The importance of the dimension of Hilbert space

[mehrosadate...@gmail.com]

Hi every one,

I have a problem that is related to the dimension of Hilbert space. In my code I want to plot the number photons in a special system.
My code is in this way:

from qutip import *
import matplotlib.pyplot as plt
import numpy as np
N=50
a=destroy(N)
psi0=basis(N,0)
times=np.linspace(0,3,500)
H4=4*a.dag()*a.dag()*a*a+1j*((a.dag()*a.dag())-(a*a))
solution4=mcsolve(H4,psi0,times,[],[a.dag()*a*a.dag()*a])
n4=solution4.expect[0]
plt.plot(times,np.real(n4),lw=1.5,ls='-',color='b')
plt.xlabel(r'$\chi t$',fontsize=20,fontweight='bold')
plt.ylabel(r'$ \hat{n}$',fontsize=20,fontweight='bold')
plt.show()

The result is physically acceptable. I expect that by increasing the dimension of Hilbert space, the result get more exact. But by increasing N (like N=400) I see that the result is not physically acceptable.(It worths to mention that for N=400 I select  "times=np.linspace(0,3,8000)").
Is there any problem in my code?
can anybody help me please?


Best Regards
Mehrosadat

[mehrosadate...@gmail.com]

any ideas?!?

[mehrosadate...@gmail.com]

Hi
I have a question that is also related to the dimension of Hilbert space.
May selecting a high number for the dimension of Hilbert space cause a bug in a code?
I have a problem not only with mcslove but also with mesolve.
when I increase the number of the dimension of Hilbert space, I receive a result that is not physically acceptable (instead of getting a better result).
Is there any restriction in increasing the dimension of Hilbert space?
Can any body help me?

Best Regards
Mehrosadat