Quantum dynamics of the parabolic model

Kvanttimekaniikan teoriassa suljettuja, ympäristöstään eristettyjä systeemejä koskevat tulokset ovat hyvin tunnettuja. Eräs tärkeä erityispiirre tällaisille systeemeille on, että niiden aikakehitys on unitaarista. Oletus siitä, että systeemi on suljettu, on osaltaan tietysti vain yksinkertaistus. Käytännössä kaikki kvanttimekaaniset systeemit vuorovaikuttavat ympäristönsä kanssa ja tästä johtuen niiden dynamiikka monimutkaistuu oleellisesti. Kuitenkin tietyissä tapauksissa systeemin aikakehitys voidaan ratkaista, ainakin approksimatiivisesti. Tärkeimpinä esimerkkeinä on ympäristön joko nopea tai erittäin hidas muutos kvanttisysteemin ominaiseen aikaskaalaan verrattuna. Näistä erityisesti jälkimmäinen on käyttökelpoinen oletus monissa fysikaalisissa tilanteissa. Tällöin voidaan suorittaa niin sanottu adiabaattinen approksimaatio. Sen mukaan systeemi, joka on aikakehityksen generoivan Hamiltonin operaattorin ominaistilassa, pysyy vastaavassa ominaistilassa ympäristön muuttuessa äärettömän hitaasti, mikäli systeemin eri energiatasot eivät leikkaa toisiaan. Todellisissa tilanteissa muutos ei tietenkään voi olla äärettömän hidasta ja myös energiatasojen leikkaukset ovat mahdollisia, jolloin tapahtuu transitio eri ominaistilojen välillä. Energiatasojen leikkauksilla on oleellisia vaikutuksia erittäin monissa fysikaalisissa prosesseissa ja niitä kuvaamaan on luotu monia malleja kvanttimekaniikan alkuajoista lähtien aina tähän päivään saakka. Nykyinen teknologinen kehitys on avannut uudenlaisen mahdollisuuden ilmiön kokeelliseen varmentamiseen ja hyödyntämiseen. Tämän vuoksi kyseisten mallien dynamiikan ja erityisesti energiatasojen useiden peräkkäisten leikkausten aiheuttamien koherenssi-ilmiöiden selvittäminen on tärkeää. Tässä työssä käsitellään kvanttimekaanisia kaksitasosysteemejä, joissa esiintyy energiatasojen leikkauksia sekä niiden pitkän aikavälin dynamiikkaa. Tutkielmassa perehdytään tarkemmin kahteen tiettyyn malliin. Näistä ensimmäinen, Landau-Zener -malli, on tunnetuin ja sovelluksissa käytetyin malli. Kuitenkin erityisen mielenkiinnon kohteena on niin kutsuttu parabolinen malli, jolle johdetaan eri approksimaatioita käyttäen asymptoottiset transitiotodennäköisyydet eri tilojen välille. Näitä verrataan numeerisiin tuloksiin.

Theoretical investigation of electronic excitation transfer between chlorophylls in light-harvesting antenna of photosystem ii using quantum computers

The excitation energy transfer between chlorophylls in major and minor antenna complexes of photosystem II (PSII) was investigated using quantum Fourier transforms. These transforms have an important role in the efficiency of quantum algorithms of quantum computers. The equation 2n=N was used to make the connection between excitation energy transfers using quantum Fourier transform, where n is the number of qubits required for simulation of transfers and N is the number of chlorophylls in the antenna complexes.

Probing the (empirical) quantum structure embedded in the periodic table with an effective Bohr model

The atomic shell structure can be observed by inspecting the experimental periodic properties of the Periodic Table. The (quantum) shell structure emerges from these properties and in this way quantum mechanics can be explicitly shown considering the (semi-)quantitative periodic properties. These periodic properties can be obtained with a simple effective Bohr model. An effective Bohr model with an effective quantum defect (u) was considered as a probe in order to show the quantum structure embedded in the Periodic Table. u(Z) shows a quasi-smoothed dependence of Z, i.e., u(Z) ≈ Z2/5 - 1.

