import subprocess import math as mth import cmath as cmt import numpy as npy import scipy.linalg as sla alpha = 2 beta = 0 gamma = 1 delta = 1+1j norm = npy.linalg.norm([alpha, beta, gamma, delta]) state = npy.array([alpha / norm, beta / norm, gamma / norm, delta / norm]) dt = 0.05 iterations = 20 H = npy.array([[1,0,0,1j],[0,2,0,0],[0,0,3,0],[-1j,0,0,4]]) M0 = [[1,0,0,0],[0,1,0,0],[0,0,-1,0],[0,0,0,-1]] M1 = [[0,0,1,0],[0,0,0,1],[1,0,0,0],[0,1,0,0]] M2 = [[0,0,-1j,0],[0,0,0,-1j],[1j,0,0,0],[0,1j,0,0]] M3 = [[0,0,0,1],[0,0,-1,0],[0,-1,0,0],[1,0,0,0]] def time_evolution(state, dt = dt): return npy.dot(state, sla.expm(-1j * dt * H)) def fibration(state): x0=npy.dot(npy.conj(state),npy.dot(M0,state)) x1=npy.dot(npy.conj(state),npy.dot(M1,state)) x2=npy.dot(npy.conj(state),npy.dot(M2,state)) V=npy.dot(state,npy.dot(M3,state)) x3=V.real x4=V.imag return ([x0.real,x1.real,x2.real,x3,x4]) f = open("data", "w") for i in range(iterations + 1): hopf_state = fibration(state) f.write(f"{hopf_state[3]}; {hopf_state[4]}; {(i + 1) / (iterations + 1)}\n") print(hopf_state) state = time_evolution(state) f.close() subprocess.run(["gnuplot", "gnuplot_2d.plt"])