from SimpleQmap import Qmap, StandardMap import matplotlib.pyplot as plt import numpy as np dim = 70 k = 1.0 qmin, qmax = 0.0, 1.0 pmin, pmax = 0.0, 1.0 domain = [[qmin, qmax], [pmin, pmax]] map = StandardMap(k=k) qmap = Qmap(map, dim, domain) evals, evecs = qmap.eigen() # get eigen value and eigen vectors print("is unitary?", np.all(np.abs(np.abs(evals * np.conj(evals)) - np.ones(dim)) < 1e-12)) fig = plt.figure(figsize=(6, 6)) theta = np.linspace(-np.pi, np.pi, 500) z = np.exp(-1.j * theta) plt.plot(evals.real, evals.imag, 'o', markersize=8) plt.plot(z.real, z.imag, '-k') plt.xlim(-1.1, 1.1) plt.ylim(-1.1, 1.1) plt.grid() plt.xlabel(r"$Re[u_n]$", fontsize=20) plt.ylabel(r"$Im[u_n]$", fontsize=20) plt.tight_layout() plt.savefig("eigen_values.png") plt.show()
from SimpleQmap import Qmap, StandardMap import matplotlib.pyplot as plt import numpy as np dim = 70 k = 1.0 qmin, qmax = 0.0, 1.0 pmin, pmax = -2.0, 2.0 tmax = 7 map = StandardMap(k=k) domain = [[qmin, qmax], [pmin, pmax]] qmap = Qmap(map, dim, domain) #state = qmap.getState().cs(0.5,0.5) state = qmap.getState() state.insert(int(dim / 2), 1.0 + 0.j) init = state.p2q() qmap.setInit(init) for i in range(tmax): state = qmap.getIn() print("%d-th step" % i, state.norm()) pvec = state.prep() zero_index = (pvec.abs2() == 0.0) pvec[zero_index] = 1e-32 + 0.0j par = 1. * i / tmax plt.plot(state.scaleinfo.x[1], pvec.abs2(), '-', linewidth=3,
from SimpleQmap import Qmap, StandardMap import matplotlib.pyplot as plt import numpy as np dim = 70 k = 1.0 qmin, qmax = 0.0, 1.0 pmin, pmax = 0.0, 1.0 domain = [[qmin,qmax],[pmin,pmax]] map = StandardMap(k=k) qmap = Qmap(map, dim, domain) evals, evecs = qmap.eigen() # get eigen value and eigen vectors print("is unitary?",np.all(np.abs(np.abs(evals*np.conj(evals))-np.ones(dim))<1e-12)) fig = plt.figure(figsize=(6,6)) theta = np.linspace(-np.pi,np.pi, 500) z = np.exp(-1.j*theta) plt.plot(evals.real, evals.imag, 'o',markersize=8) plt.plot(z.real, z.imag, '-k') plt.xlim(-1.1,1.1) plt.ylim(-1.1,1.1) plt.grid() plt.xlabel(r"$Re[u_n]$",fontsize=20) plt.ylabel(r"$Im[u_n]$",fontsize=20) plt.tight_layout() plt.savefig("eigen_values.png") plt.show()
from SimpleQmap import Qmap, StandardMap import matplotlib.pyplot as plt import numpy as np dim = 70 k = 1.0 qmin, qmax = 0.0, 1.0 pmin, pmax = -2.0, 2.0 tmax = 7 map = StandardMap(k=k) domain = [[qmin,qmax],[pmin,pmax]] qmap = Qmap(map, dim, domain) #state = qmap.getState().cs(0.5,0.5) state = qmap.getState() state.insert(int(dim/2), 1.0+0.j) init = state.p2q() qmap.setInit(init) for i in range(tmax): state = qmap.getIn() print("%d-th step" % i, state.norm()) pvec = state.prep() zero_index = (pvec.abs2() == 0.0) pvec[zero_index] = 1e-32 + 0.0j par = 1.*i/tmax plt.plot(state.scaleinfo.x[1],pvec.abs2(), '-',linewidth=3,color=plt.cm.jet(par), label='%d step' % i) # state.savetxt("evolv_qrep_%d.dat" % i) qmap.evolve()