6th_sem_03 Plotting variation of Relative rms fluctuations in Energy (E) with Temperature (T) for different no of Bosons using Python & Matplotlib

Plotting variation of Relative RMS fluctuations in Energy (E) with Temperature (T) for different no of Bosons using Python & Matplotlib

The relative rms fluctuations is, 

• The simplified form of Partition function and mean energy & mean of square of energy is,

• For 2 particle system,

• For 3 particle system,

• For 3 particle system,

You can derive the simplified forms of these functions from the energy configuration table by the assumption, 

Now the program for the plotting curve is,

import numpy as np import matplotlib.pyplot as plt x=np.linspace(0.01,20,10000) #for N=2 z2=1+np.exp(-2/x)+np.exp(-1/x) #Partation function E2=(2*np.exp(-2/x)+np.exp(-1/x))/z2 #<e> E22=(4*np.exp(-2/x)+np.exp(-1/x))/z2 #<E^2> Ef2=np.sqrt(E22-E2**2)/E2 #for N=3 z3=1+np.exp(-3/x)+np.exp(-1/x)+np.exp(-2/x) E3=(3*np.exp(-3/x)+np.exp(-1/x)+2*np.exp(-2/x))/z3 E23=(9*np.exp(-3/x)+np.exp(-1/x)+4*np.exp(-2/x))/z3 Ef3=np.sqrt(E23-E3**2)/E3 #for N=4 z4=1+np.exp(-4/x)+np.exp(-1/x)+np.exp(-2/x)+np.exp(-3/x) E4=(3*np.exp(-3/x)+np.exp(-1/x)+2*np.exp(-2/x)+4*np.exp(-4/x))/z4 E24=(9*np.exp(-3/x)+np.exp(-1/x)+4*np.exp(-2/x)+16*np.exp(-4/x))/z4 Ef4=np.sqrt(E24-E4**2)/E4 plt.plot(x,Ef2,'b',x,Ef3,'r',x,Ef4,'g') plt.xlabel('Temperature(T)') plt.ylabel('Relative rms fluctuations in E') plt.title('Relative rms fluctuations in E for Bosons Vs. Temperature') plt.grid() plt.ylim(0.7,1.6) plt.legend(['N=2','N=3','N=4']) plt.show()

Output:

This is the output of the program

So we see that the relative rms fluctuations in E decreases with the increase in no of perticles of the system.



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