Josephson Effect ED

Use exact diagonalization to study the Josephson effect in case of lead order parameter $\Delta$ substantially larger than the system order parameter (no quasiparticle excitations at the leads, leads reflect fully). The Hilbert space of the problem is handled by QuSpin. The physics behind the method is considered e.g. in a review article by Meden.

Usage:

There are many ways to install the required QuSpin package. The standard way is to make an Anaconda environment by e.g.

conda create --name josephsonED

conda install -n josephsonED matplotlib

conda install -n josephsonED -c weinbe58 omp quspin

The environment can be then activated or deactivated by

conda active josephsonED

conda deactivate

Then you can run the codes by

python3 example_name.py

There are two versions of the code:

• Josephson_ED_varied_number.py considers the system in two independent blocks: the even particle (up spin + down spin particles) number and the odd particle number. This version gives sensible results. Now it considers sawtooth lattice but one can also build other models

• Josephson_ED_constant_ph.py considers the system in many independent branches: on each the up spin particle number + down spin hole number is constant (conserved quantity within the considered Hamiltonian).