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[en] The study of natural circulation loops is a subject of special concern for the engineering design of advanced nuclear reactors, as natural convection provides an efficient and completely passive heat removal system. However, under certain circumstances thermal-fluid-dynamical instabilities may appear, threatening the reactor safety as a whole.On the other hand, fuzzy logic controllers provide an ideal framework to approach highly non-linear control problems. In the present work, we develop a software-based fuzzy logic controller and study its application to chaotic natural convection loops.We numerically analyse the linguistic control of the loop known as the Welander problem in such conditions that, if the controller were not present, the circulation flow would be non-periodic unstable.We also design a Taka gi-Sugeno fuzzy controller based on a fuzzy model of a natural convection loop with a toroidal geometry, in order to stabilize a Lorenz-chaotic behaviour.Finally, we show experimental results obtained in a rectangular natural circulation loop
[es]Los circuitos termofluidodinamicos de conveccion natural estan cobrando especial importancia en el diseno de reactores nucleares avanzados, debido a que la conveccion natural suministra un sistema eficiente de remocion de calor completamente pasivo.Sin embargo, bajo ciertas condiciones, estos sistemas presentan inestabilidades que pueden llegar a poner en riesgo la seguridad integral del reactor.Por otro lado, los controladores basados en logica difusa proveen un entorno ideal para atacar problemas de control altamente no lineales.En este trabajo desarrollamos un software que implementa un control basado en logica difusa, y estudiamos su aplicacion a loops de conveccion natural caoticos.Analizamos numericamente el control linguistico del loop conocido como el problema de Welander en condiciones tales que, de no existir el control, el caudal de circulacion presentaria un comportamiento inestable no periodico.Disenamos tambien un controlador difuso a partir de un modelo matematico de Takagi y Sugeno para un loop de conveccion natural en geometria toroidal para estabilizar un comportamiento caotico de Lorenz.Finalmente, mostramos resultados experimentales obtenidos en un loop rectangular de conveccion natural
[en] Tunneling is a fundamental effect of quantum mechanics, which allows waves to penetrate into regions that are inaccessible by classical dynamics. We study this phenomenon for generic non-integrable systems with a mixed phase space, where tunneling occurs between the classically separated phase-space regions of regular and chaotic motion. We derive a semiclassical prediction for the corresponding tunneling rates from the regular region to the chaotic sea. This prediction is based on paths which connect the regular and the chaotic region in complexified phase space. We show that these complex paths can be constructed despite the obstacle of natural boundaries. For the standard map we demonstrate that tunneling rates can be predicted with high accuracy, by using only a few dominant complex paths. This gives the semiclassical foundation for the long-conjectured and often-observed exponential scaling with Planck's constant of regular-to-chaotic tunneling rates.
[en] This thesis presents an account of experimental and numerical investigations of two quantum systems whose respective classical analogues are chaotic. These are the δ-kicked rotor, a paradigm in classical chaos theory, and the novel δ-kicked accelerator, created by application of a constant external acceleration or torque to the rotor. The experimental realisation of these systems has been achieved by the exposure of laser-cooled caesium atoms to approximate δ-kicks from a pulsed, high-intensity, vertical standing wave of laser light. Gravity's effect on the atoms can be controlled by appropriate shifting of the profile of the standing wave. Numerical simulations of the systems are based on a diffractive model of the potential's effect. Each system's dynamics are characterised by the final form of the momentum distribution and the dependence of the atoms' mean kinetic energy on the number and time period of the δ-kicks. The phenomena of dynamical localisation and quantum resonances in the δ-kicked rotor, which have no counterparts in the system's classical analogue, are observed and investigated. Similar experiments on the δ-kicked accelerator reveal the striking phenomenon of the quantum accelerator mode, in which a large momentum is transferred to a substantial fraction of the atomic ensemble. This feature, absent in the system's classical analogue, is characterised and an analytic explanation is presented. The effect on each quantum system of decoherence, introduced through spontaneous emission in the atoms, is examined and comparison is made with the results of classical simulations. While having little effect on the classical systems, the level of decoherence used is found to degrade quantum signatures of behaviour. Classical-like behaviour is, to some extent, restored, although significant quantum features remain. Possible applications of the quantum accelerator mode are discussed. These include use as a tool in atom optics and interferometry, a technique for measuring gravity, and a method of preparing atoms in a particular region of phase space. This may allow measurement of quantum phase space stability, and hence investigation of quantum chaos and quantum-classical correspondence. (author)
[en] Many systems in nature, e.g. atoms, molecules and planetary motion, can be described as Hamiltonian systems. In such systems, the transport between different regions of phase space determines some of their most important properties like the stability of the solar system and the rate of chemical reactions. While the transport in lower-dimensional systems with two degrees of freedom is well understood, much less is known for the higher-dimensional case. A central new feature in higher-dimensional systems are transport phenomena due to resonance channels. In this thesis, we clarify the complex geometry of resonance channels in phase space and identify a turnstile mechanism that dominates the transport out of such channels. To this end, we consider the coupled standard map for numerical investigations as it is a generic example for 4D symplectic maps. At first, we visualize resonance channels in phase space revealing their highly non-trivial geometry. Secondly, we study the transport away from such channels. This is governed by families of hyperbolic 1D-tori and their stable and unstable manifolds. We provide an approach to measure the volume of a turnstile in higher dimensions as well as the corresponding transport. From the very good agreement of the two measurements we conclude that these structures are a suitable generalization of the well-known 2D turnstile mechanism to higher dimensions.
