ((-1 + p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t])^2 + 
            2 Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, 
               t]]^2))])/(((-1 + 
            p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t])^2 + 
          2 Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2) Log[
         2])) - 1/
    Log[2] (-1 + 
      Sqrt[(-1 + p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t])^2 + 
       2 Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2]) Log[
     1/2 (1 - 
        Sqrt[(-1 + p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t])^2 + 
         2 Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2])] + 
   1/Log[2] (1 + 
      Sqrt[(-1 + p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t])^2 + 
       2 Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2]) Log[
     1/2 (1 + 
        Sqrt[(-1 + p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t])^2 + 
         2 Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2])] - ((1 - 
        5 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t] + 
        10 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]^2 - 
        10 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]^3 + 
        5 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]^4 - 
        p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]^5 + 
        5 Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2 - 
        13 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t] Abs[
          x[\[Phi]x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2 + 
        11 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]^2 Abs[
          x[\[Phi]x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2 - 
        3 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]^3 Abs[
          x[\[Phi]x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2 + 
        6 Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^4 - 
        2 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t] Abs[
          x[\[Phi]x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^4 + 
        Sqrt[((-1 + p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t])^2 + 
          2 Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2)^5]) Log[
       1/(2 ((-1 + p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t])^2 + 
           2 Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2)^2) (1 - 
          5 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t] + 
          10 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]^2 - 
          10 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]^3 + 
          5 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]^4 - 
          p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]^5 + 
          5 Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2 - 
          13 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t] Abs[
            x[\[Phi]x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2 + 
          11 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]^2 Abs[
            x[\[Phi]x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2 - 
          3 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]^3 Abs[
            x[\[Phi]x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2 + 
          6 Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^4 - 
          2 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t] Abs[
            x[\[Phi]x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^4 + 
          Sqrt[((-1 + p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t])^2 + 
            2 Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, 
               t]]^2)^5])])/(2 ((-1 + 
          p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t])^2 + 
        2 Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2)^2 Log[
       2]) + ((-1 + 5 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t] - 
        10 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]^2 + 
        10 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]^3 - 
        5 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]^4 + 
        p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]^5 - 
        5 Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2 + 
        13 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t] Abs[
          x[\[Phi]x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2 - 
        11 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]^2 Abs[
          x[\[Phi]x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2 + 
        3 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]^3 Abs[
          x[\[Phi]x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2 - 
        6 Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^4 + 
        2 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t] Abs[
          x[\[Phi]x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^4 + 
        Sqrt[((-1 + p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t])^2 + 
          2 Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2)^5]) Log[-(
         1/(2 ((-1 + p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t])^2 + 
            2 Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, 
               t]]^2)^2)) (-1 + 
          5 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t] - 
          10 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]^2 + 
          10 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]^3 - 
          5 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]^4 + 
          p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]^5 - 
          5 Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2 + 
          13 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t] Abs[
            x[\[Phi]x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2 - 
          11 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]^2 Abs[
            x[\[Phi]x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2 + 
          3 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]^3 Abs[
            x[\[Phi]x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2 - 
          6 Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^4 + 
          2 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t] Abs[
            x[\[Phi]x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^4 + 
          Sqrt[((-1 + p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t])^2 + 
            2 Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, 
               t]]^2)^5])])/(2 ((-1 + 
          p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t])^2 + 
        2 Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2)^2 Log[2]) + 
   1/Log[4] (-4 ArcTanh[
        Sqrt[(-1 + p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t])^2 + 
         2 Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2]] Sqrt[(-1 +
           p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t])^2 + 
        2 Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2] + 
      2 ArcTanh[
        Sqrt[(1 - 2 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t])^2 + 
         4 Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2]] Sqrt[(1 - 
          2 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t])^2 + 
        4 Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2] + Log[4] - 
      2 Log[1 - 
         Sqrt[(-1 + p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t])^2 + 
          2 Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2]] - 
      2 Log[1 + 
         Sqrt[(-1 + p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t])^2 + 
          2 Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2]] + 
      Log[1 - Sqrt[(1 - 
           2 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t])^2 + 
         4 Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2]] + 
      Log[1 + Sqrt[(1 - 
           2 p[\[Phi]p[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t])^2 + 
         4 Abs[x[\[Phi]Abs[x[ϕ, \[CapitalOmega]Ω, \[Gamma]γ, t]]^2]]) ;

Plot[{Re[myfun[0, 0.4, 0.5, t]]}, {t, 0, 10}, 
 PlotRange -> All, PlotStyle -> {Blue, Thick}, AxesOrigin -> {0, 0}]

