The extended abstract for the EEML summer school. Accurate and efficient interatomic potentials are crucial for simulating materials at the atomic level, and machine learning interatomic potentials (MLIPs) have emerged as a powerful alternative to traditional methods. A central aspect of MLIP development is the representation of local atomic environments, which significantly impacts the accuracy, transferability, and computational cost of the resulting potentials. This extended abstract reviews recent advancements in representing atomic environments for MLIPs....
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....