Commit 6d0e0aab authored by Joseph Weston's avatar Joseph Weston

remove old tutorial script machinery

parent f1929ee7
This directory contains the code examples from the documentation.
Most scripts are present in three related but different versions that
correspond to three different usages.
* Subdirectory 'figure': scripts used for figure generation. Figures
are not displayed but saved to disk.
* Subdirectory 'include': scripts that display figures on screen.
They contain commented marks for including snippets in the
documentation.
* Subdirectory 'download': complete scripts to be offered for download
by readers. Like 'include' but with the include marks removed.
Most scripts are extracted from corresponding '*.py.diff' files inside
'figure/'. These are patches from the 'include' version to the
'figure' version. The patches include complete context and as such
can be used to recreate both files. It's these patches that are kept
under version control.
running 'make html' or 'make latex' inside '/doc' will automatically
update all these scripts according to the following scheme:
---->------------->------
/ \
/ download/x.py \
figure/x.py.diff ^ \
^ \ | \
| -> include/x.py ---(patch)---> figure/x.py
| | |
| | |
\ v /
----<----------(diff)--------------<--------
Thus, it is possible to update figure/x.py.diff, include/x.py or
figure/x.py and any changes will be propagated automatically when
'make' is run. (Only download/x.py is a dead end.) The user will be
informed about any conflicts. The makefile will only update files
that are older than their sources and is careful to propagate time
stamps in order to avoid infinite loops.
Editing only figure/x.py.diff is a sure way to avoid any conflicts.
################################################################
# Make matplotlib work without X11
################################################################
import matplotlib
matplotlib.use('Agg')
################################################################
# Prepend Kwant's build directory to sys.path
################################################################
import sys
from distutils.util import get_platform
sys.path.insert(0, "../../../../build/lib.{0}-{1}.{2}".format(
get_platform(), *sys.version_info[:2]))
################################################################
# Define constants for plotting
################################################################
pt_to_in = 1. / 72.
# Default width of figures in pts
figwidth_pt = 600
figwidth_in = figwidth_pt * pt_to_in
# Width for smaller figures
figwidth_small_pt = 400
figwidth_small_in = figwidth_small_pt * pt_to_in
# Sizes for matplotlib figures
mpl_width_in = figwidth_pt * pt_to_in
mpl_label_size = None # font sizes in points
mpl_tick_size = None
# dpi for conversion from inches
dpi = 90
@@ -1,127 +1,196 @@
# Tutorial 2.3.3. Nontrivial shapes
# =================================
#
# Physics background
# ------------------
# Flux-dependent transmission through a quantum ring
#
# Kwant features highlighted
# --------------------------
# - More complex shapes with lattices
# - Allows for discussion of subtleties of `attach_lead` (not in the
# example, but in the tutorial main text)
# - Modifcations of hoppings/sites after they have been added
+import _defs
from cmath import exp
from math import pi
import kwant
# For plotting
from matplotlib import pyplot
#HIDDEN_BEGIN_eusz
def make_system(a=1, t=1.0, W=10, r1=10, r2=20):
# Start with an empty tight-binding system and a single square lattice.
# `a` is the lattice constant (by default set to 1 for simplicity).
lat = kwant.lattice.square(a)
syst = kwant.Builder()
#### Define the scattering region. ####
# Now, we aim for a more complex shape, namely a ring (or annulus)
def ring(pos):
(x, y) = pos
rsq = x ** 2 + y ** 2
return (r1 ** 2 < rsq < r2 ** 2)
