Sunday, July 6, 2025
Random 1
import numpy as np
import matplotlib.pyplot as plt
# Physical constants
h = 6.62607015e-34 # Planck's constant (J·s)
m_p = 1.6726219e-27 # Proton mass (kg)
c = 2.99792458e8 # Speed of light (m/s)
e = 1.60217662e-19 # Elementary charge (C)
hbar = h / (2 * np.pi) # Reduced Planck's constant
mu_N = e * hbar / (2 * m_p) # Nuclear magneton (A·m^2)
n = 4 # Quantum number for stable proton vortex
# Calculate proton radius
r_p = (n * h) / (2 * np.pi * m_p * c) # ~8.41e-16 m
# Magnetic moment
mu = (e * c * r_p) / 3 # = (8/3) mu_N
mu_over_mu_N = mu / mu_N # ~2.6667
# Energy levels (in MeV)
m_p_c2 = 938 # Proton rest energy (MeV)
def energy_n(n_val):
return (n_val / 4)**2 * m_p_c2
E_4 = energy_n(4) # 938 MeV
E_5 = energy_n(5) # ~1465.625 MeV
delta_E_4_to_5 = E_5 - E_4 # ~527.625 MeV
# Visualization parameters
grid_size = 100
x = np.linspace(-10e-15, 10e-15, grid_size)
y = np.linspace(-10e-15, 10e-15, grid_size)
X, Y = np.meshgrid(x, y)
vortex_positions = [(0, 0)] # Single proton vortex at origin
# Velocity field for a single vortex
def velocity_field(X, Y, x0, y0, kappa):
r = np.sqrt((X - x0)**2 + (Y - y0)**2)
r[r == 0] = 1e-20 # Avoid division by zero
v_theta = kappa / (2 * np.pi * r)
theta = np.arctan2(Y - y0, X - x0)
vx = -v_theta * np.sin(theta)
vy = v_theta * np.cos(theta)
return vx, vy
kappa = n * h / m_p
vx, vy = velocity_field(X, Y, 0, 0, kappa)
# Plotting
plt.figure(figsize=(10, 8))
plt.streamplot(X * 1e15, Y * 1e15, vx, vy, density=1.5, color='blue')
plt.plot(0, 0, 'ro', label='Proton Vortex Center')
circle = plt.Circle((0, 0), r_p * 1e15, color='red', fill=False, label=f'r_p = {r_p:.2e} m')
plt.gca().add_artist(circle)
plt.title('Proton as a Quantized Vortex in Superfluid')
plt.xlabel('x (fm)')
plt.ylabel('y (fm)')
plt.legend()
plt.grid(True)
# Annotations
plt.text(-9, 8, f'Proton Radius: {r_p:.2e} m (~0.841 fm)', fontsize=10)
plt.text(-9, 7, f'Magnetic Moment: {mu_over_mu_N:.4f} ฮผ_N ≈ 2.6667 ฮผ_N', fontsize=10)
plt.text(-9, 6, f'ฮE (n=4 to 5): {delta_E_4_to_5:.1f} MeV', fontsize=10)
plt.axis('equal')
plt.show()
print(f"Proton Radius: {r_p:.2e} m")
print(f"Magnetic Moment: {mu_over_mu_N:.4f} ฮผ_N")
print(f"Transition Energy (n=4 to n=5): {delta_E_4_to_5:.1f} MeV")
print("Compare to resonances: Delta(1232) ~294 MeV, N(1535) ~597 MeV")
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