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.

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.

Microscopic simulation of pigment coating consolidation

The control of coating layer properties is becoming increasingly important as a result of an emerging demand for novel coated paper-based products and an increasing popularity of new coating application methods. The governing mechanisms of microstructure formation dynamics during consolidation and drying are nevertheless, still poorly understood. Some of the difficulties encountered by experimental methods can be overcome by the utilisation of numerical modelling and simulation-based studies of the consolidation process. The objective of this study was to improve the fundamental understanding of pigment coating consolidation and structure formation mechanisms taking place on the microscopic level. Furthermore, it is aimed to relate the impact of process and suspension properties to the microstructure of the coating layer. A mathematical model based on a modified Stokesian dynamics particle simulation technique was developed and applied in several studies of consolidation-related phenomena. The model includes particle-particle and particle-boundary hydrodynamics, colloidal interactions, Born repulsion, and a steric repulsion model. The Brownian motion and a free surface model were incorporated to enable the specific investigation of consolidation and drying. Filter cake stability was simulated in various particle systems, and subjected to a range of base substrate absorption rates and system temperatures. The stability of the filter cake was primarily affected by the absorption rate and size of particles. Temperature was also shown to have an influence. The consolidation of polydisperse systems, with varying wet coating thicknesses, was studied using imposed pilot trial and model-based drying conditions. The results show that drying methods have a clear influence on the microstructure development, on small particle distributions in the coating layer and also on the mobility of particles during consolidation. It is concluded that colloidal properties can significantly impact coating layer shrinkage as well as the internal solids concentration profile. Visualisations of particle system development in time and comparison of systems at different conditions are useful in illustrating coating layer structure formation mechanisms. The results aid in understanding the underlying mechanisms of pigment coating layer consolidation. Guidance is given regarding the relationship between coating process conditions and internal coating slurry properties and their effects on the microstructure of the coating.

Numerical Simulation of Stochastic Di erential Equations

Stochastic differential equation (SDE) is a differential equation in which some of the terms and its solution are stochastic processes. SDEs play a central role in modeling physical systems like finance, Biology, Engineering, to mention some. In modeling process, the computation of the trajectories (sample paths) of solutions to SDEs is very important. However, the exact solution to a SDE is generally difficult to obtain due to non-differentiability character of realizations of the Brownian motion. There exist approximation methods of solutions of SDE. The solutions will be continuous stochastic processes that represent diffusive dynamics, a common modeling assumption for financial, Biology, physical, environmental systems. This Masters' thesis is an introduction and survey of numerical solution methods for stochastic differential equations. Standard numerical methods, local linearization methods and filtering methods are well described. We compute the root mean square errors for each method from which we propose a better numerical scheme. Stochastic differential equations can be formulated from a given ordinary differential equations. In this thesis, we describe two kind of formulations: parametric and non-parametric techniques. The formulation is based on epidemiological SEIR model. This methods have a tendency of increasing parameters in the constructed SDEs, hence, it requires more data. We compare the two techniques numerically.

Excessive functions, Appell polynomials and optimal stopping

The main topic of the thesis is optimal stopping. This is treated in two research articles. In the first article we introduce a new approach to optimal stopping of general strong Markov processes. The approach is based on the representation of excessive functions as expected suprema. We present a variety of examples, in particular, the Novikov-Shiryaev problem for Lévy processes. In the second article on optimal stopping we focus on differentiability of excessive functions of diffusions and apply these results to study the validity of the principle of smooth fit. As an example we discuss optimal stopping of sticky Brownian motion. The third research article offers a survey like discussion on Appell polynomials. The crucial role of Appell polynomials in optimal stopping of Lévy processes was noticed by Novikov and Shiryaev. They described the optimal rule in a large class of problems via these polynomials. We exploit the probabilistic approach to Appell polynomials and show that many classical results are obtained with ease in this framework. In the fourth article we derive a new relationship between the generalized Bernoulli polynomials and the generalized Euler polynomials.

Covariant Phase Observables in Quantum Mechanics

The aim of this thesis is to present a solution to the quantum phase problem of the single-mode optical field. The solution is based on the use of phase shift covariant normalized positive operator measures. These measures describe realistic direct coherent state phase measurements such as the phase measurement schemes based on eight-port homodyne detection or heterodyne detection. The structure of covariant operator measures and, more generally, covariant sesquilinear form measures is analyzed in this work. Four different characterizations for phase shift covariant normalized positive operator measures are presented. The canonical covariant operator measure is definded and its properties are studied. Finally, some other suggested phase theories are introduced to investigate their connections to the covariant sesquilinear form measures.