#HIDDEN_END_eusz
# and add the corresponding lattice points using the `shape`-function
#HIDDEN_BEGIN_lcak
syst[lat.shape(ring, (0, r1 + 1))] = 4 * t
syst[lat.neighbors()] = -t
#HIDDEN_END_lcak
# In order to introduce a flux through the ring, we introduce a phase on
# the hoppings on the line cut through one of the arms. Since we want to
# change the flux without modifying the Builder instance repeatedly, we
# define the modified hoppings as a function that takes the flux as its
# parameter phi.
#HIDDEN_BEGIN_lvkt
def hopping_phase(site1, site2, phi):
return -t * exp(1j * phi)
def crosses_branchcut(hop):
ix0, iy0 = hop[0].tag
# builder.HoppingKind with the argument (1, 0) below
# returns hoppings ordered as ((i+1, j), (i, j))
return iy0 < 0 and ix0 == 1 # ix1 == 0 then implied
# Modify only those hopings in x-direction that cross the branch cut
def hops_across_cut(syst):
for hop in kwant.builder.HoppingKind((1, 0), lat, lat)(syst):
if crosses_branchcut(hop):
yield hop
syst[hops_across_cut] = hopping_phase
#HIDDEN_END_lvkt
#### Define the leads. ####
# left lead
#HIDDEN_BEGIN_qwgr
sym_lead = kwant.TranslationalSymmetry((-a, 0))
lead = kwant.Builder(sym_lead)
def lead_shape(pos):
(x, y) = pos
return (-W / 2 < y < W / 2)
lead[lat.shape(lead_shape, (0, 0))] = 4 * t
lead[lat.neighbors()] = -t
#HIDDEN_END_qwgr
#### Attach the leads and return the system. ####
#HIDDEN_BEGIN_skbz
syst.attach_lead(lead)
syst.attach_lead(lead.reversed())
#HIDDEN_END_skbz
return syst
+def make_system_note1(a=1, t=1.0, W=10, r1=10, r2=20):
+ lat = kwant.lattice.square(a)
+ syst = kwant.Builder()
+ def ring(pos):
+ (x, y) = pos
+ rsq = x**2 + y**2
+ return ( r1**2 < rsq < r2**2)
+ syst[lat.shape(ring, (0, 11))] = 4 * t
+ syst[lat.neighbors()] = -t
+ sym_lead0 = kwant.TranslationalSymmetry((-a, 0))
+ lead0 = kwant.Builder(sym_lead0)
+ def lead_shape(pos):
+ (x, y) = pos
+ return (-1 < x < 1) and ( 0.5 * W < y < 1.5 * W )
+ lead0[lat.shape(lead_shape, (0, W))] = 4 * t
+ lead0[lat.neighbors()] = -t
+ lead1 = lead0.reversed()
+ syst.attach_lead(lead0)
+ syst.attach_lead(lead1)
+ return syst
+
+
+def make_system_note2(a=1, t=1.0, W=10, r1=10, r2=20):
+ lat = kwant.lattice.square(a)
+ syst = kwant.Builder()
+ def ring(pos):
+ (x, y) = pos
+ rsq = x**2 + y**2
+ return ( r1**2 < rsq < r2**2)
+ syst[lat.shape(ring, (0, 11))] = 4 * t
+ syst[lat.neighbors()] = -t
+ sym_lead0 = kwant.TranslationalSymmetry((-a, 0))
+ lead0 = kwant.Builder(sym_lead0)
+ def lead_shape(pos):
+ (x, y) = pos
+ return (-1 < x < 1) and ( -W/2 < y < W/2 )
+ lead0[lat.shape(lead_shape, (0, 0))] = 4 * t
+ lead0[lat.neighbors()] = -t
+ lead1 = lead0.reversed()
+ syst.attach_lead(lead0)
+ syst.attach_lead(lead1, lat(0, 0))
+ return syst
+
+
def plot_conductance(syst, energy, fluxes):
# compute conductance
normalized_fluxes = [flux / (2 * pi) for flux in fluxes]
data = []
for flux in fluxes:
smatrix = kwant.smatrix(syst, energy, params=dict(phi=flux))
data.append(smatrix.transmission(1, 0))
- pyplot.figure()
+ fig = pyplot.figure()
pyplot.plot(normalized_fluxes, data)
- pyplot.xlabel("flux [flux quantum]")
- pyplot.ylabel("conductance [e^2/h]")
- pyplot.show()
+ pyplot.xlabel("flux [flux quantum]",
+ fontsize=_defs.mpl_label_size)
+ pyplot.ylabel("conductance [e^2/h]",
+ fontsize=_defs.mpl_label_size)
+ pyplot.setp(fig.get_axes()[0].get_xticklabels(),
+ fontsize=_defs.mpl_tick_size)
+ pyplot.setp(fig.get_axes()[0].get_yticklabels(),
+ fontsize=_defs.mpl_tick_size)
+ fig.set_size_inches(_defs.mpl_width_in, _defs.mpl_width_in * 3. / 4.)
+ fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
+ fig.savefig("ab_ring_result.pdf")
+ fig.savefig("ab_ring_result.png", dpi=_defs.dpi)
def main():
syst = make_system()
# Check that the system looks as intended.
- kwant.plot(syst)
+ size = (_defs.figwidth_in, _defs.figwidth_in)
+ for extension in ('pdf', 'png'):
+ kwant.plot(syst, file="ab_ring_syst." + extension,
+ fig_size=size, dpi=_defs.dpi)
+
# Finalize the system.
syst = syst.finalized()
# We should see a conductance that is periodic with the flux quantum
plot_conductance(syst, energy=0.15, fluxes=[0.01 * i * 3 * 2 * pi
for i in range(100)])
+ # Finally, some plots needed for the notes
+ syst = make_system_note1()
+ for extension in ('pdf', 'png'):
+ kwant.plot(syst, file="ab_ring_note1." + extension,
+ fig_size=size, dpi=_defs.dpi)
+ syst = make_system_note2()
+ for extension in ('pdf', 'png'):
+ kwant.plot(syst, file="ab_ring_note2." + extension,
+ fig_size=size, dpi=_defs.dpi)
+
+
# Call the main function if the script gets executed (as opposed to imported).
# See <http://docs.python.org/library/__main__.html>.
if __name__ == '__main__':
main()
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This diff is collapsed.
