Oxygen adsorption on clean and oxygen precovered Cu(100)

Kuparipinnan hapettumisen alkuvaiheet ovat vielä nykyisin tutkijoille epäselviä. Kuitenkin, jotta hapettumisprosessia voitaisiin säädellä, on sangen tärkeää ymmärtää mistä varsinainen hapettuminen lähtee liikkeelle ja mitkä ovat hapettumisen seuraavat vaiheet. Tähän kysymykseen haetaan vastauksia tässä työssä käyttäen puhtaasti teoreettisia menetelmiä pinnan käsittelyssä. Aikaisempien teoreettisten ja kokeellisten tutkimusten välillä on pieni ristiriita liittyen hapen tarttumistodennäköisyyteen. Teoreettisten tutkimusten mukaan happi ei puhtaalle pinnalle tullessaan näe potentiaalivallia, mutta kokeelliset tutkimukset osoittavat sellaisen kuitenkin olevan. Tuohon ristiriitaan pureudutaan käyttäen aikaisemmista laskuista poikkeavaa kvanttimekaaniseen molekyylidynamiikkaan perustuvaa lähestymistapaa. Työssä havaitaan, että aikaisemmin yleisesti käytetty menetelmä hukkaa huomattavan määrän tietoa ja siten tutkijat eivät voi ainoastaan tyytyä tarkastelemaan kyseisellä menetelmällä saatuja tuloksia. Kuparipinnalle havaittiin, että korkeilla molekyylin kineettisen energian arvolla aikaisemmin suoritetut laskut hajottavista trajektoreista pitävät paikkansa, mutta matalilla kineettisen energian arvoilla molekyyli kohtaa erittäin voimakkaan ``steering'' vaikutuksen ja trajektorit joiden piti olla hajottavia johtavatkin molekulaariseen adsorptioon. Kun hapen konsentraatio pinnalla on suurempi kuin 0.5 ML, pinta rekonstruoituu. Myös rekonstruktion jälkeistä pintaa on tutkittu samanlaisilla menetelmillä kuin puhdasta pintaa. Rekonstruoituneelle pinnalle ei löydetty hajottavia trajektoreita ja havaittiin, että hapelle annetun kineettisen energian matalilla arvoilla myös tässä tapauksessa on erittäin voimakas ``steering'' vaikutus.

Studies on the Multifaceted Interaction of Atoms and an Electromagnetic Field

In this Thesis the interaction of an electromagnetic field and matter is studied from various aspects in the general framework of cold atoms. Our subjects cover a wide spectrum of phenomena ranging from semiclassical few-level models to fully quantum mechanical interaction with structured reservoirs leading to non-Markovian open quantum system dynamics. Within closed quantum systems, we propose a selective method to manipulate the motional state of atoms in a time-dependent double-well potential and interpret the method in terms of adiabatic processes. Also, we derive a simple wave-packet model, based on distributions of generalized eigenstates, explaining the finite visibility of interference in overlapping continuous-wave atom lasers. In the context of open quantum systems, we develop an unraveling of non-Markovian dynamics in terms of piecewise deterministic quantum jump processes confined in the Hilbert space of the reduced system - the non-Markovian quantum jump method. As examples, we apply it for simple 2- and 3-level systems interacting with a structured reservoir. Also, in the context of ion-cavity QED we study the entanglement generation based on collective Dicke modes in experimentally realistic conditions including photonic losses and an atomic spontaneous decay.

The solutions and tunneling properties for a linear potential and an inverted harmonic oscillator in an infinite well

In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schrödinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.

The solutions and tunneling properties for a linear potential and an inverted harmonic oscillator in an infinite well

In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schrödinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.

Moment Operators of Observables in Quantum Mechanics, with Applications to Quantization and Homodyne Detection

The questions studied in this thesis are centered around the moment operators of a quantum observable, the latter being represented by a normalized positive operator measure. The moment operators of an observable are physically relevant, in the sense that these operators give, as averages, the moments of the outcome statistics for the measurement of the observable. The main questions under consideration in this work arise from the fact that, unlike a projection valued observable of the von Neumann formulation, a general positive operator measure cannot be characterized by its first moment operator. The possibility of characterizing certain observables by also involving higher moment operators is investigated and utilized in three different cases: a characterization of projection valued measures among all the observables is given, a quantization scheme for unbounded classical variables using translation covariant phase space operator measures is presented, and, finally, a mathematically rigorous description is obtained for the measurements of rotated quadratures and phase space observables via the high amplitude limit in the balanced homodyne and eight-port homodyne detectors, respectively. In addition, the structure of the covariant phase space operator measures, which is essential for the above quantization, is analyzed in detail in the context of a (not necessarily unimodular) locally compact group as the phase space.

Dialogue in the crisis of representation : realism and antirealism in the context of the conversation between theologians and quantum physicists in Göttingen 1949-1961

The aim of this study is to analyse the content of the interdisciplinary conversations in Göttingen between 1949 and 1961. The task is to compare models for describing reality presented by quantum physicists and theologians. Descriptions of reality indifferent disciplines are conditioned by the development of the concept of reality in philosophy, physics and theology. Our basic problem is stated in the question: How is it possible for the intramental image to match the external object?Cartesian knowledge presupposes clear and distinct ideas in the mind prior to observation resulting in a true correspondence between the observed object and the cogitative observing subject. The Kantian synthesis between rationalism and empiricism emphasises an extended character of representation. The human mind is not a passive receiver of external information, but is actively construing intramental representations of external reality in the epistemological process. Heidegger's aim was to reach a more primordial mode of understanding reality than what is possible in the Cartesian Subject-Object distinction. In Heidegger's philosophy, ontology as being-in-the-world is prior to knowledge concerning being. Ontology can be grasped only in the totality of being (Dasein), not only as an object of reflection and perception. According to Bohr, quantum mechanics introduces an irreducible loss in representation, which classically understood is a deficiency in knowledge. The conflicting aspects (particle and wave pictures) in our comprehension of physical reality, cannot be completely accommodated into an entire and coherent model of reality. What Bohr rejects is not realism, but the classical Einsteinian version of it. By the use of complementary descriptions, Bohr tries to save a fundamentally realistic position. The fundamental question in Barthian theology is the problem of God as an object of theological discourse. Dialectics is Barth¿s way to express knowledge of God avoiding a speculative theology and a human-centred religious self-consciousness. In Barthian theology, the human capacity for knowledge, independently of revelation, is insufficient to comprehend the being of God. Our knowledge of God is real knowledge in revelation and our words are made to correspond with the divine reality in an analogy of faith. The point of the Bultmannian demythologising programme was to claim the real existence of God beyond our faculties. We cannot simply define God as a human ideal of existence or a focus of values. The theological programme of Bultmann emphasised the notion that we can talk meaningfully of God only insofar as we have existential experience of his intervention. Common to all these twentieth century philosophical, physical and theological positions, is a form of anti-Cartesianism. Consequently, in regard to their epistemology, they can be labelled antirealist. This common insight also made it possible to find a common meeting point between the different disciplines. In this study, the different standpoints from all three areas and the conversations in Göttingen are analysed in the frameworkof realism/antirealism. One of the first tasks in the Göttingen conversations was to analyse the nature of the likeness between the complementary structures inquantum physics introduced by Niels Bohr and the dialectical forms in the Barthian doctrine of God. The reaction against epistemological Cartesianism, metaphysics of substance and deterministic description of reality was the common point of departure for theologians and physicists in the Göttingen discussions. In his complementarity, Bohr anticipated the crossing of traditional epistemic boundaries and the generalisation of epistemological strategies by introducing interpretative procedures across various disciplines.