[en] Tunneling is one of the most prominent features of quantum mechanics. While the tunneling process in one-dimensional integrable systems is well understood, its quantitative prediction for systems with a mixed phase space is a long-standing open challenge. In such systems regions of regular and chaotic dynamics coexist in phase space, which are classically separated but quantum mechanically coupled by the process of dynamical tunneling. We derive a prediction of dynamical tunneling rates which describe the decay of states localized inside the regular region towards the so-called chaotic sea. This approach uses a fictitious integrable system which mimics the dynamics inside the regular domain and extends it into the chaotic region. Excellent agreement with numerical data is found for kicked systems, billiards, and optical microcavities, if nonlinear resonances are negligible. Semiclassically, however, such nonlinear resonance chains dominate the tunneling process. Hence, we combine our approach with an improved resonance-assisted tunneling theory and derive a unified prediction which is valid from the quantum to the semiclassical regime. We obtain results which show a drastically improved accuracy of several orders of magnitude compared to previous studies. (orig.)
[en] Hamiltonian systems typically exhibit a mixed phase space in which regions of regular and chaotic dynamics coexist. The chaotic transport is restricted due to partial barriers, since they only allow for a small flux between different regions of phase space. In systems with a two-dimensional (2D) phase space these partial barriers are well understood. However, in systems with a four-dimensional (4D) phase space their dynamical origin is an open question. Thus, we study these partial barriers and the related chaotic transport in 4D maps. For the chaotic transport, we observe a slow power-law decay of the Poincaré recurrence statistics. This is caused by long-trapped orbits exploring stochastic layers of resonance channels. Moreover, we analyze them and find clear signatures of partial transport barriers. We identify normally hyperbolic invariant manifolds (NHIMs) as the relevant objects determining the flux across these barriers. In addition, NHIMs also form the backbone for the explicit construction of partial barriers. This allows us to determine the flux by measuring the turnstile volume. Moreover, we conjecture the existence of a relevant partial barrier with minimal flux by generalizing a cantorus barrier present in 2D maps. Local properties of the flux are studied and explained in terms of the NHIM.
[en] Dissipation of energy and the loss of quantum coherence are the main hallmarks of open quantum systems, which refers to a system coupled to many degrees of freedom of an uncontrollable environment. Due to this coupling, the system gradually loses its quantum properties and behaves more "classical". On the other hand, in the regime of large quantum numbers, semiclassical theory helps to understand quantum systems using information about their classical limit, allowing to observe interference effects between classical trajectories. This thesis aims to use the semiclassical approach to study open quantum systems. In this work, a novel notion of temperature for strongly coupled systems is developed., as well as a semiclassical treatment of decoherence in classically chaotic systems. Further, a new approach to catch interference between dissipative classical trajectories is studied, which opens the possibility to observe path interference in quantum thermodynamics.
[en] Generic Hamiltonian systems have a mixed phase space, in which regular and chaotic motion coexist. In the chaotic sea the classical transport is limited by partial barriers, which allow for a flux Φ given by the corresponding turnstile area. Quantum mechanically the transport is suppressed if Planck's constant is large compared to the classical flux, h >> Φ, while for h << Φ classical transport is recovered. For the transition between these limiting cases there are many open questions, in particular concerning the correct scaling parameter and the width of the transition. To investigate this transition in a controlled way, we design a kicked system with a particularly simple phase-space structure, consisting of two chaotic regions separated by one dominant partial barrier. We find a universal scaling with the single parameter Φ/h and a transition width of almost two orders of magnitude in Φ/h. In order to describe this transition, we consider several matrix models. While the numerical data is not well described by the random matrix model proposed by Bohigas, Tomsovic, and Ullmo, a deterministic 2 x 2-model, a channel coupling model, and a unitary model are presented, which describe the transitional behavior of the designed kicked system. This is also confirmed for the generic standard map, suggesting a universal scaling behavior for the quantum transition of a partial barrier. (orig.)
