$x^2$ potential

In [1]:

    

import pickle
import numpy as np
import pycuda.gpuarray as gpuarray
from scipy.special import hyp1f1
import scipy.fftpack as fftpack
import pylab as plt
import time

#-------------------------------------------------------------------------------------
from pywignercuda_path import SetPyWignerCUDA_Path
SetPyWignerCUDA_Path()
from GPU_Wigner2D_GPitaevskii import *


    

In [2]:

    

%matplotlib inline


    

In [3]:

    

class frame( GPU_Wigner2D_GPitaevskii_Bloch ):
    def __init__ (self,V_Source, V_Drain, gaussianSeparation):
        X_gridDIM = 2*512
        P_gridDIM =   512
        
        X_amplitude  = 32
        P_amplitude  = 18
        
        hBar = 1.
        dt    = 0.01
        
        timeSteps =        1000
        skipFrames =         50
        
        mass = 1.      
        
        #
        self.xScale = 2.16074     #  with this scale the x axis reads in micro meters
        
        self.energyScale = 0.5    #  with this scale the energy reads in KHz
        
        self.timeScale = 2        #  with this scale the time reads in mili seconds
        
        # Potential and derivative of potential in computational units
        X2_constant = 0.075            # Enveloping Harmonic oscillator
        gaussianSeparation = 0.75
        V_Drain =  3.
        V_Source = 2.
        k = 5. # 1/width of Gaussian potentials
        
        self.GPitaevskiiCoeff = 1.
        
        kinematicString  = '0.5*p*p/{mass}'.format(mass=mass)
        
        potentialString  = '(-0.1+{0}*pow(x,2) + {V_Source}*exp(-{k}*(x+{d})*(x+{d})))*Heaviside(-x-{d})'.format(
                        X2_constant, d=gaussianSeparation, V_Source=V_Source, k=k)
        
        potentialString += ' +( -0.1+4*(x+{d})+{V_Source} )*Heaviside(x+{d})   '.format(
                        d=gaussianSeparation, V_Source=V_Source, k=k)
        
                
        self.SetTimeTrack( dt, timeSteps, skipFrames,
        fileName='/home/rcabrera/DATA/Wigner2D_GPitaevskii/ATransistor_Ground_'+str(V_Source)+'.hdf5' )
        
        GPU_Wigner2D_GPitaevskii_Bloch.__init__(self,
            X_gridDIM,P_gridDIM,X_amplitude,P_amplitude,hBar,mass,potentialString,kinematicString)

    def Set_Initial_Condition(self):
        """
        """
        self.W_init = np.exp( -(self.X+1)**2/30. - self.P**2/30.  )
        
        norm =  np.sum(self.W_init)*self.dX*self.dP
        
        self.W_init /= norm


    

In [4]:

    

chemicalPotential = 50 #computational units

V_Source = 60 - chemicalPotential
V_Drain = 70 - chemicalPotential

gaussianSeparation = 1.


instance = frame( V_Source, V_Drain, gaussianSeparation)
print '							'
print ' 	Wigner2D propagator with damping	'
print '							'
print ' energy scale = ', instance.energyScale

instance.Set_Initial_Condition()

#instance.Set_Initial_Condition_HalfHarmonicOscillator()

#instance.Set_Initial_Condition_Boltzmann_HalfHarmonicOscillator()


    

    




							
 	Wigner2D propagator with damping	
							
 energy scale =  0.5

In [5]:

    

#print 'Potential'
fig, ax = plt.subplots(figsize=(15, 5))
ax.plot( instance.X_range* instance.xScale , 
        instance.Potential(0,instance.X_range)* instance.energyScale ,'-' , color='r')


ax.set_xlim( -instance.X_amplitude*instance.xScale/4 , instance.X_amplitude*instance.xScale/4 )
ax.set_ylim(-0.1 , 3 )
ax.set_aspect(4)
axis_font = {'fontname':'Times', 'size':'24'}
ax.set_xlabel('$ x [\\mu m]$', **axis_font  )
ax.set_ylabel('$ V\, [Hz]$', **axis_font  )
ax.grid('on')


    

    




