Search results for "aikariippuva"
showing 4 items of 4 documents
Aikariippuvan Diracin yhtälön numeerisesta ratkaisemisesta
2017
Tässä opinnäytetyössä tarkastellaan Diracin yhtälön numeerista ratkaisemista sekä tähän liittyviä haasteita. Diracin yhtälö on keskeinen kvanttifysiikan ilmiöitä kuvaava yhtälö, jonka ratkaisemiseen on esitetty kirjallisuudessa useita erilaisia menetelmiä. Tässä opinnäytetyössä keskitytään tarkastelemaan menetelmää, jossa yhtälön ratkaisemiseen sovelletaan operaattorinjakoa ja karakteristista menetelmää. Yhtälön ratkaiseminen vaatii paljon aikaa ja laskentaresursseja, joten laskennan tehostaminen rinnakkaislaskennan keinoin on välttämätöntä. In this paper the numerical solution of the Dirac equation is studied along with its challenges. The Dirac equation is a central equation describing th…
Many-particle theory for time-dependent quantum transport in nanostructures
2012
During the recent decades, molecular electronics has established its place as one of the promising fields in the nanoscience. The possibility to manufacture and control molecular junctions where single molecules are squeezed between the conducing electrodes has opened up new possibilities to develop nanoscale devices which could be employed as building blocks for future nanoelectronic applications. The driving force for this new branch of physics has been the experimental advances but also theoretical methods have been under intensive study and many theoretical tools have been developed to understand the electron transport processes in the nanoscale systems. This thesis focuses on developin…
Efficient design and modeling strategies for follow-up studies with time-varying covariates
2015
Epidemiological studies can often be designed in several ways, some of which may be more optimal than others. Possible designs may differ in the required resources or the ability to provide reliable answers to the questions under study. In addition, once the data are collected, the selected modeling approach may affect how efficiently the data are utilized. The purpose of this dissertation is to investigate efficient designs and analysis meth ods in follow-up studies with longitudinal measurements. A key question is how to select optimally a subcohort for a new longitudinal covariate measurement if we cannot afford to measure the entire cohort. Another key question we consider is how to determine …
Application of time-dependent many-body perturbation theory to excitation spectra of selected finite model systems
2016
In this thesis, an approximate method introduced to solve time-dependent many-body problems known as time-dependent many-body perturbation theory is studied. Many-body perturbation theory for interacting electrons and phonons is reviewed. In particular, the electron propagator G and an unconventional two-component phonon propagator, which satisfy coupled integral Dyson equations, are introduced. In practice, the associated integral kernels known as the electron Σ and phonon self-energies need to be approximated. The conserving approximations known as the Hartree (-Fock) and the first and second Born approximations, which respect the continuity equation between the electron density and curren…