@@ -1,52 +1,62 @@
# Tutorial 2.4.1. Band structure calculations
# ===========================================
#
# Physics background
# ------------------
# band structure of a simple quantum wire in tight-binding approximation
#
# Kwant features highlighted
# --------------------------
# - Computing the band structure of a finalized lead.
+import _defs
import kwant
# For plotting.
from matplotlib import pyplot
#HIDDEN_BEGIN_zxip
def make_lead(a=1, t=1.0, W=10):
# Start with an empty lead with a single square lattice
lat = kwant.lattice.square(a)
sym_lead = kwant.TranslationalSymmetry((-a, 0))
lead = kwant.Builder(sym_lead)
# build up one unit cell of the lead, and add the hoppings
# to the next unit cell
for j in range(W):
lead[lat(0, j)] = 4 * t
if j > 0:
lead[lat(0, j), lat(0, j - 1)] = -t
lead[lat(1, j), lat(0, j)] = -t
return lead
#HIDDEN_END_zxip
#HIDDEN_BEGIN_pejz
def main():
lead = make_lead().finalized()
- kwant.plotter.bands(lead, show=False)
- pyplot.xlabel("momentum [(lattice constant)^-1]")
- pyplot.ylabel("energy [t]")
- pyplot.show()
+ fig = kwant.plotter.bands(lead, show=False)
+ pyplot.xlabel("momentum [(lattice constant)^-1]",
+ fontsize=_defs.mpl_label_size)
+ pyplot.ylabel("energy [t]", fontsize=_defs.mpl_label_size)
+ pyplot.setp(fig.get_axes()[0].get_xticklabels(),
+ fontsize=_defs.mpl_tick_size)
+ pyplot.setp(fig.get_axes()[0].get_yticklabels(),
+ fontsize=_defs.mpl_tick_size)
+ fig.set_size_inches(_defs.mpl_width_in, _defs.mpl_width_in * 3. / 4.)
+ fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
+ for extension in ('pdf', 'png'):
+ fig.savefig("band_structure_result." + extension, dpi=_defs.dpi)
+
#HIDDEN_END_pejz
# Call the main function if the script gets executed (as opposed to imported).
# See <http://docs.python.org/library/__main__.html>.
if __name__ == '__main__':
main()
@@ -1,144 +1,161 @@
# Tutorial 2.4.2. Closed systems
# ==============================
#
# Physics background
# ------------------
# Fock-darwin spectrum of a quantum dot (energy spectrum in
# as a function of a magnetic field)
#
# Kwant features highlighted
# --------------------------
# - Use of `hamiltonian_submatrix` in order to obtain a Hamiltonian
# matrix.
+import _defs
from cmath import exp
import numpy as np
import kwant
# For eigenvalue computation
#HIDDEN_BEGIN_tibv
import scipy.sparse.linalg as sla
#HIDDEN_END_tibv
# For plotting
from matplotlib import pyplot
def make_system(a=1, t=1.0, r=10):
# Start with an empty tight-binding system and a single square lattice.
# `a` is the lattice constant (by default set to 1 for simplicity).
#HIDDEN_BEGIN_qlyd
lat = kwant.lattice.square(a, norbs=1)
syst = kwant.Builder()
# Define the quantum dot
def circle(pos):
(x, y) = pos
rsq = x ** 2 + y ** 2
return rsq < r ** 2
def hopx(site1, site2, B):
# The magnetic field is controlled by the parameter B
y = site1.pos[1]
return -t * exp(-1j * B * y)
syst[lat.shape(circle, (0, 0))] = 4 * t
# hoppings in x-direction
syst[kwant.builder.HoppingKind((1, 0), lat, lat)] = hopx
# hoppings in y-directions
syst[kwant.builder.HoppingKind((0, 1), lat, lat)] = -t
# It's a closed system for a change, so no leads
return syst
#HIDDEN_END_qlyd
#HIDDEN_BEGIN_yvri
def plot_spectrum(syst, Bfields):
energies = []
for B in Bfields:
# Obtain the Hamiltonian as a sparse matrix
ham_mat = syst.hamiltonian_submatrix(params=dict(B=B), sparse=True)
# we only calculate the 15 lowest eigenvalues
ev = sla.eigsh(ham_mat.tocsc(), k=15, sigma=0,
return_eigenvectors=False)
energies.append(ev)
- pyplot.figure()
+ fig = pyplot.figure()
pyplot.plot(Bfields, energies)
- pyplot.xlabel("magnetic field [arbitrary units]")
- pyplot.ylabel("energy [t]")
- pyplot.show()
+ pyplot.xlabel("magnetic field [arbitrary units]",
+ fontsize=_defs.mpl_label_size)
+ pyplot.ylabel("energy [t]", fontsize=_defs.mpl_label_size)
+ pyplot.setp(fig.get_axes()[0].get_xticklabels(),
+ fontsize=_defs.mpl_tick_size)
+ pyplot.setp(fig.get_axes()[0].get_yticklabels(),
+ fontsize=_defs.mpl_tick_size)
+ fig.set_size_inches(_defs.mpl_width_in, _defs.mpl_width_in * 3. / 4.)