/usr/lib/pymodules/python2.7/matplotlib/font_manager.py:1236: UserWarning: findfont: Font family ['Times'] not found. Falling back to Bitstream Vera Sans
  (prop.get_family(), self.defaultFamily[fontext]))
/usr/lib/pymodules/python2.7/matplotlib/font_manager.py:1246: UserWarning: findfont: Could not match :family=Bitstream Vera Sans:style=normal:variant=normal:weight=normal:stretch=normal:size=24.0. Returning /usr/share/matplotlib/mpl-data/fonts/ttf/cmb10.ttf
  UserWarning)






    

In [6]:

    

init_time = time.time()

W = instance.Run()

print 'computation time = ', (time.time() - init_time)/60. , 'min'


    

    




 X_gridDIM =  1024    P_gridDIM =  512
 dx =  0.0625  dp =  0.0703125
 dLambda =  0.0981747704247  dTheta =  0.174532925199
  
         GPU memory Total        5.24945068359 GB
         GPU memory Free         5.09395599365 GB
Initial W Norm =  (1+0j)
         GPU memory Free  post gpu loading  5.07051849365 GB
 ------------------------------------------------------------------------------- 
     Split Operator Propagator  GPU with damping                                 
 ------------------------------------------------------------------------------- 
        
        
step  0
step  50
step  100
step  150
step  200
step  250
step  300
step  350
step  400
step  450
step  500
step  550
step  600
step  650
step  700
step  750
step  800
step  850
step  900
step  950
step  1000
computation time =  0.316726016998 min

In [7]:

    

plot_init = instance.PlotWignerFrame( instance.W_init , ((-15.,15) ,(-8,8))  , (-0.01,0.1) , (0,60,1) )


    

    




min =  4.26696594697e-23  max =  0.0106103651966
normalization =  1.0






    




/usr/lib/pymodules/python2.7/matplotlib/collections.py:608: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison
  if self._edgecolors_original != 'face':
/usr/lib/pymodules/python2.7/matplotlib/collections.py:548: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison
  if self._edgecolors == 'face':






    

In [8]:

    

plot_end = instance.PlotWignerFrame( instance.W_0 , ((-10.,5) ,(-8,8))  , (-0.3,0.3) , (0,60,0.5))


    

    




min =  -0.00550340069036  max =  0.313344145839
normalization =  1.0






    

In [9]:

    

fig, ax = plt.subplots(figsize=(12, 7))

ax.plot( instance.TotalEnergyHistory  ,
        '-' , label = '$Total Energy$' , linewidth=1.)



ax.legend(bbox_to_anchor=(1.05, 1), loc=2, prop={'size':22})
ax.set_ylim( 0 , 9)
ax.set_xlabel('t')
ax.set_ylabel(' ')
ax.grid();


    

In [10]:

    

fig, ax = plt.subplots(figsize=(12, 6))

ax.plot(  instance.NonLinearEnergyHistory
        , '-' , label = '$Non Linear Energy$' , linewidth=1.)


ax.legend(bbox_to_anchor=(1.05, 1), loc=2, prop={'size':22})
#ax.set_ylim( 1.19 , 1.21 )
ax.set_xlabel('t')
ax.set_ylabel(' ')
ax.grid();


    

In [11]:

    

fig, ax = plt.subplots(figsize=(12, 6))

ax.plot(  instance.purity , '-' , label = '$purity $',linewidth=2.)


ax.legend(bbox_to_anchor=(1.05, 1), loc=2, prop={'size':22})
#ax.set_ylim( 0.99 , 1.01 )
ax.set_xlabel('t')
ax.set_ylabel(' ')
ax.grid();


    

In [12]:

    

%time instance.Run_ExitedState1( )


    

    




