here’s an example program using the QuTiP library to simulate a simple quantum field theory. In this example, we simulate a single harmonic oscillator mode using the creation and annihilation operators.
pythonCopy codeimport numpy as np
from qutip import *
# Set up the Hamiltonian for a single harmonic oscillator mode
omega = 1.0 # Frequency of the oscillator
N = 10 # Maximum number of excitations
a = destroy(N) # Annihilation operator
H = omega * a.dag() * a # Hamiltonian
# Set up the initial state as a coherent state
alpha = 2.0 # Complex amplitude of the coherent state
psi0 = coherent(N, alpha)
# Set up the time vector for the simulation
t = np.linspace(0, 10, 100)
# Solve the Schrodinger equation to obtain the time evolution of the state
result = sesolve(H, psi0, t)
# Plot the expectation value of the number operator as a function of time
import matplotlib.pyplot as plt
plt.plot(t, result.expect[0])
plt.xlabel('Time')
plt.ylabel('Expectation value of number operator')
plt.show()
This program sets up the Hamiltonian for a single harmonic oscillator mode, which describes the energy of the oscillator as a function of its position and momentum. We then set up the initial state as a coherent state, which is a quantum superposition of many different number states with a complex amplitude. We then use the sesolve function from QuTiP to solve the Schrodinger equation and obtain the time evolution of the state. Finally, we plot the expectation value of the number operator as a function of time, which gives us the average number of excitations in the oscillator at each point in time.
physics 