Animate tow level systems

5 files changed, 72 insertions, 28 deletions

diff --git a/gnuplot/anim2d.plt b/gnuplot/anim2d.plt
new file mode 100644
index 0000000..38b8d5a
--- /dev/null
+++ b/gnuplot/anim2d.plt
@@ -0,0 +1,15 @@
+set size square
+set xrange [-1.1:1.1]
+set yrange [-1.1:1.1]
+set xlabel "Re(V)"
+set ylabel "Im(V)"
+set xzeroaxis
+set yzeroaxis
+set object circle at 0,0 size 1
+
+do for [ii=start:end] {
+    plot 'data' every ::1::ii * states using 4:5:6 w points palette pointsize 2 pointtype 7
+    pause 0.1
+}
+
+pause mouse close
diff --git a/gnuplot/animation.plt b/gnuplot/anim3d.plt
index 6228a53..99cfe10 100644
--- a/gnuplot/animation.plt
+++ b/gnuplot/anim3d.plt
@@ -4,7 +4,7 @@ set isosamples 34,34
 
 do for [ii=start:end] {
     splot cos(u)*cos(v),cos(u)*sin(v),sin(u) w l lc rgb "#42a4f5", \
-        'data' every ::1::ii * states w points palette pointsize 2 pointtype 7#, \
+        'data' every ::1::ii * states using 1:2:3:6 w points palette pointsize 2 pointtype 7#, \
     pause 0.1
 }
 
diff --git a/plot.py b/plot.py
new file mode 100644
index 0000000..6d8e449
--- /dev/null
+++ b/plot.py
@@ -0,0 +1,15 @@
+import os
+import subprocess
+
+
+def plot(start, end, states = 1, script = "anim3d.plt"):
+    path = 'gnuplot/'
+    if os.name == 'nt':
+        path.replace('/','\\')
+    subprocess.run(["gnuplot",
+        "-e", f"states={states};",
+        "-e", f"start={start};" ,
+        "-e", f"end={end};",
+        "-c", path + script])
+
+
diff --git a/single_dequantify.py b/single_dequantify.py
index f43f9f1..99ebdc4 100644
--- a/single_dequantify.py
+++ b/single_dequantify.py
@@ -1,5 +1,5 @@
 import sys
-import subprocess
+import plot
 import math as mth
 import cmath as cmt
 import numpy as npy
@@ -7,7 +7,7 @@ import scipy.linalg as sla
 
 dt = 0.08
 iterations = 100
-state_num = 1
+state_num = 3
 
 H = npy.array([[1,0],[0,2]])
 
@@ -40,8 +40,6 @@ def sphere2cart(phi, theta):
              -1 * mth.cos(theta)
         ]
 
-f = open("data", "w")
-
 states = []
 for i in range(state_num):
     (alpha, beta) = init_state(i)
@@ -49,7 +47,7 @@ for i in range(state_num):
     state = npy.array([alpha / norm, beta / norm])
     states.append(state)
 
-
+f = open("data", "w")
 for i in range(iterations):
     for j in range(state_num):
         (phi, theta) = bloch_map(states[j])
@@ -57,18 +55,9 @@ for i in range(iterations):
         colour = i / iterations
         if state_num > 1:
             colour = j / state_num
-        f.write(f"{coords[0]}; {coords[1]}; {coords[2]}; {colour}\n")
+        f.write(f"{coords[0]}; {coords[1]}; {coords[2]}; 0; 0; {colour}\n")
         states[j] = time_evolution(states[j])
-
 f.close()
 
-import os
+plot.plot(1, iterations, state_num, "anim2d.plt")
 
-path = 'gnuplot/'
-if os.name == 'nt':
-    path.replace('/','\\')
-subprocess.run(["gnuplot",
-    "-e", f"states={state_num};",
-    "-e", f"start={iterations};" ,
-    "-e", f"end={iterations};",
-    "-c", path + "animation.plt"])
diff --git a/twoqbit_dequantify.py b/twoqbit_dequantify.py
index b6e0abb..efc3304 100644
--- a/twoqbit_dequantify.py
+++ b/twoqbit_dequantify.py
@@ -1,3 +1,5 @@
+import sys
+import plot
 import subprocess
 import math as mth
 import cmath as cmt
@@ -8,23 +10,36 @@ alpha = 2
 beta  = 0
 gamma = 1
 delta = 1+1j
+state_num = 1
 
 norm  = npy.linalg.norm([alpha, beta, gamma, delta])
 state = npy.array([alpha / norm, beta / norm, gamma / norm, delta / norm])
 
 dt = 0.05
-iterations = 20
+iterations = 200
 
-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]]
 
+if len(sys.argv) == 3:
+    alpha = complex(sys.argv[1])
+    beta = complex(sys.argv[2])
+
+def init_state(i):
+    alpha = 1
+    beta  = 1
+    if state_num > 1:
+        alpha = i / state_num
+        beta  = (state_num - i) / state_num
+    H = npy.array([[1,0,0,1j],[0,2,0,0],[0,0,3,0],[-1j,0,0,4]])
+    return ([alpha, beta, gamma, delta], H)
+
 
 def time_evolution(state, dt = dt):
-    return npy.dot(state, sla.expm(-1j * dt * H))
+    return (npy.dot(state[0], sla.expm(-1j * dt * state[1])), state[1])
 
 def fibration(state):
     x0=npy.dot(npy.conj(state),npy.dot(M0,state))
@@ -37,14 +52,24 @@ def fibration(state):
     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)
+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")
+        states[j] = time_evolution(states[j])
 f.close()
 
-subprocess.run(["gnuplot", "gnuplot_2d.plt"])
+#plot.plot(iterations, iterations, state_num, "anim3d.plt")
+plot.plot(iterations, iterations, state_num, "anim2d.plt")
+