         GPU memory Total        5.24945068359 GB
         GPU memory Free         5.08614349365 GB
Initial W Norm =  (1+0j)
         GPU memory Free  post gpu loading  5.05489349365 GB
 ------------------------------------------------------------------------------- 
     Split Operator Propagator  GPU with damping                                 
 ------------------------------------------------------------------------------- 
        
        
step  0
step  50
step  100
step  150
step  200
step  250
dt =  0.01
dt =  0.005
dt =  0.0025
dt =  0.00125
dt =  0.000625
dt =  0.0003125
dt =  0.00015625
dt =  7.8125e-05
dt =  3.90625e-05
dt =  1.953125e-05
dt =  9.765625e-06
dt =  4.8828125e-06
step  300
dt =  2.44140625e-06
dt =  1.220703125e-06
dt =  6.103515625e-07
dt =  3.0517578125e-07
dt =  1.52587890625e-07
dt =  7.62939453125e-08
dt =  3.81469726563e-08
dt =  1.90734863281e-08
dt =  9.53674316406e-09
dt =  4.76837158203e-09
dt =  2.38418579102e-09
dt =  1.19209289551e-09
dt =  5.96046447754e-10
dt =  2.98023223877e-10
dt =  1.49011611938e-10
dt =  7.45058059692e-11
dt =  3.72529029846e-11
dt =  1.86264514923e-11
dt =  9.31322574615e-12
dt =  4.65661287308e-12
dt =  2.32830643654e-12
dt =  1.16415321827e-12
dt =  5.82076609135e-13
dt =  2.91038304567e-13
dt =  1.45519152284e-13
dt =  7.27595761418e-14
dt =  3.63797880709e-14
dt =  1.81898940355e-14
dt =  9.09494701773e-15
dt =  4.54747350886e-15
dt =  2.27373675443e-15
dt =  1.13686837722e-15
dt =  5.68434188608e-16
dt =  2.84217094304e-16
dt =  1.42108547152e-16
step  350
dt =  7.1054273576e-17
dt =  3.5527136788e-17
dt =  1.7763568394e-17
dt =  8.881784197e-18
dt =  4.4408920985e-18
dt =  2.22044604925e-18
dt =  1.11022302463e-18
dt =  5.55111512313e-19
dt =  2.77555756156e-19
dt =  1.38777878078e-19
dt =  6.93889390391e-20
dt =  3.46944695195e-20
dt =  1.73472347598e-20
dt =  8.67361737988e-21
dt =  4.33680868994e-21
dt =  2.16840434497e-21
dt =  1.08420217249e-21
dt =  5.42101086243e-22
dt =  2.71050543121e-22
dt =  1.35525271561e-22
dt =  6.77626357803e-23
dt =  3.38813178902e-23
dt =  1.69406589451e-23
dt =  8.47032947254e-24
dt =  4.23516473627e-24
dt =  2.11758236814e-24
dt =  1.05879118407e-24
dt =  5.29395592034e-25
dt =  2.64697796017e-25
dt =  1.32348898008e-25
dt =  6.61744490042e-26
dt =  3.30872245021e-26
dt =  1.65436122511e-26
dt =  8.27180612553e-27
dt =  4.13590306277e-27
dt =  2.06795153138e-27
dt =  1.03397576569e-27
dt =  5.16987882846e-28
dt =  2.58493941423e-28
dt =  1.29246970711e-28
dt =  6.46234853557e-29
dt =  3.23117426779e-29
dt =  1.61558713389e-29
dt =  8.07793566946e-30
dt =  4.03896783473e-30
dt =  2.01948391737e-30
dt =  1.00974195868e-30
dt =  5.04870979341e-31
dt =  2.52435489671e-31
dt =  1.26217744835e-31
step  400
dt =  6.31088724177e-32
dt =  3.15544362088e-32
dt =  1.57772181044e-32
dt =  7.88860905221e-33
dt =  3.94430452611e-33
dt =  1.97215226305e-33
dt =  9.86076131526e-34
dt =  4.93038065763e-34
dt =  2.46519032882e-34
dt =  1.23259516441e-34