Quantum transport phenomena and shallow impurity states in CdSb

This work is dedicated to investigation of the energy spectrum of one of the most anisotropic narrow-gap semiconductors, CdSb. At the beginning of the present studies even the model of its energy band structure was not clear. Measurements of galvanomagnetic effects in wide temperature range (1.6 - 300 K) and in magnetic fields up to 30 T were chosen for clarifying of the energy spectrum in the intentionally undoped CdSb single crystals and doped with shallow impurities (In, Ag). Detection of the Shubnikov - de Haas oscillations allowed estimating the fundamental energy spectrum parameters. The shapes of the Fermi surfaces of electrons (sphere) and holes (ellipsoid), the number of the equivalent extremums for valence band (2) and their positions in the Brillouin zone were determined for the first time in this work. Also anisotropy coefficients, components of the tensor of effective masses of carriers, effective masses of density of states, nonparabolicity of the conduction and valence bands, g-factor and its anisotropy for n- and p-CdSb were estimated for the first time during these studies. All the results obtained are compared with the cyclotron resonance data and the corresponding theoretical calculations for p-CdSb. This is basic information for the analyses of the complex transport properties of CdSb and for working out the energy spectrum model of the shallow energy levels of defects and impurities in this semiconductor. It was found out existence of different mechanisms of hopping conductivity in the presence of metal - insulator transition induced by magnetic field in n- and p-CdSb. Quite unusual feature opened in CdSb is that different types of hopping conductivity may take place in the same crystal depending on temperature, magnetic field or even orientation of crystal in magnetic field. Transport properties of undoped p-CdSb samples show that the anisotropy of the resistivity in weak and strong magnetic fields is determined completely by the anisotropy of the effective mass of the holes. Temperature and magnetic field dependence of the Hall coefficient and magnetoresistance is attributed to presence of two groups of holes with different concentrations and mobilities. The analysis demonstrates that below Tcr ~ 20 K and down to ~ 6 - 7 K the low-mobile carriers are itinerant holes with energy E2 ≈ 6 meV. The high-mobile carriers, at all temperatures T < Tcr, are holes activated thermally from a deeper acceptor band to itinerant states of a shallower acceptor band with energy E1 ≈ 3 meV. Analysis of temperature dependences of mobilities confirms the existence of the heavy-hole band or a non-equivalent maximum and two equivalent maxima of the light-hole valence band. Galvanomagnetic effects in n-CdSb reveal the existence of two groups of carriers. These are the electrons of a single minimum in isotropic conduction band and the itinerant electrons of the narrow impurity band, having at low temperatures the energies above the bottom of the conduction band. It is found that above this impurity band exists second impurity band of only localized states and the energy of both impurity bands depend on temperature so that they sink into the band gap when temperature is increased. The bands are splitted by the spin, and in strong magnetic fields the energy difference between them decreases and redistribution of the electrons between the two impurity bands takes place. Mobility of the conduction band carriers demonstrates that scattering in n-CdSb at low temperatures is strongly anisotropic. This is because of domination from scattering on the neutral impurity centers and increasing of the contribution to mobility from scattering by acoustic phonons when temperature increases. Metallic conductivity in zero or weak magnetic field is changed to activated conductivity with increasing of magnetic field. This exhibits a metal-insulator transition (MIT) induced by the magnetic field due to shift of the Fermi level from the interval of extended states to that of the localized states of the electron spectrum near the edge of the conduction band. The Mott variablerange hopping conductivity is observed in the low- and high-field intervals on the insulating side of the MIT. The results yield information about the density of states, the localization radius of the resonant impurity band with completely localized states and about the donor band. In high magnetic fields this band is separated from the conduction band and lies below the resonant impurity bands.

Induction motor versus permanent magnet synchronous motor in motion control applications: a comparative study

High dynamic performance of an electric motor is a fundamental prerequisite in motion control applications, also known as servo drives. Recent developments in the field of microprocessors and power electronics have enabled faster and faster movements with an electric motor. In such a dynamically demanding application, the dimensioning of the motor differs substantially from the industrial motor design, where feasible characteristics of the motor are for example high efficiency, a high power factor, and a low price. In motion control instead, such characteristics as high overloading capability, high-speed operation, high torque density and low inertia are required. The thesis investigates how the dimensioning of a high-performance servomotor differs from the dimensioning of industrial motors. The two most common servomotor types are examined; an induction motor and apermanent magnet synchronous motor. The suitability of these two motor types indynamically demanding servo applications is assessed, and the design aspects that optimize the servo characteristics of the motors are analyzed. Operating characteristics of a high performance motor are studied, and some methods for improvements are suggested. The main focus is on the induction machine, which is frequently compared to the permanent magnet synchronous motor. A 4 kW prototype induction motor was designed and manufactured for the verification of the simulation results in the laboratory conditions. Also a dynamic simulation model for estimating the thermal behaviour of the induction motor in servo applications was constructed. The accuracy of the model was improved by coupling it with the electromagnetic motor model in order to take into account the variations in the motor electromagnetic characteristics due to the temperature rise.

