Commit 6413c295 authored by Joseph Weston's avatar Joseph Weston

whitespace fix

parent 3659dad3
Pipeline #19065 passed with stages
in 38 minutes and 47 seconds
......@@ -37,7 +37,7 @@ The eigenstates satisfy :math:`a^\dagger a | n \rangle = n | n \rangle` with the
Landau level index :math:`n \geq 0`, and in coordinate representation are proportional to
.. math::
\psi_n (x, y) = \left( \frac{\partial}{ \partial w} - \frac{w^*}{4 l_B^2} \right)
w^n e^{-|w|^2/4l_B^2},
......@@ -47,7 +47,7 @@ with :math:`w = x + i y`. The matrix elements of the ladder operators are
\langle n | a | m \rangle = \sqrt{m}~\delta_{n, m-1}, \quad \quad
\langle n | a^\dagger | m \rangle = \sqrt{m + 1}~\delta_{n, m+1}.
Truncating the basis to the first :math:`N` Landau levels allows us to approximate
the Hamiltonian as a discrete, finite matrix.
......@@ -56,16 +56,16 @@ We can now formulate the algorithm that Kwant uses to compute Landau levels.
1. We take a generic continuum Hamiltonian, written in terms of the kinetic
momentum :math:`\vec{k}`. The Hamiltonian must be translationally
invariant along the directions perpendicular to the field direction.
2. We substitute the momenta perpendicular to the magnetic field with the ladder
operators :math:`a` and :math:`a^\dagger`.
3. We construct a `kwant.builder.Builder` using a special lattice which includes
the Landau level index :math:`n` as a degree of freedom on each site. The directions
normal to the field direction are not included in the builder, because they are
encoded in the Landau level index.
This procedure is automated with `kwant.continuum.discretize_landau`.
This procedure is automated with `kwant.continuum.discretize_landau`.
As an example, let us take the Bernevig-Hughes-Zhang model that we first considered in the
discretizer tutorial ":ref:`discretize-bhz-model`":
......@@ -155,7 +155,7 @@ with the Landau levels shown as dashed lines.
h = landau_syst.hamiltonian_submatrix(params=params)
for ev in scipy.linalg.eigvals(h):
ax.axhline(ev, linestyle='--')
The dispersion and the Landau levels diverge with increasing energy, because the real space
discretization of the ribbon gives a worse approximation to the dispersion at higher energies.
......@@ -229,4 +229,4 @@ to construct our heterostructure:
.. rubric:: Footnotes
.. [#] `Wikipedia <https://en.wikipedia.org/wiki/Landau_quantization>`_ has
a nice introduction to Landau quantization.
\ No newline at end of file
a nice introduction to Landau quantization.
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