dt =  6.16297582204e-35
dt =  3.08148791102e-35
dt =  1.54074395551e-35
dt =  7.70371977755e-36
dt =  3.85185988877e-36
dt =  1.92592994439e-36
dt =  9.62964972194e-37
dt =  4.81482486097e-37
dt =  2.40741243048e-37
dt =  1.20370621524e-37
dt =  6.01853107621e-38
dt =  3.00926553811e-38
dt =  1.50463276905e-38
dt =  7.52316384526e-39
dt =  3.76158192263e-39
dt =  1.88079096132e-39
dt =  9.40395480658e-40
dt =  4.70197740329e-40
dt =  2.35098870164e-40
dt =  1.17549435082e-40
dt =  5.87747175411e-41
dt =  2.93873587706e-41
dt =  1.46936793853e-41
dt =  7.34683969264e-42
dt =  3.67341984632e-42
dt =  1.83670992316e-42
dt =  9.1835496158e-43
dt =  4.5917748079e-43
dt =  2.29588740395e-43
dt =  1.14794370197e-43
dt =  5.73971850987e-44
dt =  2.86985925494e-44
dt =  1.43492962747e-44
dt =  7.17464813734e-45
dt =  3.58732406867e-45
dt =  1.79366203434e-45
dt =  8.96831017168e-46
dt =  4.48415508584e-46
dt =  2.24207754292e-46
dt =  1.12103877146e-46
step  450
dt =  5.6051938573e-47
dt =  2.80259692865e-47
dt =  1.40129846432e-47
dt =  7.00649232162e-48
dt =  3.50324616081e-48
dt =  1.75162308041e-48
dt =  8.75811540203e-49
dt =  4.37905770102e-49
dt =  2.18952885051e-49
dt =  1.09476442525e-49
dt =  5.47382212627e-50
dt =  2.73691106313e-50
dt =  1.36845553157e-50
dt =  6.84227765784e-51
dt =  3.42113882892e-51
dt =  1.71056941446e-51
dt =  8.5528470723e-52
dt =  4.27642353615e-52
dt =  2.13821176807e-52
dt =  1.06910588404e-52
dt =  5.34552942018e-53
dt =  2.67276471009e-53
dt =  1.33638235505e-53
dt =  6.68191177523e-54
dt =  3.34095588762e-54
dt =  1.67047794381e-54
dt =  8.35238971904e-55
dt =  4.17619485952e-55
dt =  2.08809742976e-55
dt =  1.04404871488e-55
dt =  5.2202435744e-56
dt =  2.6101217872e-56
dt =  1.3050608936e-56
dt =  6.525304468e-57
dt =  3.262652234e-57
dt =  1.631326117e-57
dt =  8.156630585e-58
dt =  4.0783152925e-58
dt =  2.03915764625e-58
dt =  1.01957882312e-58
dt =  5.09789411562e-59
dt =  2.54894705781e-59
dt =  1.27447352891e-59
dt =  6.37236764453e-60
dt =  3.18618382226e-60
dt =  1.59309191113e-60
dt =  7.96545955566e-61
dt =  3.98272977783e-61
dt =  1.99136488892e-61
dt =  9.95682444458e-62
step  500
dt =  4.97841222229e-62
dt =  2.48920611114e-62
dt =  1.24460305557e-62
dt =  6.22301527786e-63
dt =  3.11150763893e-63
dt =  1.55575381947e-63
dt =  7.77876909733e-64
dt =  3.88938454866e-64
dt =  1.94469227433e-64
dt =  9.72346137166e-65
dt =  4.86173068583e-65
dt =  2.43086534291e-65
dt =  1.21543267146e-65
dt =  6.07716335729e-66
dt =  3.03858167864e-66
dt =  1.51929083932e-66
dt =  7.59645419661e-67
dt =  3.7982270983e-67
dt =  1.89911354915e-67
dt =  9.49556774576e-68
dt =  4.74778387288e-68
dt =  2.37389193644e-68
dt =  1.18694596822e-68
dt =  5.9347298411e-69
dt =  2.96736492055e-69
dt =  1.48368246027e-69
dt =  7.41841230137e-70
dt =  3.70920615069e-70
dt =  1.85460307534e-70
dt =  9.27301537672e-71
dt =  4.63650768836e-71
dt =  2.31825384418e-71
dt =  1.15912692209e-71
dt =  5.79563461045e-72