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.

Market Study of Electric Drive Motion Control Business

Tämän diplomityön tavoitteena oli tutkia älykkäiden paikoituskäyttöjen markkinoita ja liiketoimintamalleja. Työn pääongelmina oli määritellä alalla käytössä olevaa terminologiaa, määrittää markkinoiden koko paikoitusominaisuudet omaaville kolmivaihetaajuusmuuttajille, tutkia viiden alalla toimivan paikoituskäyttötoimittajan liiketoimintarakenteita ja tuotteita teknisestä näkökulmasta sekä esitellä kaksi teollisuuden käyttökohdetta paikoituskäytölle. Työn sisältö voidaan jakaa neljään eri osioon. Terminologian määrittely- ja markkinatutkimusosiot perustuvat pääasiassa kirjallisuustutkimukseen. Paikoituskäyttöjen toimittajia sekä niiden tuotteita käsittelevä osuus perustuu kirjallisuustutkimukseen sekä teknisiin esitteisiin ja manuaaleihin. Paikoituskäyttöjen sovellusesimerkit on selvitetty haastatteluin. Työ painottuu paikoituskäyttötoimittajien tuotteiden, tuoteominaisuuksien ja tuotetarjonnan tarkasteluun. Työn tuloksena on määritelty paikoituskäyttöjen liiketoiminnan tärkeimmät termit, paikoituskäyttöjen markkinoiden koko sekä markkinoiden koko paikoitusominaisuudet omaavalle kolmivaihetaajuusmuuttajalle. Alalla toimivien paikoituskäyttötoimittajien liiketoimintarakenne on selvitetty, jonka mukaan toimittajat on profiloitu komponentti-, komponenttipaketti-, toimialakeskeisiksi tai automaatiotoimittajiksi. Toimittajien paikoituskäyttötuotteet on luokiteltu viiteen eri luokkaan niiden teknisten ominaisuuksien perusteella. Lisäksi paikoituskäyttöjen suorituskyvyt on selvitetty säätimien momentti-, nopeus-, ja paikoituslaskenta-aikatasojen sekä kenttäväyläliityntöjen suhteen. Työssä kuvatut vanerinsorvausprosessi sekä FMS -materiaalinkäsittelyprosessi esittävät paikoituskäyttöjen potentiaalisia sovelluskohteita.

Structural and optical properties of InAs/GaAs quantum structures

The goal of the thesis was to study fundamental structural and optical properties of InAs islands and In(Ga)As quantum rings. The research was carried out at the Department of Micro and Nanosciences of Helsinki University of Technology. A good surface quality can be essential for the potential applications in optoelectronic devices. For such device applications it is usually necessary to control size, density and arrangement of the islands. In order to study the dependence of the structural properties of the islands and the quantum rings on growth conditions, atomic force microscope was used. Obtained results reveal that the size and the density of the In(Ga)As quantum rings strongly depend on the growth temperature, the annealing time and the thickness of the partial capping layer. From obtained results it is possible to conclude that to get round shape islands and high density one has to use growth temperature of 500 ̊C. In the case of formation of In(Ga)As quantum rings the effect of mobility anisotropy is observed that so the shape of the rings is not symmetric. To exclude this effect it is preferable to use a higher annealing temperature of 570 ̊C. Optical properties were characterized by PL spectroscopy. PL emission was observed from buried InAs quantum dots and In(Ga)As quantum rings grown with different annealing time and temperature and covered with a various thickness of the partial capping layer.

Photoluminescence of GaAs/AlGaAs quantum wells

In this thesis is studied the influence of uniaxial deformation of GaAs/AlGaAs quantum well structures to photoluminescence. Uniaxial deformation was applied along [110] and polarization ratio of photoluminescence at T = 77 K and 300 K was measured. Also the physical origin of photoluminescence lines in spectrum was determined and the energy band splitting value between states of heavy and light holes was estimated. It was found that the dependencies of polarization ratio on uniaxial deformation for bulk GaAs and GaAs/AlGaAs are different. Two observed lines in photoluminescence spectrum are induced by free electron recombination to energy sublevels of valence band corresponding to heavy and light holes. Those sublevels are splited due to the combination of size quantization and external pressure. The quantum splitting energy value was estimated. Also was shown a method, which allows to determine the energy splitting value of sublevels at room temperature and at comparatively low uniaxial deformation, when the other method for determining of the splitting becomes impossible.