[en] One of the main goals of classical and quantum physics is to solve the many-body problem. In nuclear theory, several methods have been developed and provide accurate results. In this thesis, we remind how symmetry can be used to obtain analytical solutions of the quantum many-body problem. We emphasize that unitary Lie algebras play a crucial role in quantum mechanics and propose and implement a method to build irreducible representations of this algebra from its highest-weight state. Calculations of bosonic and fermionic spectra are performed with realistic and with random interactions. Studies with rotational invariant two-body random interactions have unveiled high degree of order (a marked statistical preference is found for ground states with angular momentum equal to zero). In the second chapter of this thesis, it is argued that the spectral properties of this kind of interaction depend on the choice of the valence space. In particular, we propose a geometrical method to predict the properties of the ground state in certain cases. We also present numerical results when the geometrical approach can not be applied. In the third chapter, we study the link between quantum chaos and nuclear spectra calculated with realistic interactions. (author)
[en] Ultracold atoms and Bose-Einstein condensates (BECs) have evolved to one of the most experimentally controllable and tunable systems, through an enormous experimental progress in manipulating, cooling, and trapping techniques. To utilize ultracold atoms and BECs in future quantum metrology schemes, a detailed knowledge of their dynamics is necessary. We study theoretically the dynamics of ultracold atoms and BECs in typical one-dimensional trap geometries with external potentials. The external potentials range from harmonic traps with defects, to periodic, aperiodic and disorder potentials. Disorder potentials are especially interesting in connection with Anderson localization. We investigate the dynamics of BECs within the Gross-Pitaevskii equation (GPE) which is equivalent to a nonlinear Schroedinger equation. The GPE plays an important role in the description of BECs and is strictly valid only for the dynamics of the condensate. The GPE does not take into account any excitations out of the condensate, i.e. depletion. We investigate the properties of the GPE and find that for some parameter ranges of the above potentials the solutions of the GPE exhibit wave chaos as measured by the exponential divergence of nearby wave functions in Hilbert space. The emergence of strong local random fluctuations leads to the hypothesis that wave chaos is closely connected to depletion. We utilize the multiconfigurational time-dependent Hartree for bosons (MCDTHB) method to give a numerical proof for the connection between wave chaos of the GPE and depletion of the condensate. It is shown that the validity of the GPE is limited by the appearance of wave chaos. Despite a strong depletion of the condensate, coarse-grained observables such as the width of the atom cloud are well reproduced within the GPE. Accordingly, experimental results for these coarse-grained observables may agree well with the predictions of the GPE although the system does not correspond to a BEC. The found depletion mechanism can be detected experimentally by investigation of local fluctuations or higher order coherence. (author)
[de]Ultrakalte Atome und Bose-Einstein-Kondensate gehoeren zu den am besten experimentell kontrollierbaren und einstellbaren physikalischen Systemen, was durch einen enormen experimentellen Fortschritt in der Manipulation und Kuehlung sowie durch die Entwicklung von Atomfallen erreicht wurde. Die Anwendung von Bose-Einstein-Kondensaten in zukuenftigen Quantenmessverfahren erfordert eine detaillierte Kenntnis der Dynamik der Atome. In der Dissertation wird die Dynamik von ultrakalten Gasen und Bose-Einstein-Kondensaten in typischen eindimensional Fallen mit externen Potentialen untersucht. Zu den untersuchten Potentialen gehoeren harmonische Potentiale mit Defekten, periodische und aperiodische Potentiale sowie Unordnungspotentiale. Letztere sind besonders im Zusammenhang mit der Anderson Lokalisierung von Interesse. Es wird die Dynamik der Bose-Einstein-Kondensate im Rahmen der Gross-Pitaevskii-Gleichung untersucht. Die Gross-Pitaevskii-Gleichung entspricht einer nichtlinearen Schroedinger Gleichung und spielt eine wichtige Rolle in der Beschreibung von Bose-Einstein-Kondensaten. Streng genommen ist die Gross-Pitaevskii-Gleichung nur fuer die Dynamik des Kondensats gueltig. Im Rahmen dieser Gleichung werden keine Anregungen aus dem Kondensat heraus beruecksichtigt. Basierend auf der Untersuchung der Eigenschaften der Gross-Pitaevskii-Gleichung wird in dieser Arbeit gezeigt, dass die Loesungen der Gleichung Wellenchaos aufweisen koennen. Das Wellenchaos manifestiert sich als exponentielle Divergenz von urspruenglich nahe beieinander liegenden Wellenfunktionen im Hilbert Raum fuer bestimmte Parameter der externen Potentiale. Dabei entstehen starke willkuerliche lokale Fluktuationen die zu der Hypothese fuehren, dass das Wellenchaos mit der Anregung des Kondensats in Verbindung steht. Zur ueberpruefung dieser Hypothese wird die zeitabhaengige Multikonfigurations-Hartree-Methode fuer Bosonen (englische Abkuerzung MCTDHB) angewandt. Mit Hilfe dieser Methode wird ein numerischer Beweis fuer den Zusammenhang zwischen Wellenchaos und Anregungen des Kondensats gegeben. Damit wird der Gueltigkeitsbereich der Gross-Pitaevskii-Gleichung mit Auftreten von Wellenchaos abgegrenzt. Trotzdem werden manche gemittelten Observablen, wie etwa die mittlere Breite der Atomwolke, ueber den Gueltigkeitsbereich der Gross-Pitaevskii-Gleichung hinaus richtig reproduziert. Entsprechend koennen ultrakalte Gase im Experiment in diesen gemittelten Observablen gute uebereinstimmung mit der Gross-Pitaevskii-Gleichung liefern, obwohl es sich nicht um ein Bose-Einstein- Kondensat handelt. Der gefunden Anregungsmechanismus ist experimentell zugaenglich durch die Beobachtung lokaler Fluktuationen und Kohaerenz hoeher Ordnung. (author)