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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"])
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