From 37f611b55f0f74010e092fb6b1640be5b460a67e Mon Sep 17 00:00:00 2001
From: Joseph Weston <joseph@weston.cloud>
Date: Wed, 22 May 2019 12:16:34 +0200
Subject: [PATCH] add whatsnew entry and documentation pages
---
doc/source/pre/whatsnew/1.5.rst | 38 ++++++++++++++++++++++++
doc/source/reference/kwant.continuum.rst | 9 ++++++
2 files changed, 47 insertions(+)
diff --git a/doc/source/pre/whatsnew/1.5.rst b/doc/source/pre/whatsnew/1.5.rst
index 9a9c085c..9340cec9 100644
--- a/doc/source/pre/whatsnew/1.5.rst
+++ b/doc/source/pre/whatsnew/1.5.rst
@@ -12,3 +12,41 @@ the code are inserted directly into the document thanks to the magic of
`jupyter-sphinx <https://github.com/jupyter-widgets/jupyter-sphinx/>`_.
It has never been easier to get started contributing to Kwant by
helping us improve our documentation.
+
+Discretization onto a Landau level basis
+----------------------------------------
+The Hamiltonian for a system infinite in at least two dimensions and with
+a constant applied magnetic field may be expressed in a basis of Landau levels.
+The momenta in the plane perpendicular to the magnetic field direction are
+written in terms of the Landau level ladder operators:
+
+.. math::
+ k_x = \sqrt{\frac{B}{2}} (a + a^\dagger) \quad\quad
+ k_y = i \sqrt{\frac{B}{2}} (a - a^\dagger)
+
+The Hamiltonian is then expressed in terms of these ladder operators, which
+allows for a straight-forward discretization in the basis of Landau levels,
+provided that the basis is truncated after $N$ levels.
+`kwant.continuum.discretize_landau` makes this procedure simple::
+
+ syst = kwant.continuum.discretize_landau("k_x**2 + k_y**2", N)
+ syst.finalized().hamiltonian_submatrix(params=dict(B=0.5))
+
+`~kwant.continuum.discretize_landau` produces a regular Kwant Builder that
+can be inspected or finalized as usual. 3D Hamiltonians for systems that
+extend into the direction perpendicular to the magnetic field are also
+possible::
+
+ template = kwant.continuum.discretize_landau("k_x**2 + k_y**2 + k_z**2 + V(z)", N)
+
+This will produce a Builder with a single translational symmetry, which can be
+directly finalized, or can be used as a template for e.g. a heterostructure stack
+in the direction of the magnetic field::
+
+ def stack(site):
+ z, = site.pos
+ return 0 <= z < 10
+
+ template = kwant.continuum.discretize_landau("k_x**2 + k_y**2 + k_z**2 + V(z)", N)
+ syst = kwant.Builder()
+ syst.fill(template, stack, (0,))
diff --git a/doc/source/reference/kwant.continuum.rst b/doc/source/reference/kwant.continuum.rst
index d6799438..6ad52d32 100644
--- a/doc/source/reference/kwant.continuum.rst
+++ b/doc/source/reference/kwant.continuum.rst
@@ -11,6 +11,7 @@ Discretizer
discretize
discretize_symbolic
build_discretized
+ discretize_landau
Symbolic helpers
----------------
@@ -19,3 +20,11 @@ Symbolic helpers
sympify
lambdify
+ to_landau_basis
+
+Other
+-----
+.. autosummary::
+ :toctree: generated/
+
+ LandauLattice
--
GitLab