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Mahdisadjadi/specific_heat_two_level_states.py

Created December 22, 2017 01:31
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Generate picture of a specific heat two level states
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specific_heat_two_level_states.py
'''
This code generates a picture of the specific
heat of a two-level system. It also shows
the limits in low- and high-temperatures
regions, in addition to the location of
the maximum specific heat.
Mahdi Sadjadi, 2017.
'''
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.ticker import FuncFormatter, MaxNLocator
for param in ['axes.labelsize','xtick.labelsize','ytick.labelsize']:
plt.rcParams[param] = 15
f = lambda x: x**2 * np.exp(-x) / (1+np.exp(-x))**2
g = lambda x: x**2 /4
h = lambda x: (x)**2 * np.exp(-(x))
fig,ax = plt.subplots(1,1,figsize=(7,7))
x = np.linspace(0,10,100)
ax.plot(x,f(x),'-k',lw=2,label='Exact')
x = np.linspace(0,2,20)
ax.plot(x,g(x),':r',lw=2,label=r'$x^2/4$')
x = np.linspace(2,10,20)
ax.plot(x,h(x),':b',lw=2,label=r'$x^2 e^{-x}$')
ax.vlines(2.4, 0, 0.5, linestyles='dashed',color='k')
ax.text(2.6,0.1,r'$T_0 \approx 2.4 T $',fontsize=20)
ax.set_xlim(0,10)
ax.set_ylim(0,0.5)
ax.set_xlabel(r'$x = \frac{T_0}{T}$')
ax.set_ylabel(r'$k_B^{-1} C(T_0,T)$')
ax.legend()
plt.tight_layout()
plt.savefig('./specific_heat_ts.pdf',dpi=100,transparent=True)
plt.show(fig)
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