Advanced algorithms for the analysis of data sequences in Matlab

Cílem této práce je se seznámení s možnostmi programu Matlab z hlediska detailní analýzy deterministických dynamických systémů. Jedná se především o analýzu časové posloupnosti a o nalezení Lyapunových exponentů. Dalším cílem je navrhnout algoritmus umožňující specifikovat chování systému na základě znalosti příslušných diferenciálních rovnic. To znamená, nalezení chaotických systémů.This work aims to familiarize with the possibilities of Matlab in terms of detailed analysis of deterministic dynamical systems. This is essentially a analysis of time series and finding Lyapunov exponents. Another objective is to design an algorithm allowing to specify the system behavior based on knowledge of the relevant differential equations. That means finding chaotic systems.

Qualitative modeling of chaotic logical circuits and walking droplets: a dynamical systems approach

Logical circuits and wave-particle duality have been studied for most of the 20th century. During the current century scientists have been thinking differently about these well-studied systems. Specifically, there has been great interest in chaotic logical circuits and hydrodynamic quantum analogs. Traditional logical circuits are designed with minimal uncertainty. While this is straightforward to achieve with electronic logic, other logic families such as fluidic, chemical, and biological, naturally exhibit uncertainties due to their inherent nonlinearity. In recent years, engineers have been designing electronic logical systems via chaotic circuits. While traditional boolean circuits have easily determined outputs, which renders dynamical models unnecessary, chaotic logical circuits employ components that behave erratically for certain inputs. There has been an equally dramatic paradigm shift for studying wave-particle systems. In recent years, experiments with bouncing droplets (called walkers) on a vibrating fluid bath have shown that quantum analogs can be studied at the macro scale. These analogs help us ask questions about quantum mechanics that otherwise would have been inaccessible. They may eventually reveal some unforeseen properties of quantum mechanics that would close the gap between philosophical interpretations and scientific results. Both chaotic logical circuits and walking droplets have been modeled as differential equations. While many of these models are very good in reproducing the behavior observed in experiments, the equations are often too complex to analyze in detail and sometimes even too complex for tractable numerical solution. These problems can be simplified if the models are reduced to discrete dynamical systems. Fortunately, both systems are very naturally time-discrete. For the circuits, the states change very rapidly and therefore the information during the process of change is not of importance. And for the walkers, the position when a wave is produced is important, but the dynamics of the droplets in the air are not. This dissertation is an amalgam of results on chaotic logical circuits and walking droplets in the form of experimental investigations, mathematical modeling, and dynamical systems analysis. Furthermore, this thesis makes connections between the two topics and the various scientific disciplines involved in their studies

Symmetry in Chaotic Systems and Circuits

Symmetry can play an important role in the field of nonlinear systems and especially in the design of nonlinear circuits that produce chaos. Therefore, this Special Issue, titled “Symmetry in Chaotic Systems and Circuits”, presents the latest scientific advances in nonlinear chaotic systems and circuits that introduce various kinds of symmetries. Applications of chaotic systems and circuits with symmetries, or with a deliberate lack of symmetry, are also presented in this Special Issue. The volume contains 14 published papers from authors around the world. This reflects the high impact of this Special Issue