    A[\[Phi]_, \[CapitalOmega]_, \[Gamma]_] = \[Sqrt](1 - 
    2 \[CapitalOmega] Cos[\[Phi]] + \[CapitalOmega]^2 - \
\[Gamma]^2);(*= \[Sqrt](|1-\[CapitalOmega] Exp[I \
\[Phi]](|^2)-\[Gamma]^2)=\[Sqrt](J^2-\[Gamma]^2). If J>\[Gamma] \
system is PT symmetric, otherwise its not.*)
alpha[\[Phi]_, \[CapitalOmega]_, \[Gamma]_, t_] = 
 Cos[A[\[Phi], \[CapitalOmega], \[Gamma]]* t] - \[Gamma]/
   A[\[Phi], \[CapitalOmega], \[Gamma]] Sin[
    A[\[Phi], \[CapitalOmega], \[Gamma]] *t]; 
beta[\[Phi]_, \[CapitalOmega]_, \[Gamma]_, t_] = -I (
   1 - \[CapitalOmega]* Exp[-I \[Phi]])/
   A[\[Phi], \[CapitalOmega], \[Gamma]] Sin[
    A[\[Phi], \[CapitalOmega], \[Gamma]]* t];

rho[\[Phi]_, \[CapitalOmega]_, \[Gamma]_, 
   t_] = (1/(
    Abs[alpha[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
     Abs[beta[\[Phi], \[CapitalOmega], \[Gamma], t]]^2) ) {{Abs[
      alpha[\[Phi], \[CapitalOmega], \[Gamma], t]]^2, 
     alpha[\[Phi], \[CapitalOmega], \[Gamma], t]*
      Conjugate[
       beta[\[Phi], \[CapitalOmega], \[Gamma], 
        t]]}, {beta[\[Phi], \[CapitalOmega], \[Gamma], t]*
      Conjugate[alpha[\[Phi], \[CapitalOmega], \[Gamma], t]], 
     Abs[beta[\[Phi], \[CapitalOmega], \[Gamma], t]]^2}};
p[\[Phi]_, \[CapitalOmega]_, \[Gamma]_, t_] = 
  rho[\[Phi], \[CapitalOmega], \[Gamma], t][[2]][[2]];
x[\[Phi]_, \[CapitalOmega]_, \[Gamma]_, t_] = 
  rho[\[Phi], \[CapitalOmega], \[Gamma], t][[1]][[2]];

myfun[\[Phi]_, \[CapitalOmega]_, \[Gamma]_, 
   t_] = -(((-1 + 
          p[\[Phi], \[CapitalOmega], \[Gamma], 
           t]) ((-1 + 
             p[\[Phi], \[CapitalOmega], \[Gamma], 
              t]) p[\[Phi], \[CapitalOmega], \[Gamma], t] + 
          Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2) Log[((-1 + 
            p[\[Phi], \[CapitalOmega], \[Gamma], 
             t]) ((-1 + 
               p[\[Phi], \[CapitalOmega], \[Gamma], 
                t]) p[\[Phi], \[CapitalOmega], \[Gamma], t] + 
            Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2))/(
         2 ((-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
            2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], 
               t]]^2))])/(((-1 + 
            p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
          2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2) Log[
         2])) - 1/
    Log[2] (-1 + 
      Sqrt[(-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
       2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]) Log[
     1/2 (1 - 
        Sqrt[(-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
         2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2])] + 
   1/Log[2] (1 + 
      Sqrt[(-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
       2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]) Log[
     1/2 (1 + 
        Sqrt[(-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
         2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2])] - ((1 - 
        5 p[\[Phi], \[CapitalOmega], \[Gamma], t] + 
        10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 - 
        10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 + 
        5 p[\[Phi], \[CapitalOmega], \[Gamma], t]^4 - 
        p[\[Phi], \[CapitalOmega], \[Gamma], t]^5 + 
        5 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
        13 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
        11 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
        3 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
        6 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 - 
        2 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 + 
        Sqrt[((-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
          2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2)^5]) Log[
       1/(2 ((-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
           2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2)^2) (1 - 
          5 p[\[Phi], \[CapitalOmega], \[Gamma], t] + 
          10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 - 
          10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 + 
          5 p[\[Phi], \[CapitalOmega], \[Gamma], t]^4 - 
          p[\[Phi], \[CapitalOmega], \[Gamma], t]^5 + 
          5 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
          13 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
          11 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
          3 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
          6 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 - 
          2 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 + 
          Sqrt[((-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
            2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], 
               t]]^2)^5])])/(2 ((-1 + 
          p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
        2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2)^2 Log[
       2]) + ((-1 + 5 p[\[Phi], \[CapitalOmega], \[Gamma], t] - 
        10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 + 
        10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 - 
        5 p[\[Phi], \[CapitalOmega], \[Gamma], t]^4 + 
        p[\[Phi], \[CapitalOmega], \[Gamma], t]^5 - 
        5 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
        13 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
        11 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
        3 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
        6 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 + 
        2 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 + 
        Sqrt[((-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
          2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2)^5]) Log[-(
         1/(2 ((-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
            2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], 
               t]]^2)^2)) (-1 + 
          5 p[\[Phi], \[CapitalOmega], \[Gamma], t] - 
          10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 + 
          10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 - 
          5 p[\[Phi], \[CapitalOmega], \[Gamma], t]^4 + 
          p[\[Phi], \[CapitalOmega], \[Gamma], t]^5 - 
          5 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
          13 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
          11 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
          3 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
          6 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 + 
          2 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 + 
          Sqrt[((-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
            2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], 
               t]]^2)^5])])/(2 ((-1 + 
          p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
        2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2)^2 Log[2]) + 
   1/Log[4] (-4 ArcTanh[
        Sqrt[(-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
         2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]] Sqrt[(-1 +
           p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
        2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2] + 
      2 ArcTanh[
        Sqrt[(1 - 2 p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
         4 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]] Sqrt[(1 - 
          2 p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
        4 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2] + Log[4] - 
      2 Log[1 - 
         Sqrt[(-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
          2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]] - 
      2 Log[1 + 
         Sqrt[(-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
          2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]] + 
      Log[1 - Sqrt[(1 - 
           2 p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
         4 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]] + 
      Log[1 + Sqrt[(1 - 
           2 p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
         4 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]]) ;