GLOBAL AND LOCAL REACTIVITY DESCRIPTORS FOR PICLORAM HERBICIDE: A THEORETICAL QUANTUM STUDY

In this work, we studied the reactivity of picloram in the aqueous phase at the B3LYP/6-311++G(2d,2p) and MP2/6-311++G(2d,2p) levels of theory through global and local reactivity descriptors. The results obtained at the MP2 level indicate that the cationic form of picloram exhibits the highest hardness while the anionic form is the most nucleophilic. From the Fukui function values, the most reactive site for electrophilic and free radical attacks are on the nitrogen in the pyridine ring. The more reactive sites for nucleophilic attacks are located on the nitrogen atom of the amide group and on the carbon atoms located at positions 2 and 3 in the pyridine ring.

Ba-DOPED ZnO MATERIALS: A DFT SIMULATION TO INVESTIGATE THE DOPING EFFECT ON FERROELECTRICITY

ZnO is a semiconductor material largely employed in the development of several electronic and optical devices due to its unique electronic, optical, piezo-, ferroelectric and structural properties. This study evaluates the properties of Ba-doped wurtzite-ZnO using quantum mechanical simulations based on the Density Functional Theory (DFT) allied to hybrid functional B3LYP. The Ba-doping caused increase in lattice parameters and slight distortions at the unit cell angle in a wurtzite structure. In addition, the doping process presented decrease in the band-gap (Eg) at low percentages suggesting band-gap engineering. For low doping amounts, the wavelength characteristic was observed in the visible range; whereas, for middle and high doping amounts, the wavelength belongs to the Ultraviolet range. The Ba atoms also influence the ferroelectric property, which is improved linearly with the doping amount, except for doping at 100% or wurtzite-BaO. The ferroelectric results indicate the ZnO:Ba is an strong option to replace perovskite materials in ferroelectric and flash-type memory devices.

Thermal modelling of semiconductor switches in three-level Neutral Point Clamped Medium Voltage DTC-inverter

The aim of this thesis is to investigate the thermal loading of medium voltage three-level NPC inverter’s semiconductor IGCT switches in different operation points. The objective is to reach both a fairly accurate off-line simulation program and also so simple a simulation model that its implementation into an embedded system could be reasonable in practice and a real time use should become feasible. Active loading limitation of the inverter can be realized with a thermal model which is practical in a real time use. Determining of the component heating has been divided into two parts; defining of component losses and establishing the structure of a thermal network. Basics of both parts are clarified. The simulation environment is Matlab-Simulink. Two different models are constructed – a more accurate one and a simplified one. Potential simplifications are clarified with the help of the first one. Simplifications are included in the latter model and the functionalities of both models are compared. When increasing the calculation time step a decreased number of considered components and time constants of the thermal network can be used in the simplified model. Heating of a switching component is dependent on its topological position and inverter’s operation point. The output frequency of the converter defines mainly which one of the switching components is – because of its losses and heating – the performance limiting component of the converter. Comparison of results given by different thermal models demonstrates that with larger time steps, describing of fast occurring switching losses becomes difficult. Generally articles and papers dealing with this subject are written for two-level inverters. Also inverters which apply direct torque control (DTC) are investigated rarely from the heating point of view. Hence, this thesis completes the former material.

Photoelectrocatalytical degradation of basic blue 41 dye using nanoporous semiconductor of Ti/TiO2

O presente trabalho investiga a degradação fotoeletrocatalítica do corante Azul Básico 41 (AB 41) amplamente utilizado na tintura de fibras sintéticas, utilizando um semicondutor Ti/TiO2 como fotoanodo. 100% de degradação foi obtida após 60 min de tratamento de 8,33x10-5 mol L-1 do corante em 0,1 mol L−1 Na2SO4, pH 2 sob densidade de corrente de 0,40 mA cm−2 e irradiação UV. Ainda foi obtido 80% de remoção de carbono orgânico total, cuja oxidação segue uma reação de pseudo-primeira ordem com constante de velocidade inicial de -0,040 mim-1 e uma eficiência de corrente de 51%. Os resultados são superiores á fotocatálise convencional nas mesmas condições sem a polarização do fotoanodo que leva a 65% de mineralização sob constante de velocidade de -0,024 mim-1.