Quantum shot noise in mesoscopic superconductor-semiconductor heterostructures

Shot noise in a mesoscopic electrical conductor have become one of the most attentiondrawing subject over the last decade. This is because the shot-noise measurements provide a powerful tool to study charge transport in mesoscopic systems [1]. While conventional resistance measurements yield information on the average probability for the transmission of electrons from source to drain, shot-noise provides additional information on the electron transfer process, which can not be obtained from resistance measurements. For example, one can determine the charge ‘q’ of the current carrying quasi-particles in different systems from the Poisson shot noise SI = 2q�I� [2] where �I� is the mean current of the system. For instance, the quasi-particle charge is a fraction of the electron charge ‘e’ in the fractional quantum Hall regime [3, 4, 5]. The multiple charge quanta were observed in an atomic point contact between two superconducting electrodes [6]. Shot-noise also provides information on the statistics of the electron transfer. Shot noise in general is suppressed from its classical value SI = 2e�I�, due to the correlations. In mesoscopic conductors, due to the Pauli principle in fermion statistics, electrons are highly correlated. As a results, the noise is fully suppressed in the limit of a perfect open channel T = 1. For the opposite limit of low transmission T � 1, transmission of electron follows a Poisson process and recovers the Schottky result SI = 2e�I� [2]. For many channel systems, shot-noise is suppressed to 1/2 × 2e�I� for a symmetric double barrier junction [7, 8], to 1/3 in a disordered wire [9, 10, 11, 12, 13, 14] and to 1/4 in an open chaotic cavity [15, 16, 17]. When a superconductor is involved, the shot-noise can be enhanced by virtue of the Andreev reflection process taking place at the interface between a normal metal and a superconductor. In some limiting cases, e.g. in the tunneling and disordered limit, the shot-noise can be doubled with respect to its normal state value [18, 19, 20, 21]. One of the main results of this thesis is an extensive comparison of our experimental data on conductance and shot noise measurements in a S-N junction with various theoretical models. In addition to measure shot-noise in a two-terminal geometry, one can also perform the fluctuation measurements on multi-terminal conductors. Whereas shotnoise corresponds to the autocorrelation of fluctuations from the same leads, crosscorrelation measurements of fluctuations between different leads provide a wealth of new experiments. For example, the exchange-correlations can be measured directly from these geometry [22]. Experimental attempt in mesoscopic electronic device was the correlation measurements [14, 23] on electron beam-splitter geometry [24] which is the analogue to the Hanbury-Brown Twiss (HBT) experiment in optics. In their experiment, Hanbury-Brown and Twiss demonstrated the intensity-intensity correlations of the light of a star in order to determine its diameter [25]. They measured a positive correlations between two different output photon beams as predicted to the particles obeying Bose-Einstein statistics. This behavior is often called ‘bunching’. On the other hand, a stream of the particles obeying Fermi-Dirac statistics is expected to show a anti-bunching behavior, resulting in a negative correlation of the intensity fluctuations. Latter one was confirmed by a Fermionic version of HBT experiments in single-mode, high-mobility semiconductor 2DEG systems [14, 23]. Whereas in a single electron picture, correlations between Fermions are always negative1 (anti-bunching), the correlation signal is expected to become positive if two electrons are injected simultaneously to two arms and leave the device through different leads for the coincident detection in both outputs2. One simple example is the splitting of the cooper pair in a Y-junction geometry in front of the superconductor. Fig.1.1 shows the possible experimental scheme of the correlation measurement as described here and the sample realized in an high-mobility semiconductor heterostructures. Since all three experiments were done3, only one left unfolded, ‘The positive correlations from the Fermionic system’. The main motivation of this thesis work was to find a positive correlations in the device shown in Fig.1.1. In a well defined single channel collision experiment on an electron beam splitter, it has theoretically been shown that the measured correlations are sensitive to the spin entanglement [29, 30]. This is another even more exciting issue and we would like to mention that the experimental quest for positive correlations is important for the new field of quantum computation and communication in the solid state, [31, 32] in which entangled electrons play a crucial role. A natural source of entanglement is found in superconductors in which electrons are paired in a spin-singlet state. A source of entangled electrons may therefore be based on a superconducting injector.[33, 34, 27, 35, 36, 37, 38, 38, 39, 40, 41] Even more so, an electronic beamsplitter is capable of distinguishing entangled electrons from single electrons.[29, 42] However, the positive correlations have not been observed in solid-state mesoscopic devices until today. This thesis is organized as follows. Chapter 2 is devoted to the theoretical background of the electrical transport and the current fluctuations. We introduce the basic concept of electrical transport and the shot noise in normal state and superconductor-normal metal (S-N) junction. We also briefly review the theoretical proposals and arguments about the current-current cross-correlations in threeterminal systems. In Chapter 3, we describe the sample fabrication techniques which have been done in our laboratory such as e-beam lithography, metallization and etching. We present also the characterization of our particular system, niobium (Nb) / InAs-based 2DEG junction. Chapter 4 describes the reliable low-temperature measurement technique for detecting the noise. We characterize our measurement setup using a simple RC-circuit model. In Chapter 5, our main results about the shot noise of S-N junction are presented in detail

