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.

Wigner distribution for a class of isospectral position-dependent mass systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Age constraints and fine tuning in variable-mass particle models

VAMP (variable-mass particle) scenarios, in which the mass of the cold dark matter particles is a function of the scalar field responsible for the present acceleration of the Universe, have been proposed as a solution to the cosmic coincidence problem, since in the attractor regime both dark energy and dark matter scale in the same way. We find that only a narrow region in parameter space leads to models with viable values for the Hubble constant and dark energy density today. In the allowed region, the dark energy density starts to dominate around the present epoch and consequently such models cannot solve the coincidence problem. We show that the age of the Universe in this scenario is considerably higher than the age for noncoupled dark energy models, and conclude that more precise independent measurements of the age of the Universe would be useful in distinguishing between coupled and noncoupled dark energy models.

On the generalized canonical equations of Hamilton for a time-dependent mass particle

Fundamental principles of mechanics were primarily conceived for constant mass systems. Since the pioneering works of Meshcherskii (see historical review in Mikhailov (Mech. Solids 10(5):32-40, 1975), efforts have been made in order to elaborate an adequate mathematical formalism for variable mass systems. This is a current research field in theoretical mechanics. In this paper, attention is focused on the derivation of the so-called 'generalized canonical equations of Hamilton' for a variable mass particle. The applied technique consists in the consideration of the mass variation process as a dissipative phenomenon. Kozlov's (Stek. Inst. Math 223:178-184, 1998) method, originally devoted to the derivation of the generalized canonical equations of Hamilton for dissipative systems, is accordingly extended to the scenario of variable mass systems. This is done by conveniently writing the flux of kinetic energy from or into the variable mass particle as a 'Rayleigh-like dissipation function'. Cayley (Proc. R Soc. Lond. 8:506-511, 1857) was the first scholar to propose such an analogy. A deeper discussion on this particular subject will be left for a future paper.

Merging of low-mass systems and the origin of the Fundamental Plane

We present a new set of dissipationless N-body simulations to examine the feasibility of creating bright ellipticals (following the Kormendy relation, hereafter KR) by hierarchically merging present-day early-type dwarf galaxies, and to study how the encounter parameters affect the location of the end product in the (mu(e))-R-e plane. We investigate the merging of one-component galaxies of both equal and different masses, the merging of two-component galaxy models to explore the effect of dark haloes on the final galaxy characteristics, and the merging of ultracompact dwarf galaxies. We find that the increase of (mu(e)) with R-e is attributable to an increase in the initial orbital energy. The merger remnants shift down in the (mu(e))-R-e plane and fail to reach the KR. Thus, the KR is not reproducible by mergers of dwarf early-type systems, rendering untenable the theory that present-day dwarfs are responsible for even a small fraction of the present-day ellipticals, unless a considerable amount of dissipation is invoked. However, we do find that present-day dwarfs can be formed by the merger of ultracompact dwarfs.

Equation of Motion Governing the Dynamics of Vertically Collapsing Buildings

The present paper aims at contributing to a discussion, opened by several authors, on the proper equation of motion that governs the vertical collapse of buildings. The most striking and tragic example is that of the World Trade Center Twin Towers, in New York City, about 10 years ago. This is a very complex problem and, besides dynamics, the analysis involves several areas of knowledge in mechanics, such as structural engineering, materials sciences, and thermodynamics, among others. Therefore, the goal of this work is far from claiming to deal with the problem in its completeness, leaving aside discussions about the modeling of the resistive load to collapse, for example. However, the following analysis, restricted to the study of motion, shows that the problem in question holds great similarity to the classic falling-chain problem, very much addressed in a number of different versions as the pioneering one, by von Buquoy or the one by Cayley. Following previous works, a simple single-degree-of-freedom model was readdressed and conceptually discussed. The form of Lagrange's equation, which leads to a proper equation of motion for the collapsing building, is a general and extended dissipative form, which is proper for systems with mass varying explicitly with position. The additional dissipative generalized force term, which was present in the extended form of the Lagrange equation, was shown to be derivable from a Rayleigh-like energy function. DOI: 10.1061/(ASCE)EM.1943-7889.0000453. (C) 2012 American Society of Civil Engineers.

Design of SPR systems with dynamic compensators and output variable structure control

This paper presents necessary and sufficient conditions for the following problem: given a linear time invariant plant G(s) = N(s)D(s)-1 = C(sI - A]-1B, with m inputs, p outputs, p > m, rank(C) = p, rank(B) = rank(CB) = m, £nd a tandem dynamic controller Gc(s) = D c(s)-1Nc(s) = Cc(sI - A c)-1Bc + Dc, with p inputs and m outputs and a constant output feedback matrix Ko ε ℝm×p such that the feedback system is Strictly Positive Real (SPR). It is shown that this problem has solution if and only if all transmission zeros of the plant have negative real parts. When there exists solution, the proposed method firstly obtains Gc(s) in order to all transmission zeros of Gc(s)G(s) present negative real parts and then Ko is found as the solution of some Linear Matrix Inequalities (LMIs). Then, taking into account this result, a new LMI based design for output Variable Structure Control (VSC) of uncertain dynamic plants is presented. The method can consider the following design specifications: matched disturbances or nonlinearities of the plant, output constraints, decay rate and matched and nonmatched plant uncertainties. © 2006 IEEE.

Variable structure control of switched systems based on Lyapunov-Metzler-SPR systems

This paper presents two Variable Structure Controllers (VSC) for continuous-time switched plants. It is assumed that the state vector is available for feedback. The proposed control system provides a switching rule and also the variable structure control input. The design is based on Lyapunov-Metzler (LM) inequalities and also on Strictly Positive Real (SPR) systems stability results. The definition of Lyapunov-Metzler-SPR (LMS) systems and its direct application in the design of VSC for switched systems are introduced in this paper. Two examples illustrate the design of the proposed VSC, considering a plant given by a switched system with a switched-state control law and two linear time-invariant systems, that are not controllable and also can not be stabilized with state feedback. ©2008 IEEE.