Plot[{Re[myfun[0, 0.4, 0.5, t]]}, {t, 0, 10}, 
 PlotRange -> All, PlotStyle -> {Blue, Thick}, AxesOrigin -> {0, 0}]

    A[ϕ_, Ω_, γ_] = √(1 - 
    2 Ω Cos[ϕ] + Ω^2 - \
γ^2);(*= √(|1-Ω Exp[I \
ϕ](|^2)-γ^2)=√(J^2-γ^2). If J>γ \
system is PT symmetric, otherwise its not.*)
alpha[ϕ_, Ω_, γ_, t_] = 
 Cos[A[ϕ, Ω, γ]* t] - γ/
   A[ϕ, Ω, γ] Sin[
    A[ϕ, Ω, γ] *t]; 
beta[ϕ_, Ω_, γ_, t_] = -I (
   1 - Ω* Exp[-I ϕ])/
   A[ϕ, Ω, γ] Sin[
    A[ϕ, Ω, γ]* t];

rho[ϕ_, Ω_, γ_, 
   t_] = (1/(
    Abs[alpha[ϕ, Ω, γ, t]]^2 + 
     Abs[beta[ϕ, Ω, γ, t]]^2) ) {{Abs[
      alpha[ϕ, Ω, γ, t]]^2, 
     alpha[ϕ, Ω, γ, t]*
      Conjugate[
       beta[ϕ, Ω, γ, 
        t]]}, {beta[ϕ, Ω, γ, t]*
      Conjugate[alpha[ϕ, Ω, γ, t]], 
     Abs[beta[ϕ, Ω, γ, t]]^2}};
p[ϕ_, Ω_, γ_, t_] = 
  rho[ϕ, Ω, γ, t][[2]][[2]];
x[ϕ_, Ω_, γ_, t_] = 
  rho[ϕ, Ω, γ, t][[1]][[2]];

