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Dkunb

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explanation...

Dkunb 50
September 02 2022
0 0

@acer I am trying to reproduce the graph e.1 and e.2) in the paper.  In the equation in the code, alpha = omega*T, gamma(gg)=Delta /T and  beta=d/T. N means negativity. If N greater than 0, it is possible to harvest entanglement (red color in the left figure.) and if N is less than equal to 0, it is not possible to harvest entanglement (the gray color in the left figure.) delta is sigma/T  and Lambda is Lambda*T

More explanation...

Dkunb 50
September 02 2022
0 0

@acer  On the left side figure, the red color means N>0 and grey color means N<=0

@acer The dashed line can be ignora...

Dkunb 50
September 02 2022
0 0

@acer The dashed line can be ignorable because I have not understood it well.The coloring is based on the scaling of the result of N function (*10^-11 lambda^2 --- see the color bar on the right in the figure.)- I think I need to generate Matrix (or array)of N to know the scale. And gamma (looks like r in my figure) is your gg. I want to know how to write the code to represent the graph like that. 

I am sorry that my English is not good to explain clearly. And I am very new to Maple.

PS) Could you also explain why you set up return value 10^10 in MyHandler? I try to understand your code so I can learn to write code in Maple. It is easier for me to learn from the example codes.

Thank you very much for your help!

Plot...

Dkunb 50
September 02 2022
0 0

@acer Thank you so much! How can I write the codes for the following plots based on N function?

L function...

Dkunb 50
September 02 2022
0 0

@acer  I do not see any evalf(L) in your codes and If I generated Matrix of N it showed the integral form of L.

Time...

Dkunb 50
September 01 2022
0 0

@acer Thank you again.

I run my codes and yours (I used my original L because F would be varied .)


 

> 

restart;
> 

with(plots):
> 

 

> 

F:=kappa->kappa;

proc (kappa) options operator, arrow; kappa end proc

 (1)
> 

f:=(alpha,delta)->exp(-abs(F(kappa))^2*(1+delta^2)/2-abs(F(kappa))*alpha)/abs(F(kappa));

proc (alpha, delta) options operator, arrow; exp(-(1/2)*abs(F(kappa))^2*(1+delta^2)-abs(F(kappa))*alpha)/abs(F(kappa)) end proc

 (2)
> 

L:=(alpha,delta,Lambda)->(lambda^2*exp(-alpha^2/2)/4)*(Int(f(alpha,delta),kappa= -infinity..-Lambda)+Int(f(alpha,delta),kappa= Lambda..infinity));

proc (alpha, delta, Lambda) options operator, arrow; (1/4)*lambda^2*exp(-(1/2)*alpha^2)*(Int(f(alpha, delta), kappa = -infinity .. -Lambda)+Int(f(alpha, delta), kappa = Lambda .. infinity)) end proc

 (3)
> 

CodeTools:-Usage(evalf(L(4,1,0.001)));

memory used=1.63MiB, alloc change=0 bytes, cpu time=31.00ms, real time=19.00ms, gc time=0ns

  

0.8209373770e-3*lambda^2

 (4)
> 

g:=(beta,delta)->exp(-I*kappa*beta-abs(F(kappa))^2*(1+delta^2)/2)/abs(F(kappa));

proc (beta, delta) options operator, arrow; exp(-I*kappa*beta-(1/2)*abs(F(kappa))^2*(1+delta^2))/abs(F(kappa)) end proc

 (5)
> 

E:=(omega,gamma)->exp(I*omega*gamma)*(1-erf((gamma+I*omega)/sqrt(2)));

proc (omega, gamma) options operator, arrow; exp(I*omega*gamma)*(1-erf((gamma+I*omega)/sqrt(2))) end proc

 (6)
> 

J:=(alpha,delta,Lambda,beta,gamma)->(lambda^2*exp(-alpha^2/2)/8)*abs(Int(g(beta,delta)*(E(abs(F(kappa)),gamma)+E(abs(F(kappa)),-gamma)),kappa=-infinity..-Lambda)+Int(g(beta,delta)*(E(abs(F(kappa)),gamma)+E(abs(F(kappa)),-gamma)),kappa=Lambda..infinity));

proc (alpha, delta, Lambda, beta, gamma) options operator, arrow; (1/8)*lambda^2*exp(-(1/2)*alpha^2)*abs(Int(g(beta, delta)*(E(abs(F(kappa)), gamma)+E(abs(F(kappa)), -gamma)), kappa = -infinity .. -Lambda)+Int(g(beta, delta)*(E(abs(F(kappa)), gamma)+E(abs(F(kappa)), -gamma)), kappa = Lambda .. infinity)) end proc

 (7)
> 

CodeTools:-Usage(evalf(J(4,1,0.001,8,3)));

memory used=0.62GiB, alloc change=141.00MiB, cpu time=4.70s, real time=4.72s, gc time=812.50ms

  

0.7304273935e-3*lambda^2

 (8)
> 

N := (beta,alpha)-> (J(alpha,1,0.001,beta,3)-L(alpha,1,0.001))/\lambda^2;

proc (beta, alpha) options operator, arrow; (J(alpha, 1, 0.1e-2, beta, 3)-L(alpha, 1, 0.1e-2))/lambda^2 end proc

