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import sys
import plot
import subprocess
import math as mth
import cmath as cmt
import numpy as npy
import scipy.linalg as sla
state_num = 1
dt = 0.02
accu = 100
iterations = 5000
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 init_state(i):
alpha = 2
beta = 0
gamma = 1
delta = 1+1j
if state_num > 1:
alpha = i / state_num
beta = -(state_num - i) / state_num
gamma = alpha + beta
delta = delta * i
H = npy.array([[1,0,0,1j],[0,2,0,0],[0,0,3,0],[-1j,0,0,4]])
H = sla.expm(-1j * (dt / accu) * H)
norm = npy.linalg.norm([alpha, beta, gamma, delta])
state = npy.array([alpha / norm, beta / norm, gamma / norm, delta / norm])
return (state, H)
def time_evolution(state, dt=dt):
return (npy.dot(*state), state[1])
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])
states = []
for i in range(state_num):
(co, H) = init_state(i)
norm = npy.linalg.norm(co)
state = npy.array([co[0] / norm, co[1] / norm, co[2] / norm, co[3] / norm])
states.append((state, H))
f = open("data", "w")
for i in range(iterations):
for j in range(state_num):
hopf_state = fibration(states[j][0])
colour = i / iterations
if state_num > 1:
colour = j / state_num
f.write(f"{hopf_state[0]}; {hopf_state[1]}; {hopf_state[2]}; {hopf_state[3]}; {hopf_state[4]}; {colour}\n")
for l in range(accu):
states[j] = time_evolution(states[j], dt / accu)
f.close()
plot.plot(iterations, iterations, state_num, "anim3d.plt")
#plot.plot(iterations, iterations, state_num, "anim2d.plt")
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