Non-Markovianity and Quantum Correlations in Qubit-Systems

In this Thesis I discuss the exact dynamics of simple non-Markovian systems. I focus on fundamental questions at the core of non-Markovian theory and investigate the dynamics of quantum correlations under non-Markovian decoherence. In the first context I present the connection between two different non-Markovian approaches, and compare two distinct definitions of non-Markovianity. The general aim is to characterize in exemplary cases which part of the environment is responsible for the feedback of information typical of non- Markovian dynamics. I also show how such a feedback of information is not always described by certain types of master equations commonly used to tackle non-Markovian dynamics. In the second context I characterize the dynamics of two qubits in a common non-Markovian reservoir, and introduce a new dynamical effect in a wellknown model, i.e., two qubits under depolarizing channels. In the first model the exact solution of the dynamics is found, and the entanglement behavior is extensively studied. The non-Markovianity of the reservoir and reservoirmediated-interaction between the qubits cause non-trivial dynamical features. The dynamical interplay between different types of correlations is also investigated. In the second model the study of quantum and classical correlations demonstrates the existence of a new effect: the sudden transition between classical and quantum decoherence. This phenomenon involves the complete preservation of the initial quantum correlations for long intervals of time of the order of the relaxation time of the system.

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.

Non-Markovian Dynamics in Continuous Variable Quantum Systems

The present manuscript represents the completion of a research path carried forward during my doctoral studies in the University of Turku. It contains information regarding my scientific contribution to the field of open quantum systems, accomplished in collaboration with other scientists. The main subject investigated in the thesis is the non-Markovian dynamics of open quantum systems with focus on continuous variable quantum channels, e.g. quantum Brownian motion models. Non-Markovianity is here interpreted as a manifestation of the existence of a flow of information exchanged by the system and environment during the dynamical evolution. While in Markovian systems the flow is unidirectional, i.e. from the system to the environment, in non-Markovian systems there are time windows in which the flow is reversed and the quantum state of the system may regain coherence and correlations previously lost. Signatures of a non-Markovian behavior have been studied in connection with the dynamics of quantum correlations like entanglement or quantum discord. Moreover, in the attempt to recognisee non-Markovianity as a resource for quantum technologies, it is proposed, for the first time, to consider its effects in practical quantum key distribution protocols. It has been proven that security of coherent state protocols can be enhanced using non-Markovian properties of the transmission channels. The thesis is divided in two parts: in the first part I introduce the reader to the world of continuous variable open quantum systems and non-Markovian dynamics. The second part instead consists of a collection of five publications inherent to the topic.

Non-Markovian Dynamics and the Quantum-To-Classical Transition for Quantum Brownian Motion

In this Thesis I discuss the dynamics of the quantum Brownian motion model in harmonic potential. This paradigmatic model has an exact solution, making it possible to consider also analytically the non-Markovian dynamics. The issues covered in this Thesis are themed around decoherence. First, I consider decoherence as the mediator of quantum-to-classical transition. I examine five different definitions for nonclassicality of quantum states, and show how each definition gives qualitatively different times for the onset of classicality. In particular I have found that all characterizations of nonclassicality, apart from one based on the interference term in the Wigner function, result in a finite, rather than asymptotic, time for the emergence of classicality. Second, I examine the diverse effects which coupling to a non-Markovian, structured reservoir, has on our system. By comparing different types of Ohmic reservoirs, I derive some general conclusions on the role of the reservoir spectrum in both the short-time and the thermalization dynamics. Finally, I apply these results to two schemes for decoherence control. Both of the methods are based on the non-Markovian properties of the dynamics.

Quantum Tomography with Phase Space Measurements

This thesis addresses the use of covariant phase space observables in quantum tomography. Necessary and sufficient conditions for the informational completeness of covariant phase space observables are proved, and some state reconstruction formulae are derived. Different measurement schemes for measuring phase space observables are considered. Special emphasis is given to the quantum optical eight-port homodyne detection scheme and, in particular, on the effect of non-unit detector efficiencies on the measured observable. It is shown that the informational completeness of the observable does not depend on the efficiencies. As a related problem, the possibility of reconstructing the position and momentum distributions from the marginal statistics of a phase space observable is considered. It is shown that informational completeness for the phase space observable is neither necessary nor sufficient for this procedure. Two methods for determining the distributions from the marginal statistics are presented. Finally, two alternative methods for determining the state are considered. Some of their shortcomings when compared to the phase space method are discussed.