myfun[ϕ_, Ω_, γ_, 
   t_] = -(((-1 + 
          p[ϕ, Ω, γ, 
           t]) ((-1 + 
             p[ϕ, Ω, γ, 
              t]) p[ϕ, Ω, γ, t] + 
          Abs[x[ϕ, Ω, γ, t]]^2) Log[((-1 + 
            p[ϕ, Ω, γ, 
             t]) ((-1 + 
               p[ϕ, Ω, γ, 
                t]) p[ϕ, Ω, γ, t] + 
            Abs[x[ϕ, Ω, γ, t]]^2))/(
         2 ((-1 + p[ϕ, Ω, γ, t])^2 + 
            2 Abs[x[ϕ, Ω, γ, 
               t]]^2))])/(((-1 + 
            p[ϕ, Ω, γ, t])^2 + 
          2 Abs[x[ϕ, Ω, γ, t]]^2) Log[
         2])) - 1/
    Log[2] (-1 + 
      Sqrt[(-1 + p[ϕ, Ω, γ, t])^2 + 
       2 Abs[x[ϕ, Ω, γ, t]]^2]) Log[
     1/2 (1 - 
        Sqrt[(-1 + p[ϕ, Ω, γ, t])^2 + 
         2 Abs[x[ϕ, Ω, γ, t]]^2])] + 
   1/Log[2] (1 + 
      Sqrt[(-1 + p[ϕ, Ω, γ, t])^2 + 
       2 Abs[x[ϕ, Ω, γ, t]]^2]) Log[
     1/2 (1 + 
        Sqrt[(-1 + p[ϕ, Ω, γ, t])^2 + 
         2 Abs[x[ϕ, Ω, γ, t]]^2])] - ((1 - 
        5 p[ϕ, Ω, γ, t] + 
        10 p[ϕ, Ω, γ, t]^2 - 
        10 p[ϕ, Ω, γ, t]^3 + 
        5 p[ϕ, Ω, γ, t]^4 - 
        p[ϕ, Ω, γ, t]^5 + 
        5 Abs[x[ϕ, Ω, γ, t]]^2 - 
        13 p[ϕ, Ω, γ, t] Abs[
          x[ϕ, Ω, γ, t]]^2 + 
        11 p[ϕ, Ω, γ, t]^2 Abs[
          x[ϕ, Ω, γ, t]]^2 - 
        3 p[ϕ, Ω, γ, t]^3 Abs[
          x[ϕ, Ω, γ, t]]^2 + 
        6 Abs[x[ϕ, Ω, γ, t]]^4 - 
        2 p[ϕ, Ω, γ, t] Abs[
          x[ϕ, Ω, γ, t]]^4 + 
        Sqrt[((-1 + p[ϕ, Ω, γ, t])^2 + 
          2 Abs[x[ϕ, Ω, γ, t]]^2)^5]) Log[
       1/(2 ((-1 + p[ϕ, Ω, γ, t])^2 + 
           2 Abs[x[ϕ, Ω, γ, t]]^2)^2) (1 - 
          5 p[ϕ, Ω, γ, t] + 
          10 p[ϕ, Ω, γ, t]^2 - 
          10 p[ϕ, Ω, γ, t]^3 + 
          5 p[ϕ, Ω, γ, t]^4 - 
          p[ϕ, Ω, γ, t]^5 + 
          5 Abs[x[ϕ, Ω, γ, t]]^2 - 
          13 p[ϕ, Ω, γ, t] Abs[
            x[ϕ, Ω, γ, t]]^2 + 
          11 p[ϕ, Ω, γ, t]^2 Abs[
            x[ϕ, Ω, γ, t]]^2 - 
          3 p[ϕ, Ω, γ, t]^3 Abs[
            x[ϕ, Ω, γ, t]]^2 + 
          6 Abs[x[ϕ, Ω, γ, t]]^4 - 
          2 p[ϕ, Ω, γ, t] Abs[
            x[ϕ, Ω, γ, t]]^4 + 
          Sqrt[((-1 + p[ϕ, Ω, γ, t])^2 + 
            2 Abs[x[ϕ, Ω, γ, 
               t]]^2)^5])])/(2 ((-1 + 
          p[ϕ, Ω, γ, t])^2 + 
        2 Abs[x[ϕ, Ω, γ, t]]^2)^2 Log[
       2]) + ((-1 + 5 p[ϕ, Ω, γ, t] - 
        10 p[ϕ, Ω, γ, t]^2 + 
        10 p[ϕ, Ω, γ, t]^3 - 
        5 p[ϕ, Ω, γ, t]^4 + 
        p[ϕ, Ω, γ, t]^5 - 
        5 Abs[x[ϕ, Ω, γ, t]]^2 + 
        13 p[ϕ, Ω, γ, t] Abs[
          x[ϕ, Ω, γ, t]]^2 - 
        11 p[ϕ, Ω, γ, t]^2 Abs[
          x[ϕ, Ω, γ, t]]^2 + 
        3 p[ϕ, Ω, γ, t]^3 Abs[
          x[ϕ, Ω, γ, t]]^2 - 
        6 Abs[x[ϕ, Ω, γ, t]]^4 + 
        2 p[ϕ, Ω, γ, t] Abs[
          x[ϕ, Ω, γ, t]]^4 + 
        Sqrt[((-1 + p[ϕ, Ω, γ, t])^2 + 
          2 Abs[x[ϕ, Ω, γ, t]]^2)^5]) Log[-(
         1/(2 ((-1 + p[ϕ, Ω, γ, t])^2 + 
            2 Abs[x[ϕ, Ω, γ, 
               t]]^2)^2)) (-1 + 
          5 p[ϕ, Ω, γ, t] - 
          10 p[ϕ, Ω, γ, t]^2 + 
          10 p[ϕ, Ω, γ, t]^3 - 
          5 p[ϕ, Ω, γ, t]^4 + 
          p[ϕ, Ω, γ, t]^5 - 
          5 Abs[x[ϕ, Ω, γ, t]]^2 + 
          13 p[ϕ, Ω, γ, t] Abs[
            x[ϕ, Ω, γ, t]]^2 - 
          11 p[ϕ, Ω, γ, t]^2 Abs[
            x[ϕ, Ω, γ, t]]^2 + 
          3 p[ϕ, Ω, γ, t]^3 Abs[
            x[ϕ, Ω, γ, t]]^2 - 
          6 Abs[x[ϕ, Ω, γ, t]]^4 + 
          2 p[ϕ, Ω, γ, t] Abs[
            x[ϕ, Ω, γ, t]]^4 + 
          Sqrt[((-1 + p[ϕ, Ω, γ, t])^2 + 
            2 Abs[x[ϕ, Ω, γ, 
               t]]^2)^5])])/(2 ((-1 + 
          p[ϕ, Ω, γ, t])^2 + 
        2 Abs[x[ϕ, Ω, γ, t]]^2)^2 Log[2]) + 
   1/Log[4] (-4 ArcTanh[
        Sqrt[(-1 + p[ϕ, Ω, γ, t])^2 + 
         2 Abs[x[ϕ, Ω, γ, t]]^2]] Sqrt[(-1 +
           p[ϕ, Ω, γ, t])^2 + 
        2 Abs[x[ϕ, Ω, γ, t]]^2] + 
      2 ArcTanh[
        Sqrt[(1 - 2 p[ϕ, Ω, γ, t])^2 + 
         4 Abs[x[ϕ, Ω, γ, t]]^2]] Sqrt[(1 - 
          2 p[ϕ, Ω, γ, t])^2 + 
        4 Abs[x[ϕ, Ω, γ, t]]^2] + Log[4] - 
      2 Log[1 - 
         Sqrt[(-1 + p[ϕ, Ω, γ, t])^2 + 
          2 Abs[x[ϕ, Ω, γ, t]]^2]] - 
      2 Log[1 + 
         Sqrt[(-1 + p[ϕ, Ω, γ, t])^2 + 
          2 Abs[x[ϕ, Ω, γ, t]]^2]] + 
      Log[1 - Sqrt[(1 - 
           2 p[ϕ, Ω, γ, t])^2 + 
         4 Abs[x[ϕ, Ω, γ, t]]^2]] + 
      Log[1 + Sqrt[(1 - 
           2 p[ϕ, Ω, γ, t])^2 + 
         4 Abs[x[ϕ, Ω, γ, t]]^2]]) ;