The effect of fractional order in variable structure control

This paper studies fractional variable structure controllers. Two cases are considered namely, the sliding reference model and the control action, that are generalized from integer into fractional orders. The test bed consists in a mechanical manipulator and the effect of the fractional approach upon the system performance is evaluated. The results show that fractional dynamics, both in the switching surface and the control law are important design algorithms in variable structure controllers.

Modeling and control of electromechanical systems

The material presented in the these notes covers the sessions Modelling of electromechanical systems, Passive control theory I and Passive control theory II of the II EURON/GEOPLEX Summer School on Modelling and Control of Complex Dynamical Systems.We start with a general description of what an electromechanical system is from a network modelling point of view. Next, a general formulation in terms of PHDS is introduced, and some of the previous electromechanical systems are rewritten in this formalism. Power converters, which are variable structure systems (VSS), can also be given a PHDS form.We conclude the modelling part of these lectures with a rather complex example, showing the interconnection of subsystems from several domains, namely an arrangement to temporally store the surplus energy in a section of a metropolitan transportation system based on dc motor vehicles, using either arrays of supercapacitors or an electric poweredflywheel. The second part of the lectures addresses control of PHD systems. We first present the idea of control as power connection of a plant and a controller. Next we discuss how to circumvent this obstacle and present the basic ideas of Interconnection and Damping Assignment (IDA) passivity-based control of PHD systems.

Dynamic simulation for closed loops in heating systems with decision-making support

Nowadays utilising the proper HVAC system is essential both in extreme weather conditions and dense buildings design. Hydraulic loops are the most common parts in all air conditioning systems. This article aims to investigate the performance of different hydraulic loop arrangements in variable flow systems. Technical, economic and environmental assessments have been considered in this process. A dynamic system simulation is generated to evaluate the system performance and an economic evaluation is conducted by whole life cost assessment. Moreover, environmental impacts have been studied by considering the whole life energy consumption, CO2 emission, the embodied energy and embodied CO2 of the system components. Finally, decision-making in choosing the most suitable hydraulic system among five well-known alternatives has been proposed.

CONTROL OF UNCERTAIN DYNAMIC-SYSTEMS USING STRICTLY POSITIVE REAL SYSTEMS

This paper presents necessary and sufficient conditions to turn a linear time-invariant system with p outputs, m inputs, p greater-than-or-equal-to m and using only inputs and outputs measurements into a Strictly Positive Real (SPR).Two results are presented. In the first, the system compensation is made by two static compensators, one of which forward feeds the outputs and the second back feeds the outputs of the nominal system.The second result presents conditions for the Walcott and Zak variable structure observer-controller synthesis. In this problem, if the nominal system is given by {A,B,C}, then the compensated system is given by {A+GC,B,FC} where F and G are the constant compensation matrices. These results are useful in the control system with uncertainties.

Linear matrix inequality-based robust model predictive control for time-delayed systems

This work addresses the solution to the problem of robust model predictive control (MPC) of systems with model uncertainty. The case of zone control of multi-variable stable systems with multiple time delays is considered. The usual approach of dealing with this kind of problem is through the inclusion of non-linear cost constraint in the control problem. The control action is then obtained at each sampling time as the solution to a non-linear programming (NLP) problem that for high-order systems can be computationally expensive. Here, the robust MPC problem is formulated as a linear matrix inequality problem that can be solved in real time with a fraction of the computer effort. The proposed approach is compared with the conventional robust MPC and tested through the simulation of a reactor system of the process industry.

Modal testing and numerical modeling of the dynamic properties of layered sheet-steel structure

Recently, due to the increasing total construction and transportation cost and difficulties associated with handling massive structural components or assemblies, there has been increasing financial pressure to reduce structural weight. Furthermore, advances in material technology coupled with continuing advances in design tools and techniques have encouraged engineers to vary and combine materials, offering new opportunities to reduce the weight of mechanical structures. These new lower mass systems, however, are more susceptible to inherent imbalances, a weakness that can result in higher shock and harmonic resonances which leads to poor structural dynamic performances. The objective of this thesis is the modeling of layered sheet steel elements, to accurately predict dynamic performance. During the development of the layered sheet steel model, the numerical modeling approach, the Finite Element Analysis and the Experimental Modal Analysis are applied in building a modal model of the layered sheet steel elements. Furthermore, in view of getting a better understanding of the dynamic behavior of layered sheet steel, several binding methods have been studied to understand and demonstrate how a binding method affects the dynamic behavior of layered sheet steel elements when compared to single homogeneous steel plate. Based on the developed layered sheet steel model, the dynamic behavior of a lightweight wheel structure to be used as the structure for the stator of an outer rotor Direct-Drive Permanent Magnet Synchronous Generator designed for high-power wind turbines is studied.

Evolución del sistema de información empresarial SAP en la Universidad Del Rosario

Esta propuesta documenta cómo fue el proceso de implementación de SAP en la Universidad del Rosario (UR). Además permite determinar los factores que la definen cómo una implementación exitosa. En esta investigación no tiene en cuenta la implementación de los sistemas de gestión académica, de recursos humanos o e-learning ya que el estudio solo está centrado en el área administrativa. También se estudia el grado de madurez de los sistemas de información de la Universidad, usando el modelo de Luftam validado en el contexto de las tecnologías. La gran pregunta de investigación es: ¿Cómo fue la implementación de SAP en la UR y cómo esto fue una implementación exitosa?