dt =  2.89781730522e-72
dt =  1.44890865261e-72
dt =  7.24454326306e-73
dt =  3.62227163153e-73
dt =  1.81113581577e-73
dt =  9.05567907883e-74
dt =  4.52783953941e-74
dt =  2.26391976971e-74
dt =  1.13195988485e-74
dt =  5.65979942427e-75
dt =  2.82989971213e-75
dt =  1.41494985607e-75
dt =  7.07474928033e-76
dt =  3.53737464017e-76
dt =  1.76868732008e-76
dt =  8.84343660042e-77
step  550
dt =  4.42171830021e-77
dt =  2.2108591501e-77
dt =  1.10542957505e-77
dt =  5.52714787526e-78
dt =  2.76357393763e-78
dt =  1.38178696882e-78
dt =  6.90893484408e-79
dt =  3.45446742204e-79
dt =  1.72723371102e-79
dt =  8.63616855509e-80
dt =  4.31808427755e-80
dt =  2.15904213877e-80
dt =  1.07952106939e-80
dt =  5.39760534693e-81
dt =  2.69880267347e-81
dt =  1.34940133673e-81
dt =  6.74700668367e-82
dt =  3.37350334183e-82
dt =  1.68675167092e-82
dt =  8.43375835458e-83
dt =  4.21687917729e-83
dt =  2.10843958865e-83
dt =  1.05421979432e-83
dt =  5.27109897162e-84
dt =  2.63554948581e-84
dt =  1.3177747429e-84
dt =  6.58887371452e-85
dt =  3.29443685726e-85
dt =  1.64721842863e-85
dt =  8.23609214315e-86
dt =  4.11804607157e-86
dt =  2.05902303579e-86
dt =  1.02951151789e-86
dt =  5.14755758947e-87
dt =  2.57377879473e-87
dt =  1.28688939737e-87
dt =  6.43444698684e-88
dt =  3.21722349342e-88
dt =  1.60861174671e-88
dt =  8.04305873354e-89
dt =  4.02152936677e-89
dt =  2.01076468339e-89
dt =  1.00538234169e-89
dt =  5.02691170846e-90
dt =  2.51345585423e-90
dt =  1.25672792712e-90
dt =  6.28363963558e-91
dt =  3.14181981779e-91
dt =  1.5709099089e-91
dt =  7.85454954448e-92
step  600
dt =  3.92727477224e-92
dt =  1.96363738612e-92
dt =  9.8181869306e-93
dt =  4.9090934653e-93
dt =  2.45454673265e-93
dt =  1.22727336632e-93
dt =  6.13636683162e-94
dt =  3.06818341581e-94
dt =  1.53409170791e-94
dt =  7.67045853953e-95
dt =  3.83522926976e-95
dt =  1.91761463488e-95
dt =  9.58807317441e-96
dt =  4.7940365872e-96
dt =  2.3970182936e-96
dt =  1.1985091468e-96
dt =  5.99254573401e-97
dt =  2.996272867e-97
dt =  1.4981364335e-97
dt =  7.49068216751e-98
dt =  3.74534108375e-98
dt =  1.87267054188e-98
dt =  9.36335270938e-99
dt =  4.68167635469e-99
dt =  2.34083817735e-99
dt =  1.17041908867e-99
dt =  5.85209544337e-100
dt =  2.92604772168e-100
dt =  1.46302386084e-100
dt =  7.31511930421e-101
dt =  3.6575596521e-101
dt =  1.82877982605e-101
dt =  9.14389913026e-102
dt =  4.57194956513e-102
dt =  2.28597478256e-102
dt =  1.14298739128e-102
dt =  5.71493695641e-103
dt =  2.85746847821e-103
dt =  1.4287342391e-103
dt =  7.14367119551e-104
dt =  3.57183559776e-104
dt =  1.78591779888e-104
dt =  8.92958899439e-105
dt =  4.4647944972e-105
dt =  2.2323972486e-105
dt =  1.1161986243e-105
dt =  5.5809931215e-106
dt =  2.79049656075e-106
dt =  1.39524828037e-106
dt =  6.97624140187e-107
step  650
dt =  3.48812070093e-107
dt =  1.74406035047e-107
dt =  8.72030175234e-108
dt =  4.36015087617e-108
dt =  2.18007543808e-108
dt =  1.09003771904e-108
