Math

This is a summary of the computational method I used for my master’s thesis [1]. I will focus on the Hartree-Fock approximation. Model The problem we were trying to attack was the correct modeling of the Majorana zero modes in a superconducting nanowire with a quantum dot attached at one of the ends of the wire. The Hamiltonian describing the system is $$ \begin{align*} H &= \sum_{j=1}^{N-1} \left( -t c_{j+1}^\dagger c_j + \Delta c_{j+1}^\dagger c_j^\dagger + \text{H....

Final term paper for the course of Open Quantum Systems. Introduction Master equations govern the time evolution of a quantum system interacting with an environment and can be written in a variety of forms. Time-independent or memoryless master equations can be expressed in the well-known Lindblad form. In fact, any master equation local in time, Markovian or non-Markovian, can also be written in a Lindblad-like form. A diagonalization procedure results in a unique, canonical representation of the equation, which can be used to fully characterize the non-Markovianity of the time evolution....