Plot[{Re[myfun[0, 0.4, 0.5, t]]}, {t, 0, 10}, 
 PlotRange -> All, PlotStyle -> {Blue, Thick}, AxesOrigin -> {0, 0}]
deleted 614 characters in body
Source Link
Roman
Roman
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How can one resolve the issue? ---------------------------Un-related text------------------------------ aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

How can one resolve the issue? ---------------------------Un-related text------------------------------ aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

How can one resolve the issue?

deleted 16 characters in body
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H. Kenan
H. Kenan
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    A[\[Phi]_, \[CapitalOmega]_, \[Gamma]_] = \[Sqrt](1 - 
    2 \[CapitalOmega] Cos[\[Phi]] + \[CapitalOmega]^2 - \
\[Gamma]^2);(*= \[Sqrt](|1-\[CapitalOmega] Exp[I \
\[Phi]](|^2)-\[Gamma]^2)=\[Sqrt](J^2-\[Gamma]^2). If J>\[Gamma] \
system is PT symmetric, otherwise its not.*)
alpha[\[Phi]_, \[CapitalOmega]_, \[Gamma]_, t_] = 
 Cos[A[\[Phi], \[CapitalOmega], \[Gamma]]* t] - \[Gamma]/
   A[\[Phi], \[CapitalOmega], \[Gamma]] Sin[
    A[\[Phi], \[CapitalOmega], \[Gamma]] *t]; 
beta[\[Phi]_, \[CapitalOmega]_, \[Gamma]_, t_] = -I (
   1 - \[CapitalOmega]* Exp[-I \[Phi]])/
   A[\[Phi], \[CapitalOmega], \[Gamma]] Sin[
    A[\[Phi], \[CapitalOmega], \[Gamma]]* t];

rho[\[Phi]_, \[CapitalOmega]_, \[Gamma]_, 
   t_] = (1/(
    Abs[alpha[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
     Abs[beta[\[Phi], \[CapitalOmega], \[Gamma], t]]^2) ) {{Abs[
      alpha[\[Phi], \[CapitalOmega], \[Gamma], t]]^2, 
     alpha[\[Phi], \[CapitalOmega], \[Gamma], t]*
      Conjugate[
       beta[\[Phi], \[CapitalOmega], \[Gamma], 
        t]]}, {beta[\[Phi], \[CapitalOmega], \[Gamma], t]*
      Conjugate[alpha[\[Phi], \[CapitalOmega], \[Gamma], t]], 
     Abs[beta[\[Phi], \[CapitalOmega], \[Gamma], t]]^2}};
p[\[Phi]_, \[CapitalOmega]_, \[Gamma]_, t_] = 
  rho[\[Phi], \[CapitalOmega], \[Gamma], t][[2]][[2]];
x[\[Phi]_, \[CapitalOmega]_, \[Gamma]_, t_] = 
  rho[\[Phi], \[CapitalOmega], \[Gamma], t][[1]][[2]];

funQ\[Rho]out[\[Phi]_myfun[\[Phi]_, \[CapitalOmega]_, \[Gamma]_, 
   t_] = -(((-1 + 
          p[\[Phi], \[CapitalOmega], \[Gamma], 
           t]) ((-1 + 
             p[\[Phi], \[CapitalOmega], \[Gamma], 
              t]) p[\[Phi], \[CapitalOmega], \[Gamma], t] + 
          Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2) Log[((-1 + 
            p[\[Phi], \[CapitalOmega], \[Gamma], 
             t]) ((-1 + 
               p[\[Phi], \[CapitalOmega], \[Gamma], 
                t]) p[\[Phi], \[CapitalOmega], \[Gamma], t] + 
            Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2))/(
         2 ((-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
            2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], 
               t]]^2))])/(((-1 + 
            p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
          2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2) Log[
         2])) - 1/
    Log[2] (-1 + 
      Sqrt[(-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
       2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]) Log[
     1/2 (1 - 
        Sqrt[(-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
         2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2])] + 
   1/Log[2] (1 + 
      Sqrt[(-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
       2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]) Log[
     1/2 (1 + 
        Sqrt[(-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
         2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2])] - ((1 - 
        5 p[\[Phi], \[CapitalOmega], \[Gamma], t] + 
        10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 - 
        10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 + 
        5 p[\[Phi], \[CapitalOmega], \[Gamma], t]^4 - 
        p[\[Phi], \[CapitalOmega], \[Gamma], t]^5 + 
        5 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
        13 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
        11 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
        3 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
        6 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 - 
        2 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 + 
        Sqrt[((-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
          2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2)^5]) Log[
       1/(2 ((-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
           2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2)^2) (1 - 
          5 p[\[Phi], \[CapitalOmega], \[Gamma], t] + 
          10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 - 
          10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 + 
          5 p[\[Phi], \[CapitalOmega], \[Gamma], t]^4 - 
          p[\[Phi], \[CapitalOmega], \[Gamma], t]^5 + 
          5 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
          13 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
          11 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
          3 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
          6 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 - 
          2 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 + 
          Sqrt[((-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
            2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], 
               t]]^2)^5])])/(2 ((-1 + 
          p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
        2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2)^2 Log[
       2]) + ((-1 + 5 p[\[Phi], \[CapitalOmega], \[Gamma], t] - 
        10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 + 
        10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 - 
        5 p[\[Phi], \[CapitalOmega], \[Gamma], t]^4 + 
        p[\[Phi], \[CapitalOmega], \[Gamma], t]^5 - 
        5 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
        13 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
        11 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
        3 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
        6 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 + 
        2 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 + 
        Sqrt[((-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
          2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2)^5]) Log[-(
         1/(2 ((-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
            2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], 
               t]]^2)^2)) (-1 + 
          5 p[\[Phi], \[CapitalOmega], \[Gamma], t] - 
          10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 + 
          10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 - 
          5 p[\[Phi], \[CapitalOmega], \[Gamma], t]^4 + 
          p[\[Phi], \[CapitalOmega], \[Gamma], t]^5 - 
          5 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
          13 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
          11 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
          3 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
          6 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 + 
          2 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 + 
          Sqrt[((-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
            2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], 
               t]]^2)^5])])/(2 ((-1 + 
          p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
        2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2)^2 Log[2]) + 
   1/Log[4] (-4 ArcTanh[
        Sqrt[(-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
         2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]] Sqrt[(-1 +
           p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
        2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2] + 
      2 ArcTanh[
        Sqrt[(1 - 2 p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
         4 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]] Sqrt[(1 - 
          2 p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
        4 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2] + Log[4] - 
      2 Log[1 - 
         Sqrt[(-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
          2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]] - 
      2 Log[1 + 
         Sqrt[(-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
          2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]] + 
      Log[1 - Sqrt[(1 - 
           2 p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
         4 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]] + 
      Log[1 + Sqrt[(1 - 
           2 p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
         4 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]]) ;