Spin-Mediated Consciousness: Theory, Experimental Studies, Further Development & Related Topics

We postulate that consciousness is intrinsically connected to quantum spin since the latter is the origin of quantum effects in both Bohm and Hestenes quantum formulisms and a fundamental quantum process associated with the structure of space-time. Applying these ideas to the particular structures and dynamics of the brain, we have developed a detailed model of quantum consciousness. We have also carried out experiments from the perspective of our theory to test the possibility of quantum-entangling the quantum entities inside the brain with those of an external chemical substance. We found that applying magnetic pulses to the brain when an anaesthetic was placed in between caused the brain to feel the effect of said anaesthetic as if the test subject had actually inhaled the same. We further found that drinking water exposed to magnetic pulses, laser light or microwave when an anaesthetic was placed in between also causes brain effects in various degrees. Additional experiments indicate that the said brain effect is indeed the consequence of quantum entanglement. Recently we have studied non-local effects in simple physics systems. We have found that the pH value, temperature and gravity of a liquid in the detecting reservoirs can be non-locally affected through manipulating another liquid in a remote reservoir quantum-entangled with the former. In particular, the pH value changes in the same direction as that being manipulated; the temperature can change against that of local environment; and the gravity can change against local gravity. We suggest that they are mediated by quantum entanglement between nuclear and/or electron spins in treated liquid and discuss the profound implications of these results. This paper now also includes materials on further development of the theory and related topics.Comment: 92 pages; expanded content; minor corrections; for additional information, please visit http://quantumbrain.or

Is it the boundaries or disorder that dominates electron transport in semiconductor `billiards'?

Semiconductor billiards are often considered as ideal systems for studying dynamical chaos in the quantum mechanical limit. In the traditional picture, once the electron's mean free path, as determined by the mobility, becomes larger than the device, disorder is negligible and electron trajectories are shaped by specular reflection from the billiard walls alone. Experimental insight into the electron dynamics is normally obtained by magnetoconductance measurements. A number of recent experimental studies have shown these measurements to be largely independent of the billiards exact shape, and highly dependent on sample-to-sample variations in disorder. In this paper, we discuss these more recent findings within the full historical context of work on semiconductor billiards, and offer strong evidence that small-angle scattering at the sub-100 nm length-scale dominates transport in these devices, with important implications for the role these devices can play for experimental tests of ideas in quantum chaos.Comment: Submitted to Fortschritte der Physik for special issue on Quantum Physics with Non-Hermitian Operator

From Quantum Optics to Quantum Technologies

Quantum optics is the study of the intrinsically quantum properties of light. During the second part of the 20th century experimental and theoretical progress developed together; nowadays quantum optics provides a testbed of many fundamental aspects of quantum mechanics such as coherence and quantum entanglement. Quantum optics helped trigger, both directly and indirectly, the birth of quantum technologies, whose aim is to harness non-classical quantum effects in applications from quantum key distribution to quantum computing. Quantum light remains at the heart of many of the most promising and potentially transformative quantum technologies. In this review, we celebrate the work of Sir Peter Knight and present an overview of the development of quantum optics and its impact on quantum technologies research. We describe the core theoretical tools developed to express and study the quantum properties of light, the key experimental approaches used to control, manipulate and measure such properties and their application in quantum simulation, and quantum computing.Comment: 20 pages, 3 figures, Accepted, Prog. Quant. Ele