Masters Thesis Defense by Sebastian M. Dreizler

Titel “Thermalisation of an Oscillator to a Non-Markovian Bath via Infinite Order Moyal Expansion”

Abstract: Presented is an approach to applying kinetic theory to non-Markovian problems in quantum dissipation. More precisely, a bosonic mode coupled to a Drude-Lorentz bath is considered, representing a non-Markovian problem. While the Ohmic limit of this system is well-studied, addressing the strongly non-Markovian regime poses additional challenges. A kinetic equation is derived by transforming the Dyson equation into a semi-classical Boltzmann equation using the Moyal expansion. This results in a first-order differential equation in time. However, in strongly non-Markovian regimes, the first-order gradient expansion may be insufficient, necessitating the inclusion of higher-order terms. The resulting infinite-dimensional differential equation can be reduced to a third-order differential equation in time, which potentially corresponds to the Moore-Gibson-Thompson equation, originally introduced by Stokes as an application of the Navier-Stokes equation for viscous matter.

Moreover, it is shown that the final differential equation, within the quasiparticle approximation, can reproduce Kirchhoff’s law. Finally, a sketch is provided on how the methods used can be generalized to more complex systems.

Censor er Prof. Mads Brandbyge fra DTU

Jens Paaske er vejleder