Plot[{Re[funQ\[Rho]out[0Re[myfun[0, 0.4, 0.5, t]]}, {t, 0, 10}, 
 PlotRange -> All, PlotStyle -> {Blue, Thick}, AxesOrigin -> {0, 0}]

    A[\[Phi]_, \[CapitalOmega]_, \[Gamma]_] = \[Sqrt](1 - 
    2 \[CapitalOmega] Cos[\[Phi]] + \[CapitalOmega]^2 - \
\[Gamma]^2);(*= \[Sqrt](|1-\[CapitalOmega] Exp[I \
\[Phi]](|^2)-\[Gamma]^2)=\[Sqrt](J^2-\[Gamma]^2). If J>\[Gamma] \
system is PT symmetric, otherwise its not.*)
alpha[\[Phi]_, \[CapitalOmega]_, \[Gamma]_, t_] = 
 Cos[A[\[Phi], \[CapitalOmega], \[Gamma]]* t] - \[Gamma]/
   A[\[Phi], \[CapitalOmega], \[Gamma]] Sin[
    A[\[Phi], \[CapitalOmega], \[Gamma]] *t]; 
beta[\[Phi]_, \[CapitalOmega]_, \[Gamma]_, t_] = -I (
   1 - \[CapitalOmega]* Exp[-I \[Phi]])/
   A[\[Phi], \[CapitalOmega], \[Gamma]] Sin[
    A[\[Phi], \[CapitalOmega], \[Gamma]]* t];

rho[\[Phi]_, \[CapitalOmega]_, \[Gamma]_, 
   t_] = (1/(
    Abs[alpha[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
     Abs[beta[\[Phi], \[CapitalOmega], \[Gamma], t]]^2) ) {{Abs[
      alpha[\[Phi], \[CapitalOmega], \[Gamma], t]]^2, 
     alpha[\[Phi], \[CapitalOmega], \[Gamma], t]*
      Conjugate[
       beta[\[Phi], \[CapitalOmega], \[Gamma], 
        t]]}, {beta[\[Phi], \[CapitalOmega], \[Gamma], t]*
      Conjugate[alpha[\[Phi], \[CapitalOmega], \[Gamma], t]], 
     Abs[beta[\[Phi], \[CapitalOmega], \[Gamma], t]]^2}};
p[\[Phi]_, \[CapitalOmega]_, \[Gamma]_, t_] = 
  rho[\[Phi], \[CapitalOmega], \[Gamma], t][[2]][[2]];
x[\[Phi]_, \[CapitalOmega]_, \[Gamma]_, t_] = 
  rho[\[Phi], \[CapitalOmega], \[Gamma], t][[1]][[2]];