dt =  5.45018859521e-109
dt =  2.72509429761e-109
dt =  1.3625471488e-109
dt =  6.81273574401e-110
dt =  3.40636787201e-110
dt =  1.703183936e-110
dt =  8.51591968002e-111
dt =  4.25795984001e-111
dt =  2.12897992e-111
dt =  1.06448996e-111
dt =  5.32244980001e-112
dt =  2.66122490001e-112
dt =  1.33061245e-112
dt =  6.65306225001e-113
dt =  3.32653112501e-113
dt =  1.6632655625e-113
dt =  8.31632781252e-114
dt =  4.15816390626e-114
dt =  2.07908195313e-114
dt =  1.03954097656e-114
dt =  5.19770488282e-115
dt =  2.59885244141e-115
dt =  1.29942622071e-115
dt =  6.49713110353e-116
dt =  3.24856555176e-116
dt =  1.62428277588e-116
dt =  8.12141387941e-117
dt =  4.06070693971e-117
dt =  2.03035346985e-117
dt =  1.01517673493e-117
dt =  5.07588367463e-118
dt =  2.53794183732e-118
dt =  1.26897091866e-118
dt =  6.34485459329e-119
dt =  3.17242729664e-119
dt =  1.58621364832e-119
dt =  7.93106824161e-120
dt =  3.96553412081e-120
dt =  1.9827670604e-120
dt =  9.91383530201e-121
dt =  4.95691765101e-121
dt =  2.4784588255e-121
dt =  1.23922941275e-121
dt =  6.19614706376e-122
step  700
dt =  3.09807353188e-122
dt =  1.54903676594e-122
dt =  7.7451838297e-123
dt =  3.87259191485e-123
dt =  1.93629595742e-123
dt =  9.68147978712e-124
dt =  4.84073989356e-124
dt =  2.42036994678e-124
dt =  1.21018497339e-124
dt =  6.05092486695e-125
dt =  3.02546243348e-125
dt =  1.51273121674e-125
dt =  7.56365608369e-126
dt =  3.78182804185e-126
dt =  1.89091402092e-126
dt =  9.45457010461e-127
dt =  4.72728505231e-127
dt =  2.36364252615e-127
dt =  1.18182126308e-127
dt =  5.90910631538e-128
dt =  2.95455315769e-128
dt =  1.47727657885e-128
dt =  7.38638289423e-129
dt =  3.69319144711e-129
dt =  1.84659572356e-129
dt =  9.23297861779e-130
dt =  4.61648930889e-130
dt =  2.30824465445e-130
dt =  1.15412232722e-130
dt =  5.77061163612e-131
dt =  2.88530581806e-131
dt =  1.44265290903e-131
dt =  7.21326454515e-132
dt =  3.60663227257e-132
dt =  1.80331613629e-132
dt =  9.01658068143e-133
dt =  4.50829034072e-133
dt =  2.25414517036e-133
dt =  1.12707258518e-133
dt =  5.63536292589e-134
dt =  2.81768146295e-134
dt =  1.40884073147e-134
dt =  7.04420365737e-135
dt =  3.52210182868e-135
dt =  1.76105091434e-135
dt =  8.80525457171e-136
dt =  4.40262728586e-136
dt =  2.20131364293e-136
dt =  1.10065682146e-136
dt =  5.50328410732e-137
step  750
dt =  2.75164205366e-137
dt =  1.37582102683e-137
dt =  6.87910513415e-138
dt =  3.43955256707e-138
dt =  1.71977628354e-138
dt =  8.59888141769e-139
dt =  4.29944070884e-139
dt =  2.14972035442e-139
dt =  1.07486017721e-139
dt =  5.37430088605e-140
dt =  2.68715044303e-140
dt =  1.34357522151e-140
dt =  6.71787610757e-141
dt =  3.35893805378e-141
dt =  1.67946902689e-141
dt =  8.39734513446e-142
dt =  4.19867256723e-142
dt =  2.09933628361e-142
dt =  1.04966814181e-142
dt =  5.24834070904e-143
dt =  2.62417035452e-143
dt =  1.31208517726e-143
dt =  6.5604258863e-144
dt =  3.28021294315e-144
dt =  1.64010647157e-144
dt =  8.20053235787e-145