 (9)
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CodeTools:-Usage(contourplot(evalf(N(beta,alpha)), beta=0..10,alpha=0..10,grid=[25,25]));

memory used=138.77GiB, alloc change=1.21GiB, cpu time=16.96m, real time=15.89m, gc time=115.06s

  

 
> 

 

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Download Negativity_v2.mw
 

> 

restart;
> 

with(plots):
> 

F:=kappa->kappa;

proc (kappa) options operator, arrow; kappa end proc

 (1)
> 

f:=(alpha,delta)->exp(-abs(F(kappa))^2*(1+delta^2)/2-abs(F(kappa))*alpha)/abs(F(kappa));

proc (alpha, delta) options operator, arrow; exp(-(1/2)*abs(F(kappa))^2*(1+delta^2)-abs(F(kappa))*alpha)/abs(F(kappa)) end proc

 (2)
> 

L:=(alpha,delta,Lambda) ->
  (lambda^2*exp(-alpha^2/2)/4)*(Int(f(alpha,delta),kappa= -infinity..-Lambda)+Int(f(alpha,delta),kappa= Lambda..infinity));

proc (alpha, delta, Lambda) options operator, arrow; (1/4)*lambda^2*exp(-(1/2)*alpha^2)*(Int(f(alpha, delta), kappa = -infinity .. -Lambda)+Int(f(alpha, delta), kappa = Lambda .. infinity)) end proc

 (3)
> 

#0.0008209373770*lambda^2
forget(evalf);
CodeTools:-Usage( evalf(L(4,1,0.001)) );

memory used=1.63MiB, alloc change=0 bytes, cpu time=15.00ms, real time=19.00ms, gc time=0ns

  

0.8209373770e-3*lambda^2

 (4)
> 

g:=(beta,delta)->exp(-I*kappa*beta-abs(F(kappa))^2*(1+delta^2)/2)/abs(F(kappa));

proc (beta, delta) options operator, arrow; exp(-I*kappa*beta-(1/2)*abs(F(kappa))^2*(1+delta^2))/abs(F(kappa)) end proc

 (5)
> 

E:=(omega,gg)->exp(I*omega*gg)*(1-erf((gg+I*omega)/sqrt(2)));

proc (omega, gg) options operator, arrow; exp(I*omega*gg)*(1-erf((gg+I*omega)/sqrt(2))) end proc

 (6)
> 

MyHandler := proc(operator,operands,default_value)
               NumericStatus( overflow = false );
               return 10^10;
             end proc:
ig1template := proc(kappa)
              NumericEventHandler(overflow = MyHandler);
              evalhf(__dummy); end proc:
> 

igdum:='Re'(simplify(exp(-alpha^2/2)/8*(g(beta,delta)*(E(abs(F(kappa)),gg)+E(abs(F(kappa)),-gg))))):
J := subs(__igdum=igdum, proc(alpha,delta,Lambda,beta,gg) local ig;
  ig := subs(__dummy= __igdum, eval(ig1template));
  evalf(lambda^2*abs(Int(ig,-infinity..-Lambda,epsilon=1e-4,method=_d01amc)
                     +Int(ig,Lambda..infinity,epsilon=1e-4,method=_d01amc)));
end proc):
> 

forget(evalf);
CodeTools:-Usage( J(4,1,0.001,8,3) );

memory used=60.12MiB, alloc change=0 bytes, cpu time=344.00ms, real time=343.00ms, gc time=0ns

  

0.7304272433e-3*lambda^2

 (7)
> 

N := (beta,alpha) -> (J(alpha,1,0.001,beta,3)-L(alpha,1,0.001))/lambda^2;

proc (beta, alpha) options operator, arrow; (J(alpha, 1, 0.1e-2, beta, 3)-L(alpha, 1, 0.1e-2))/lambda^2 end proc

 (8)
> 

forget(evalf);
CodeTools:-Usage(contourplot(N, 0..10, 0..10, grid=[25,25]));

memory used=20.15GiB, alloc change=108.00MiB, cpu time=2.13m, real time=2.13m, gc time=18.75s

  

 
> 

 


 

Download Negativity_v1(2)_acc.mw

 

 

 

 

Parallelizing computation...

Dkunb 50
August 31 2022
0 0

@acer Thank you so much!!

MyHandler := proc(operator,operands,default_value)
               NumericStatus( overflow = false );
               return 10^10;
             end proc:
ig1template := proc(kappa)
              NumericEventHandler(overflow = MyHandler);
              evalhf(__dummy); end proc:

Myhandler returns 10^10 and then NumericEventHandler(overflow=10^10)? I do not understand what the code is doing (especially number 10^10...).

Also how to do  parallelizing computation over a 2D Array (over beta and alpha values), and then using listcontplot?

Thank you so much again for your help.

Thank you!...

Dkunb 50
August 12 2022
0 0

@vv Thank you!

@Kitonum yes, I did restart. I am u...

Dkunb 50
January 05 2022
0 0

@Kitonum yes, I did restart. I am using Maple 2021. It might be related to some setting in Maple 2021??

@Kitonum  I got the same issue whe...

Dkunb 50
January 05 2022
0 0

@Kitonum 

I got the same issue when running your codes, too.  

@Kitonum Thank you so much! ...

Dkunb 50
January 05 2022
0 0

@Kitonum Thank you so much! 

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