funQ\[Rho]out[\[Phi]_, \[CapitalOmega]_, \[Gamma]_, 
   t_] = -(((-1 + 
          p[\[Phi], \[CapitalOmega], \[Gamma], 
           t]) ((-1 + 
             p[\[Phi], \[CapitalOmega], \[Gamma], 
              t]) p[\[Phi], \[CapitalOmega], \[Gamma], t] + 
          Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2) Log[((-1 + 
            p[\[Phi], \[CapitalOmega], \[Gamma], 
             t]) ((-1 + 
               p[\[Phi], \[CapitalOmega], \[Gamma], 
                t]) p[\[Phi], \[CapitalOmega], \[Gamma], t] + 
            Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2))/(
         2 ((-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
            2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], 
               t]]^2))])/(((-1 + 
            p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
          2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2) Log[
         2])) - 1/
    Log[2] (-1 + 
      Sqrt[(-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
       2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]) Log[
     1/2 (1 - 
        Sqrt[(-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
         2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2])] + 
   1/Log[2] (1 + 
      Sqrt[(-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
       2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]) Log[
     1/2 (1 + 
        Sqrt[(-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
         2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2])] - ((1 - 
        5 p[\[Phi], \[CapitalOmega], \[Gamma], t] + 
        10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 - 
        10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 + 
        5 p[\[Phi], \[CapitalOmega], \[Gamma], t]^4 - 
        p[\[Phi], \[CapitalOmega], \[Gamma], t]^5 + 
        5 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
        13 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
        11 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
        3 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
        6 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 - 
        2 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 + 
        Sqrt[((-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
          2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2)^5]) Log[
       1/(2 ((-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
           2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2)^2) (1 - 
          5 p[\[Phi], \[CapitalOmega], \[Gamma], t] + 
          10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 - 
          10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 + 
          5 p[\[Phi], \[CapitalOmega], \[Gamma], t]^4 - 
          p[\[Phi], \[CapitalOmega], \[Gamma], t]^5 + 
          5 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
          13 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
          11 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
          3 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
          6 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 - 
          2 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 + 
          Sqrt[((-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
            2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], 
               t]]^2)^5])])/(2 ((-1 + 
          p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
        2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2)^2 Log[
       2]) + ((-1 + 5 p[\[Phi], \[CapitalOmega], \[Gamma], t] - 
        10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 + 
        10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 - 
        5 p[\[Phi], \[CapitalOmega], \[Gamma], t]^4 + 
        p[\[Phi], \[CapitalOmega], \[Gamma], t]^5 - 
        5 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
        13 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
        11 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
        3 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
        6 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 + 
        2 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 + 
        Sqrt[((-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
          2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2)^5]) Log[-(
         1/(2 ((-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
            2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], 
               t]]^2)^2)) (-1 + 
          5 p[\[Phi], \[CapitalOmega], \[Gamma], t] - 
          10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 + 
          10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 - 
          5 p[\[Phi], \[CapitalOmega], \[Gamma], t]^4 + 
          p[\[Phi], \[CapitalOmega], \[Gamma], t]^5 - 
          5 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
          13 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
          11 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
          3 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
          6 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 + 
          2 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 + 
          Sqrt[((-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
            2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], 
               t]]^2)^5])])/(2 ((-1 + 
          p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
        2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2)^2 Log[2]) + 
   1/Log[4] (-4 ArcTanh[
        Sqrt[(-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
         2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]] Sqrt[(-1 +
           p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
        2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2] + 
      2 ArcTanh[
        Sqrt[(1 - 2 p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
         4 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]] Sqrt[(1 - 
          2 p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
        4 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2] + Log[4] - 
      2 Log[1 - 
         Sqrt[(-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
          2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]] - 
      2 Log[1 + 
         Sqrt[(-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
          2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]] + 
      Log[1 - Sqrt[(1 - 
           2 p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
         4 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]] + 
      Log[1 + Sqrt[(1 - 
           2 p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
         4 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]]) ;

Plot[{Re[funQ\[Rho]out[0, 0.4, 0.5, t]]}, {t, 0, 10}, 
 PlotRange -> All, PlotStyle -> {Blue, Thick}, AxesOrigin -> {0, 0}]

    A[\[Phi]_, \[CapitalOmega]_, \[Gamma]_] = \[Sqrt](1 - 
    2 \[CapitalOmega] Cos[\[Phi]] + \[CapitalOmega]^2 - \
\[Gamma]^2);(*= \[Sqrt](|1-\[CapitalOmega] Exp[I \
\[Phi]](|^2)-\[Gamma]^2)=\[Sqrt](J^2-\[Gamma]^2). If J>\[Gamma] \
system is PT symmetric, otherwise its not.*)
alpha[\[Phi]_, \[CapitalOmega]_, \[Gamma]_, t_] = 
 Cos[A[\[Phi], \[CapitalOmega], \[Gamma]]* t] - \[Gamma]/
   A[\[Phi], \[CapitalOmega], \[Gamma]] Sin[
    A[\[Phi], \[CapitalOmega], \[Gamma]] *t]; 
beta[\[Phi]_, \[CapitalOmega]_, \[Gamma]_, t_] = -I (
   1 - \[CapitalOmega]* Exp[-I \[Phi]])/
   A[\[Phi], \[CapitalOmega], \[Gamma]] Sin[
    A[\[Phi], \[CapitalOmega], \[Gamma]]* t];

rho[\[Phi]_, \[CapitalOmega]_, \[Gamma]_, 
   t_] = (1/(
    Abs[alpha[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
     Abs[beta[\[Phi], \[CapitalOmega], \[Gamma], t]]^2) ) {{Abs[
      alpha[\[Phi], \[CapitalOmega], \[Gamma], t]]^2, 
     alpha[\[Phi], \[CapitalOmega], \[Gamma], t]*
      Conjugate[
       beta[\[Phi], \[CapitalOmega], \[Gamma], 
        t]]}, {beta[\[Phi], \[CapitalOmega], \[Gamma], t]*
      Conjugate[alpha[\[Phi], \[CapitalOmega], \[Gamma], t]], 
     Abs[beta[\[Phi], \[CapitalOmega], \[Gamma], t]]^2}};
p[\[Phi]_, \[CapitalOmega]_, \[Gamma]_, t_] = 
  rho[\[Phi], \[CapitalOmega], \[Gamma], t][[2]][[2]];
x[\[Phi]_, \[CapitalOmega]_, \[Gamma]_, t_] = 
  rho[\[Phi], \[CapitalOmega], \[Gamma], t][[1]][[2]];

