Strange Spectrum

import pylab as plt
import numpy as np

'''
plot A_k(w) = 1 / [(w - cos(k))^2 + gamma^2]
with k on the x-axis and w on the y-axis
'''

# sample data
side = np.linspace(-np.pi, np.pi, 1<<9)
X, Y = np.meshgrid(side, side) # x = momentum, y = frequency
g0 = 1
Z = 1 / ((Y - np.cos(X))**2 + g0**2) # z = spectrum

# plot the density map using nearest-neighbor interpolation
plt.pcolormesh(X, Y, Z)
plt.show()