dt =  4.10026617893e-145
dt =  2.05013308947e-145
dt =  1.02506654473e-145
dt =  5.12533272367e-146
dt =  2.56266636183e-146
dt =  1.28133318092e-146
dt =  6.40666590459e-147
dt =  3.20333295229e-147
dt =  1.60166647615e-147
dt =  8.00833238073e-148
dt =  4.00416619037e-148
dt =  2.00208309518e-148
dt =  1.00104154759e-148
dt =  5.00520773796e-149
dt =  2.50260386898e-149
dt =  1.25130193449e-149
dt =  6.25650967245e-150
dt =  3.12825483622e-150
dt =  1.56412741811e-150
dt =  7.82063709056e-151
dt =  3.91031854528e-151
dt =  1.95515927264e-151
dt =  9.7757963632e-152
dt =  4.8878981816e-152
step  800
dt =  2.4439490908e-152
dt =  1.2219745454e-152
dt =  6.109872727e-153
dt =  3.0549363635e-153
dt =  1.52746818175e-153
dt =  7.63734090875e-154
dt =  3.81867045437e-154
dt =  1.90933522719e-154
dt =  9.54667613594e-155
dt =  4.77333806797e-155
dt =  2.38666903398e-155
dt =  1.19333451699e-155
dt =  5.96667258496e-156
dt =  2.98333629248e-156
dt =  1.49166814624e-156
dt =  7.4583407312e-157
dt =  3.7291703656e-157
dt =  1.8645851828e-157
dt =  9.322925914e-158
dt =  4.661462957e-158
dt =  2.3307314785e-158
dt =  1.16536573925e-158
dt =  5.82682869625e-159
dt =  2.91341434813e-159
dt =  1.45670717406e-159
dt =  7.28353587031e-160
dt =  3.64176793516e-160
dt =  1.82088396758e-160
dt =  9.10441983789e-161
dt =  4.55220991895e-161
dt =  2.27610495947e-161
dt =  1.13805247974e-161
dt =  5.69026239868e-162
dt =  2.84513119934e-162
dt =  1.42256559967e-162
dt =  7.11282799835e-163
dt =  3.55641399918e-163
dt =  1.77820699959e-163
dt =  8.89103499794e-164
dt =  4.44551749897e-164
dt =  2.22275874949e-164
dt =  1.11137937474e-164
dt =  5.55689687371e-165
dt =  2.77844843686e-165
dt =  1.38922421843e-165
dt =  6.94612109214e-166
dt =  3.47306054607e-166
dt =  1.73653027304e-166
dt =  8.68265136518e-167
dt =  4.34132568259e-167
step  850
dt =  2.17066284129e-167
dt =  1.08533142065e-167
dt =  5.42665710324e-168
dt =  2.71332855162e-168
dt =  1.35666427581e-168
dt =  6.78332137904e-169
dt =  3.39166068952e-169
dt =  1.69583034476e-169
dt =  8.4791517238e-170
dt =  4.2395758619e-170
dt =  2.11978793095e-170
dt =  1.05989396548e-170
dt =  5.29946982738e-171
dt =  2.64973491369e-171
dt =  1.32486745684e-171
dt =  6.62433728422e-172
dt =  3.31216864211e-172
dt =  1.65608432106e-172
dt =  8.28042160528e-173
dt =  4.14021080264e-173
dt =  2.07010540132e-173
dt =  1.03505270066e-173
dt =  5.1752635033e-174
dt =  2.58763175165e-174
dt =  1.29381587582e-174
dt =  6.46907937912e-175
dt =  3.23453968956e-175
dt =  1.61726984478e-175
dt =  8.0863492239e-176
dt =  4.04317461195e-176
dt =  2.02158730598e-176
dt =  1.01079365299e-176
dt =  5.05396826494e-177
dt =  2.52698413247e-177
dt =  1.26349206624e-177
dt =  6.31746033118e-178
dt =  3.15873016559e-178
dt =  1.57936508279e-178
dt =  7.89682541397e-179
dt =  3.94841270698e-179
dt =  1.97420635349e-179
dt =  9.87103176746e-180
dt =  4.93551588373e-180
dt =  2.46775794187e-180
dt =  1.23387897093e-180