myfun[\[Phi]_, \[CapitalOmega]_, \[Gamma]_, 
   t_] = -(((-1 + 
          p[\[Phi], \[CapitalOmega], \[Gamma], 
           t]) ((-1 + 
             p[\[Phi], \[CapitalOmega], \[Gamma], 
              t]) p[\[Phi], \[CapitalOmega], \[Gamma], t] + 
          Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2) Log[((-1 + 
            p[\[Phi], \[CapitalOmega], \[Gamma], 
             t]) ((-1 + 
               p[\[Phi], \[CapitalOmega], \[Gamma], 
                t]) p[\[Phi], \[CapitalOmega], \[Gamma], t] + 
            Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2))/(
         2 ((-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
            2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], 
               t]]^2))])/(((-1 + 
            p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
          2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2) Log[
         2])) - 1/
    Log[2] (-1 + 
      Sqrt[(-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
       2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]) Log[
     1/2 (1 - 
        Sqrt[(-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
         2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2])] + 
   1/Log[2] (1 + 
      Sqrt[(-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
       2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]) Log[
     1/2 (1 + 
        Sqrt[(-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
         2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2])] - ((1 - 
        5 p[\[Phi], \[CapitalOmega], \[Gamma], t] + 
        10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 - 
        10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 + 
        5 p[\[Phi], \[CapitalOmega], \[Gamma], t]^4 - 
        p[\[Phi], \[CapitalOmega], \[Gamma], t]^5 + 
        5 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
        13 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
        11 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
        3 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
        6 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 - 
        2 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 + 
        Sqrt[((-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
          2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2)^5]) Log[
       1/(2 ((-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
           2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2)^2) (1 - 
          5 p[\[Phi], \[CapitalOmega], \[Gamma], t] + 
          10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 - 
          10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 + 
          5 p[\[Phi], \[CapitalOmega], \[Gamma], t]^4 - 
          p[\[Phi], \[CapitalOmega], \[Gamma], t]^5 + 
          5 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
          13 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
          11 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
          3 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
          6 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 - 
          2 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 + 
          Sqrt[((-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
            2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], 
               t]]^2)^5])])/(2 ((-1 + 
          p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
        2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2)^2 Log[
       2]) + ((-1 + 5 p[\[Phi], \[CapitalOmega], \[Gamma], t] - 
        10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 + 
        10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 - 
        5 p[\[Phi], \[CapitalOmega], \[Gamma], t]^4 + 
        p[\[Phi], \[CapitalOmega], \[Gamma], t]^5 - 
        5 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
        13 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
        11 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
        3 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
        6 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 + 
        2 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
          x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 + 
        Sqrt[((-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
          2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2)^5]) Log[-(
         1/(2 ((-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
            2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], 
               t]]^2)^2)) (-1 + 
          5 p[\[Phi], \[CapitalOmega], \[Gamma], t] - 
          10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 + 
          10 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 - 
          5 p[\[Phi], \[CapitalOmega], \[Gamma], t]^4 + 
          p[\[Phi], \[CapitalOmega], \[Gamma], t]^5 - 
          5 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
          13 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
          11 p[\[Phi], \[CapitalOmega], \[Gamma], t]^2 Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 + 
          3 p[\[Phi], \[CapitalOmega], \[Gamma], t]^3 Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2 - 
          6 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 + 
          2 p[\[Phi], \[CapitalOmega], \[Gamma], t] Abs[
            x[\[Phi], \[CapitalOmega], \[Gamma], t]]^4 + 
          Sqrt[((-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
            2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], 
               t]]^2)^5])])/(2 ((-1 + 
          p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
        2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2)^2 Log[2]) + 
   1/Log[4] (-4 ArcTanh[
        Sqrt[(-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
         2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]] Sqrt[(-1 +
           p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
        2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2] + 
      2 ArcTanh[
        Sqrt[(1 - 2 p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
         4 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]] Sqrt[(1 - 
          2 p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
        4 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2] + Log[4] - 
      2 Log[1 - 
         Sqrt[(-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
          2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]] - 
      2 Log[1 + 
         Sqrt[(-1 + p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
          2 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]] + 
      Log[1 - Sqrt[(1 - 
           2 p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
         4 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]] + 
      Log[1 + Sqrt[(1 - 
           2 p[\[Phi], \[CapitalOmega], \[Gamma], t])^2 + 
         4 Abs[x[\[Phi], \[CapitalOmega], \[Gamma], t]]^2]]) ;

Plot[{Re[myfun[0, 0.4, 0.5, t]]}, {t, 0, 10}, 
 PlotRange -> All, PlotStyle -> {Blue, Thick}, AxesOrigin -> {0, 0}]
Source Link
H. Kenan
H. Kenan
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