AbstractsPhysics

The theory of open quantum systems strives to explain the behaviour of many-body systems obeying the laws of quantum mechanics, which are in some way controlled by the effects of their environment. Examples of open systems can be found across a broad range of scientific research and include multicellular lifeforms, solar cells, and financial systems. In fact most realistic physical systems can be modelled as open many-body systems. The question which one often aims to answer in the study of these systems, is how they evolve through time and whether they settle down to a state of equilibrium (i.e. reach their steady state). Investigation of the time evolution of open quantum many-body systems has been a long-standing problem in the past decades. Although the dynamics of these systems can theoretically be described, the resulting equations are in practice very difficult to solve due to the myriad of variables at hand. In this thesis, we consider a rather general description of such a system, a many-level electron system in a photon cavity which is weakly coupled to its environment. Using a generalized master equation called the Nakajima-Zwanzig equation, we consider the steady-state of the system. We show that the assumption that the electron transport is a short-memory process induces a Dirac measure on the components of the dissipator in the equation. By investigating the relation between these components and their corresponding measures we use algebraic methods to represent these relations in terms of the physical operators at play. By casting the equation into the Liouville Tensor Space we obtain an eigenvalue problem in terms of the density operator. Within this framework we derive a computational model which solves the eigenvalue problem, thus allowing us to determine the steady-state of the system as well as an approximation of its transient behaviour over very long time scales. Hegðun fjöleinda kerfa sem lúta lögmálum skammtafræðinnar og stýrast af áhrifum ytra umhver- fis er umfjöllunarefni eðlisfræði opinna skammtakerfa. Slík kerfi má finna á ýmsum sviðum vísinda og má sem dæmi nefna fjölfrumunga, sólarrafhlöður og fjármálakerfi. Í raun má líta á flest öll kerfi eðlisfræðinnar sem opin fjöleindakerfi. Þær spurningar sem oft er leitast eftir að svara fyrir slík kerfi varðar það hvernig þróun þeirra með tíma á sér stað og hvort þau leiti í stöðugt ástand sem megi ákvarða. Rannsóknir á tímaþróun slíkra kerfa hafa reynst erfiðar viðfangs í nokkra áratugi. Jafnvel þótt hreyfifræði slíkra kerfa megi fræðilega lýsa þá reynast jöfnurnar oft of flóknar til þess að hægt sé að leysa þær vegna hins gífurlega fjölda breyta sem þar fyrirfinnast. Í þessari ritgerð athugum við fremur almenna lýsingu á slíku kerfi, þ.e. fjölstiga rafeindakerfi í ljóseindaholi sem er veiktengt við umhverfi sitt. Með því að nota skammtastýrijöfnu Nakajima og Zwanzig athugum við sístöðuástand kerfisins. Við sýnum að sú forsenda að kerfið búi við minnistap gefi af sér Dirac mál fyrir virkjastök sem lýsa orkutapi. Við nánari athugun má sjá að…