Quantum Hall effect in 2 dimensional GaInAs structure

Transport properties of GaAs / δ – Mn / GaAs / InxGa1-xAs / GaAs structure with Mn δ – layer, which is separated from InxGa1-xAs quantum well (QW) by 3 nm thick GaAs spacer was investigated. This structure with high mobility was characterized by X-ray difractometry and reflectometry. Transport and electrical properties of the structure were measured by using Pulsed Magnetic Field System (PMFS). During investigation of the Shubnikov – de Haas and the Hall effects the main parameters of QW structure such as cyclotron mass, Fermi level, g – factor, Dingle temperature and concentration of holes were estimated. Obtained results show high quality of the prepared structure. However, anomalous Hall effect at temperatures 2.09 K, 3 K, 4.2 K is not clearly observed. Attempts to identify magnetic moment were made. For this purpose the polarity of the filed was changed to the opposite at each shot. As a result hysteresis loop was not observed in the magnetic field dependences of the anomalous Hall resistivity.This can be attributed to the imperfection of the experimental setup.

Galvanomagnetic effects in InGaAs nanostructure

Investigation of galvanomagnetic effects in nanostructure GaAs/Mn/GaAs/In0.15Ga0.85As/ GaAs is presented. This nanostructure is classified as diluted magnetic semiconductor (DMS). Temperature dependence of transverse magnetoresistivity of the sample was studied. The anomalous Hall effect was detected and subtracted from the total Hall component. Special attention was paid to the measurements of Shubnikov-de Haas oscillations, which exists only in the case of magnetic field aligned perpendicularly to the plane of the sample. This confirms two-dimensional character of the hole energy spectrum in the quantum well. Such important characteristics as cyclotron mass, the Fermi energy and the Dingle temperature were calculated, using experimental data of Shubnikov-de Haas oscillations. The hole concentration and hole mobility in the quantum well also were estimated for the sample. At 4.2 K spin splitting of the maxima of transverse resistivity was observed and g-factor was calculated for that case. The values of the Dingle temperatures were obtained by two different approaches. From the comparison of these values it was concluded that the broadening of Landau levels in the investigated structure is mainly defined by the scattering of charge carriers on the defects of the crystal lattice

Non-Markovian dynamics and quantum information probes

This Thesis discusses the phenomenology of the dynamics of open quantum systems marked by non-Markovian memory effects. Non-Markovian open quantum systems are the focal point of a flurry of recent research aiming to answer, e.g., the following questions: What is the characteristic trait of non-Markovian dynamical processes that discriminates it from forgetful Markovian dynamics? What is the microscopic origin of memory in quantum dynamics, and how can it be controlled? Does the existence of memory effects open new avenues and enable accomplishments that cannot be achieved with Markovian processes? These questions are addressed in the publications forming the core of this Thesis with case studies of both prototypical and more exotic models of open quantum systems. In the first part of the Thesis several ways of characterizing and quantifying non-Markovian phenomena are introduced. Their differences are then explored using a driven, dissipative qubit model. The second part of the Thesis focuses on the dynamics of a purely dephasing qubit model, which is used to unveil the origin of non-Markovianity for a wide class of dynamical models. The emergence of memory is shown to be strongly intertwined with the structure of the spectral density function, as further demonstrated in a physical realization of the dephasing model using ultracold quantum gases. Finally, as an application of memory effects, it is shown that non- Markovian dynamical processes facilitate a novel phenomenon of timeinvariant discord, where the total quantum correlations of a system are frozen to their initial value. Non-Markovianity can also be exploited in the detection of phase transitions using quantum information probes, as shown using the physically interesting models of the Ising chain in a transverse field and a Coulomb chain undergoing a structural phase transition.