dt =  6.16939485466e-181
dt =  3.08469742733e-181
dt =  1.54234871367e-181
dt =  7.71174356833e-182
dt =  3.85587178416e-182
step  900
dt =  1.92793589208e-182
dt =  9.63967946041e-183
dt =  4.81983973021e-183
dt =  2.4099198651e-183
dt =  1.20495993255e-183
dt =  6.02479966276e-184
dt =  3.01239983138e-184
dt =  1.50619991569e-184
dt =  7.53099957845e-185
dt =  3.76549978922e-185
dt =  1.88274989461e-185
dt =  9.41374947306e-186
dt =  4.70687473653e-186
dt =  2.35343736826e-186
dt =  1.17671868413e-186
dt =  5.88359342066e-187
dt =  2.94179671033e-187
dt =  1.47089835517e-187
dt =  7.35449177583e-188
dt =  3.67724588791e-188
dt =  1.83862294396e-188
dt =  9.19311471978e-189
dt =  4.59655735989e-189
dt =  2.29827867995e-189
dt =  1.14913933997e-189
dt =  5.74569669986e-190
dt =  2.87284834993e-190
dt =  1.43642417497e-190
dt =  7.18212087483e-191
dt =  3.59106043742e-191
dt =  1.79553021871e-191
dt =  8.97765109354e-192
dt =  4.48882554677e-192
dt =  2.24441277338e-192
dt =  1.12220638669e-192
dt =  5.61103193346e-193
dt =  2.80551596673e-193
dt =  1.40275798337e-193
dt =  7.01378991683e-194
dt =  3.50689495841e-194
dt =  1.75344747921e-194
dt =  8.76723739603e-195
dt =  4.38361869802e-195
dt =  2.19180934901e-195
dt =  1.0959046745e-195
dt =  5.47952337252e-196
dt =  2.73976168626e-196
dt =  1.36988084313e-196
dt =  6.84940421565e-197
dt =  3.42470210783e-197
step  950
dt =  1.71235105391e-197
dt =  8.56175526956e-198
dt =  4.28087763478e-198
dt =  2.14043881739e-198
dt =  1.0702194087e-198
dt =  5.35109704348e-199
dt =  2.67554852174e-199
dt =  1.33777426087e-199
dt =  6.68887130435e-200
dt =  3.34443565217e-200
dt =  1.67221782609e-200
dt =  8.36108913043e-201
dt =  4.18054456522e-201
dt =  2.09027228261e-201
dt =  1.0451361413e-201
dt =  5.22568070652e-202
dt =  2.61284035326e-202
dt =  1.30642017663e-202
dt =  6.53210088315e-203
dt =  3.26605044158e-203
dt =  1.63302522079e-203
dt =  8.16512610394e-204
dt =  4.08256305197e-204
dt =  2.04128152598e-204
dt =  1.02064076299e-204
dt =  5.10320381496e-205
dt =  2.55160190748e-205
dt =  1.27580095374e-205
dt =  6.3790047687e-206
dt =  3.18950238435e-206
dt =  1.59475119218e-206
dt =  7.97375596088e-207
dt =  3.98687798044e-207
dt =  1.99343899022e-207
dt =  9.9671949511e-208
dt =  4.98359747555e-208
dt =  2.49179873777e-208
dt =  1.24589936889e-208
dt =  6.22949684444e-209
dt =  3.11474842222e-209
dt =  1.55737421111e-209
dt =  7.78687105554e-210
dt =  3.89343552777e-210
dt =  1.94671776389e-210
dt =  9.73358881943e-211
dt =  4.86679440972e-211
dt =  2.43339720486e-211
dt =  1.21669860243e-211
dt =  6.08349301214e-212
dt =  3.04174650607e-212
step  1000
dt =  1.52087325304e-212
CPU times: user 13.2 s, sys: 6.54 s, total: 19.7 s
Wall time: 19.8 s






    
Out[12]:





0

In [15]:

    

instance.PlotWignerFrame( instance.W_1 , ((-10.,5) ,(-8,8))  , (-0.3,0.3) , (0,60,0.5));


    

    




min =  -0.304102966884  max =  0.157037491253
normalization =  1.0






    

In [ ]: