Bachelor defense by Sophus Holck Bauditz

Benchmarking Lindblad equations on models of free bosons

With this project, we will study the effects of the recently developed Universal Lindblad Equation (ULE) on a system consisting of free bosons. We will start with a brief introduction of the quantum mechanical formalism, and then we will explain relevant mathematical frameworks for representing composite Hilbert spaces. This framework will then be demonstrated by simulating a particle that interacts with a small reservoir. Then we move on to work with the ULE: Firstly, we will compute an exact simulation of the time dependent probability coefficients of an excited particle interacting with a reservoir of states. This interaction is described by a combination of lowering and raising operators, effectively representing how an excited particle ’jumps’ to a lower energetic state when interacting with its environment. Secondly, the Lindblad equation is solved for the same system. This result is then benchmarked against the exact solution. Furthermore we obtain conditions for when the Lindblad equation is a precise approximation of the exact solution.