I’m currently exploring the Kwant python package because my thesis is inline with quantum transport. Kwant is a python package for numerical quantum transport calculations. The thing I like about Kwant, aside from being in python, is that it has been designed such that natural concepts of the theory of quantum theory are exposed in a simple and transparent way. Kwant offers direct support for calculations of transport properties, dispersion relations, modes, wave functions, variours Green’s functions, and out-of-equilibrium local quantities.
1. Introduction
Scattering
- solving scattering problem is a common taks in condensed matter physics
- one considers the scattering of particles in a finite system coupled to infinite leads
- solutions yields the conductance and various other transport properties
- can also be used to calculate complicated physical phenomena.
- supercurrent
- non-equilibrium density of states at a high voltage bias
- evaluation of the topological properties of a topological insulator
Numerical simulation of the scattering problem
- most popular is the recursive Green’s function algorithm (RGF)
- Kwant is develop to solve efficiently at comparatively little effort the scattering problem for arbitrary single-particle tight-binding Hamiltonians.
Kwant
- solve the scattering problem in a robust and highly efficient way
- support an easy and expressive way to define a broad range of tight-binding systems as required for exploratory research.
- uses highly efficient and robust algorithms resulting to:
- it outperform the RGF
- it avoid usual instabilities occurring with many commonly used algorithms
- Expressiveness of kwant is important for mesoscopic physics
- one writes down a Hamiltonian that is very close to what one would write on a blackboard
- Definition of a physical system amount to writing a simple Python program that operates with physical concepts such as lattices, shapes, symmetries, and potentials.
Examples of a device that was simulated
- cylindrical semiconductor wire with spin-orbit interaction, partially covered by a superconductor, used to create Majorana fermions.
2. Concepts of Quantum Transport
(kwant is suited for both infinite and finite systems with finite scattering region to which a few semi-finite periodic electrodes are connected.)
The Hamiltonian for systems in Kwant are defined as: \(\hat{H}=\sum_{ij} H_{ij}c^\dagger_{i}c_{j}\)
where \(c^\dagger_{i}c_{j}\) are the usual fermionic creation(and destruction) operatos, i and j label the different degrees of freedom of the system, and \(H_{ij}\) are the elements of an infinite Hermitian matrix