# Restarting calculations from previously saved resultsΒΆ

The physical system in this example is similar to Evolution of a scattering state under a voltage pulse in a quantum dot. For time arguments on the right of the dashed vertical line, the result is calculated with the restarted wave function.

tkwant features highlighted

• restarting calculations from previously saved results

Saving

import pickle
import functools as ft
import numpy as np

import kwant
import tkwant

def circle(pos):
(x, y) = pos
return x ** 2 + y ** 2 < radius ** 2

def make_system(a=1, gamma=1.0):
"""Make a tight binding system on a single square lattice"""
# a is the lattice constant and gamma the hopping integral
# both set by default to 1 for simplicity.

lat = kwant.lattice.square(a, norbs=1)

syst = kwant.Builder()

# Define the quantum dot
syst[lat.shape(circle, (0, 0))] = 4 * gamma
syst[lat.neighbors()] = -gamma

lead[(lat(0, j) for j in range(-radius // 2 + 1, radius // 2))] = 4 * gamma

return syst

# time-dependent voltage on top of the leads
return 0.05 * (time - 10 * np.sin(0.1 * time))

syst = make_system()

# add a time-dependent voltage to lead 0 -- this is implemented
# by adding sites to the system at the interface with the lead and
# multiplying the hoppings to these sites by exp(-1j * faraday_flux(time))
lead_syst_hoppings = [(s, site) for site in extra_sites
for s in syst.neighbors(site)
if s not in extra_sites]

syst = syst.finalized()

# create an observable for calculating the current flowing from the left lead

tmax = 150
times = np.linspace(0, tmax, 100)

# create a time-dependent wavefunction that starts in a scattering state
# originating from the left lead
wavefunction_type = ft.partial(tkwant.onebody.WaveFunction.from_kwant,
kernel_type=tkwant.onebody.kernels.Scipy)
mode = 0
psi = tkwant.onebody.ScatteringStates(syst, energy=1., lead=0, tmax=tmax,
wavefunction_type=wavefunction_type)[mode]

# evolve forward in time, calculating the current
current = []
for time in times:
psi.evolve(time)
current.append(psi.evaluate(current_operator))

# now we want to "save" our progress. we also save the timesteps with the
# calculated currents and the operator.
pickle.dump((psi, times, current, current_operator), open('state.npy', "wb"))


Restarting

import pickle
import numpy as np
from matplotlib import pyplot as plt

# pickle only saves the name reference to "faraday_flux",
# this function must be explicitly available.
return 0.05 * (time - 10 * np.sin(0.1 * time))

# load the previously saved state and for convenience also the same operator.
psi, times, current, current_operator = pickle.load(open('state.npy', 'rb'))

tmax = times[-1]
times2 = np.linspace(tmax, 2 * tmax, 100)

for time in times2:
psi.evolve(time)
current.append(psi.evaluate(current_operator))

plt.plot(np.append(times, times2), current)
plt.plot([tmax] * 2, [min(current), max(current)], 'k--')
plt.xlabel(r'time $t$')
plt.ylabel(r'current $I(t)$')
plt.show()

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 151.5151515151515, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 153.03030303030303, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 154.54545454545453, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 156.06060606060606, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 157.57575757575756, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 159.0909090909091, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 160.6060606060606, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 162.12121212121212, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 163.63636363636363, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 165.15151515151516, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 166.66666666666666, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 168.1818181818182, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 169.6969696969697, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 171.21212121212122, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 172.72727272727272, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 174.24242424242425, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 175.75757575757575, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 177.27272727272728, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 178.78787878787878, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 180.3030303030303, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 181.8181818181818, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 183.33333333333334, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 184.84848484848484, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 186.36363636363637, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 187.87878787878788, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 189.39393939393938, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 190.9090909090909, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 192.42424242424244, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 193.93939393939394, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 195.45454545454544, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 196.96969696969697, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 198.4848484848485, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 200.0, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 201.5151515151515, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 203.03030303030303, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 204.54545454545456, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 206.06060606060606, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 207.57575757575756, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 209.0909090909091, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 210.60606060606062, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 212.12121212121212, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 213.63636363636363, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 215.15151515151516, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 216.66666666666669, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 218.1818181818182, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 219.6969696969697, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 221.21212121212122, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 222.72727272727272, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 224.24242424242425, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 225.75757575757575, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 227.27272727272725, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 228.78787878787878, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 230.3030303030303, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 231.8181818181818, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 233.33333333333331, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 234.84848484848484, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 236.36363636363637, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 237.87878787878788, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 239.39393939393938, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 240.9090909090909, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 242.42424242424244, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 243.93939393939394, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 245.45454545454544, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 246.96969696969697, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 248.4848484848485, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 250.0, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 251.5151515151515, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 253.03030303030303, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 254.54545454545456, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 256.06060606060606, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 257.57575757575756, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 259.0909090909091, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 260.6060606060606, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 262.1212121212121, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 263.6363636363636, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 265.1515151515151, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 266.6666666666667, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 268.1818181818182, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 269.6969696969697, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 271.21212121212125, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 272.72727272727275, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 274.24242424242425, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 275.75757575757575, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 277.27272727272725, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 278.78787878787875, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 280.3030303030303, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 281.8181818181818, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 283.33333333333337, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 284.8484848484849, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 286.3636363636364, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 287.8787878787879, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 289.3939393939394, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 290.9090909090909, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 292.42424242424244, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 293.93939393939394, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 295.45454545454544, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 296.969696969697, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 298.4848484848485, tmax= 150

WARNING:tkwant.onebody.onebody:435:rank=0: time > tmax; time= 300.0, tmax= 150