diff options
| -rw-r--r-- | .gitignore | 3 | ||||
| -rw-r--r-- | gnuplot.plt | 21 | ||||
| -rw-r--r-- | gnuplot/animation.plt | 11 | ||||
| -rw-r--r-- | gnuplot/plotxy.plt | 11 | ||||
| -rw-r--r-- | plotting.py | 57 | ||||
| -rw-r--r-- | single_dequantify.py | 33 | ||||
| -rw-r--r-- | twoqbit_dequantify.py | 50 |
7 files changed, 99 insertions, 87 deletions
@@ -1,2 +1,3 @@ -data +data* +plotting.py __pycache__ diff --git a/gnuplot.plt b/gnuplot.plt deleted file mode 100644 index f94ccdb..0000000 --- a/gnuplot.plt +++ /dev/null @@ -1,21 +0,0 @@ -set view equal xyz -set parametric -set isosamples 34,34 -unset colorbox -unset key - -iterations = 100 -states = 6 - -do for [ii=1:iterations] { - 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#, \ - #do for [ij=1:states] { - # ic = ij * iterations + ii - # replot 'data' every ::ij * iterations::ic w points palette pointsize 2 pointtype 7#, \ - # #'data' every ::ij * iterations::ic w p palette - #} - pause 0.1 -} - -pause mouse close diff --git a/gnuplot/animation.plt b/gnuplot/animation.plt new file mode 100644 index 0000000..6228a53 --- /dev/null +++ b/gnuplot/animation.plt @@ -0,0 +1,11 @@ +set view equal xyz +set parametric +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#, \ + pause 0.1 +} + +pause mouse close diff --git a/gnuplot/plotxy.plt b/gnuplot/plotxy.plt new file mode 100644 index 0000000..b3bf993 --- /dev/null +++ b/gnuplot/plotxy.plt @@ -0,0 +1,11 @@ +set size square +#plot cos(x),sin(y) w l lc rgb "#42a4f5" +set xrange [-1.1:1.1] +set yrange [-1.1:1.1] +set xlabel "Re(V)" +set ylabel "Im(V)" +set xzeroaxis +set yzeroaxis +plot 'data' w points palette pointsize 2 pointtype 7 +; +pause mouse close diff --git a/plotting.py b/plotting.py deleted file mode 100644 index 57116c1..0000000 --- a/plotting.py +++ /dev/null @@ -1,57 +0,0 @@ -import math as mth -import cmath as cmt -import numpy as npy -from mpl_toolkits.mplot3d import Axes3D -import matplotlib.pyplot as plt -from itertools import product, combinations -from matplotlib.patches import FancyArrowPatch -from mpl_toolkits.mplot3d import proj3d - - -class Arrow3D(FancyArrowPatch): - - def __init__(self, xs, ys, zs, *args, **kwargs): - FancyArrowPatch.__init__(self, (0, 0), (0, 0), *args, **kwargs) - self._verts3d = xs, ys, zs - - def draw(self, renderer): - xs3d, ys3d, zs3d = self._verts3d - xs, ys, zs = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M) - self.set_positions((xs[0], ys[0]), (xs[1], ys[1])) - FancyArrowPatch.draw(self, renderer) - - -def kugel(historie): - fig = plt.figure() - ax = fig.gca(projection='3d') - - # draw sphere - u, v = npy.mgrid[0:2*npy.pi:20j, 0:npy.pi:10j] - x = npy.cos(u)*npy.sin(v) - y = npy.sin(u)*npy.sin(v) - z = npy.cos(v) - ax.plot_wireframe(x, y, z, color="r") - - # draw a time evolution - for blochpunkt in historie: - x = mth.cos(blochpunkt[1]) * mth.cos(blochpunkt[0]) - y = mth.cos(blochpunkt[1]) * mth.sin(blochpunkt[0]) - z = mth.sin(blochpunkt[1]) - a = Arrow3D([0, x], [0, y], [0, z], mutation_scale=20, - lw=1, arrowstyle="-|>", color="k") - ax.add_artist(a) - plt.show() - -def phi(phi): - ax = plt.axes() - plt.grid() - - x = mth.cos(phi[0]) - y = mth.sin(phi[0]) - - ax.arrow(0, 0, 0.5, 0.5, head_width=0.05, head_length=0.07) - plt.title('Zeitentwicklung von phi') - - plt.xlim(-1.1,1.1) - plt.ylim(-1.1,1.1) - plt.show() diff --git a/single_dequantify.py b/single_dequantify.py index a775ff1..f43f9f1 100644 --- a/single_dequantify.py +++ b/single_dequantify.py @@ -5,11 +5,9 @@ import cmath as cmt import numpy as npy import scipy.linalg as sla -alpha = 1 -beta = 1 dt = 0.08 iterations = 100 -state_num = 6 +state_num = 1 H = npy.array([[1,0],[0,2]]) @@ -17,6 +15,14 @@ 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 + return (alpha, beta) + def time_evolution(state, dt = dt): return npy.dot(state, sla.expm(-1j * dt * H)) @@ -38,8 +44,7 @@ f = open("data", "w") states = [] for i in range(state_num): - alpha = i / state_num - beta = (state_num - i) / state_num + (alpha, beta) = init_state(i) norm = npy.linalg.norm([alpha, beta]) state = npy.array([alpha / norm, beta / norm]) states.append(state) @@ -47,11 +52,23 @@ for i in range(state_num): for i in range(iterations): for j in range(state_num): - states[j] = time_evolution(states[j]) (phi, theta) = bloch_map(states[j]) coords = sphere2cart(phi, theta) - f.write(f"{coords[0]}; {coords[1]}; {coords[2]}; {(j + 1) / state_num}\n") + colour = i / iterations + if state_num > 1: + colour = j / state_num + f.write(f"{coords[0]}; {coords[1]}; {coords[2]}; {colour}\n") + states[j] = time_evolution(states[j]) f.close() -subprocess.run(["gnuplot", "gnuplot.plt"]) +import os + +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 new file mode 100644 index 0000000..b6e0abb --- /dev/null +++ b/twoqbit_dequantify.py @@ -0,0 +1,50 @@ +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"]) |