+ fig.subplots_adjust(left=0.15, right=0.95, top=0.95, bottom=0.15)
+ for extension in ('pdf', 'png'):
+ fig.savefig("closed_system_result." + extension, dpi=_defs.dpi)
#HIDDEN_END_yvri
def sorted_eigs(ev):
evals, evecs = ev
evals, evecs = map(np.array, zip(*sorted(zip(evals, evecs.transpose()))))
return evals, evecs.transpose()
#HIDDEN_BEGIN_wave
def plot_wave_function(syst, B=0.001):
+ size = (_defs.figwidth_in, _defs.figwidth_in)
+
# Calculate the wave functions in the system.
ham_mat = syst.hamiltonian_submatrix(sparse=True, params=dict(B=B))
evals, evecs = sorted_eigs(sla.eigsh(ham_mat.tocsc(), k=20, sigma=0))
# Plot the probability density of the 10th eigenmode.
- kwant.plotter.map(syst, np.abs(evecs[:, 9])**2,
- colorbar=False, oversampling=1)
+ for extension in ('pdf', 'png'):
+ kwant.plotter.map(
+ syst, np.abs(evecs[:, 9])**2, colorbar=False, oversampling=1,
+ file="closed_system_eigenvector." + extension,
+ fig_size=size, dpi=_defs.dpi)
#HIDDEN_END_wave
#HIDDEN_BEGIN_current
def plot_current(syst, B=0.001):
+ size = (_defs.figwidth_in, _defs.figwidth_in)
+
# Calculate the wave functions in the system.
ham_mat = syst.hamiltonian_submatrix(sparse=True, params=dict(B=B))
evals, evecs = sorted_eigs(sla.eigsh(ham_mat.tocsc(), k=20, sigma=0))
# Calculate and plot the local current of the 10th eigenmode.
J = kwant.operator.Current(syst)
current = J(evecs[:, 9], params=dict(B=B))
- kwant.plotter.current(syst, current, colorbar=False)
+ for extension in ('pdf', 'png'):
+ kwant.plotter.current(
+ syst, current, colorbar=False,
+ file="closed_system_current." + extension,
+ fig_size=size, dpi=_defs.dpi)
#HIDDEN_END_current
def main():
syst = make_system()
- # Check that the system looks as intended.
- kwant.plot(syst)
-
# Finalize the system.
syst = syst.finalized()
# The following try-clause can be removed once SciPy 0.9 becomes uncommon.
try:
# We should observe energy levels that flow towards Landau
# level energies with increasing magnetic field.
plot_spectrum(syst, [iB * 0.002 for iB in range(100)])
# Plot an eigenmode of a circular dot. Here we create a larger system for
# better spatial resolution.
syst = make_system(r=30).finalized()
plot_wave_function(syst)
plot_current(syst)
except ValueError as e:
if e.message == "Input matrix is not real-valued.":
print("The calculation of eigenvalues failed because of a bug in SciPy 0.9.")
print("Please upgrade to a newer version of SciPy.")
else:
raise
# Call the main function if the script gets executed (as opposed to imported).
# See <http://docs.python.org/library/__main__.html>.
if __name__ == '__main__':
main()
@@ -1,225 +1,239 @@
# Tutorial 2.9. Processing continuum Hamiltonians with discretize
# ===============================================================
#
# Physics background
# ------------------
# - tight-binding approximation of continuous Hamiltonians
#
# Kwant features highlighted
# --------------------------
# - kwant.continuum.discretize
+import _defs
import kwant
#HIDDEN_BEGIN_import
import kwant.continuum
#HIDDEN_END_import
import scipy.sparse.linalg
import scipy.linalg
import numpy as np
# For plotting
import matplotlib as mpl
from matplotlib import pyplot as plt
+def save_figure(file_name):
+ if not file_name:
+ return
+ for extension in ('pdf', 'png'):
+ plt.savefig('.'.join((file_name,extension)),
+ dpi=_defs.dpi, bbox_inches='tight')
+
+
def stadium_system(L=20, W=20):
#HIDDEN_BEGIN_template