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brain oscillations
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Cross-frequency coupling... Oscillations
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time-frequency analysis... neuronal oscillations
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A colloidal particle is driven across a temporally oscillating one-dimensional optical potential energy landscape and its particle motion is analysed. Different modes of dynamic mode locking are observed and are confirmed with the use of phase portraits. The effect of the oscillation frequency on the mode locked step width is addressed and the results are discussed in light of a high-frequency theory and compared to simulations. Furthermore, the influence of the coupling between the particle and the optical landscape on mode locking is probed by increasing the maximum depth of the optical landscape. Stronger coupling is seen to increase the width of mode locked steps. Finally, transport across the temporally oscillating landscape is studied by measuring the effective diffusion coefficient of a mobile particle, which is seen to be highly sensitive to the driving velocity and mode locking.
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cortical oscillations
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alpha oscillations... beta oscillations
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Studies with magnetoencephalography (MEG) are still quite rarely combined simultaneously with methods that can provide a metabolic dimension to MEG investigations. In addition, continuous blood pressure measurements which comply with MEG compatibility requirements are lacking. For instance, by combining methods reflecting neurovascular status one could obtain more information on low frequency fluctuations that have recently gained increasing interest as a mediator of functional connectivity within brain networks. This paper presents a multimodal brain imaging setup, capable to non-invasively and continuously measure cerebral hemodynamic, cardiorespiratory and blood pressure oscillations simultaneously with MEG. In the setup, all methods apart from MEG rely on the use of fibre optics. In particular, we present a method for measuring of blood pressure and cardiorespiratory oscillations continuously with MEG. The potential of this type of multimodal setup for brain research is demonstrated by our preliminary studies on human, showing effects of mild hypercapnia, gathered simultaneously with the presented modalities.
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By solving the non-relativistic Abraham–Lorentz (AL) equation, I demonstrate that the AL equation of motion is not suited for treating the Lorentz atom, because a steady-state solution does not exist. The AL equation serves as a tool, however, for deducing the appropriate parameters Ω and Γ to be used with the equation of forced oscillations in modelling the Lorentz atom. The electric polarisability, which many authors “derived” from the AL equation in recent years, is shown to violate Kramers–Kronig relations rendering obsolete the extracted photon-absorption rate, for example. Fortunately, errors turn out to be small quantitatively, as long as the light frequency ω is neither too close to nor too far from the resonance frequency Ω. The polarisability and absorption cross section are derived for the Lorentz atom by purely classical reasoning and are shown to agree with the quantum mechanical calculations of the same quantities. In particular, oscillator parameters Ω and Γ deduced by treating the atom as a quantum oscillator are found to be equivalent to those derived from the classical AL equation. The instructive comparison provides a deep insight into understanding the great success of Lorentz’s model that was suggested long before the advent of quantum theory.
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Inhhalt Title Contents Summary Zusammenfassung 1 Quantum Computing with Electron Spins 1.1 Quantum Computing - a short review 1.1.1 DiVincenzo criteria 1.1.2 Implementations 1.2 Quantum Computing with spins 1.2.1 Liquid NMR 1.2.2 Pseudo-pure states and scalability 1.2.3 Kane's proposal 1.3 Endohedral fullerenes for Quantum Computing 1.3.1 Gated concept 1.3.2 The first milestone - Quantum Cellular Automaton 2 Group V endohedral fullerenes 2.1 Production 2.1.1 Ion implantation 2.1.2 Characterisation and enrichment 2.2 Phosphorous in C60 2.3 N@C60 and P@C60 as Qubits 2.3.1 Coupling 2.3.2 Decoherence 2.4 Conclusions 3 Relaxation 3.1 Experimental details 3.2 Spin - lattice relaxation 3.3 Spin - spin relaxation 3.4 Conclusions 4 Qubit Rotations and Spin Nutations 4.1 Experimental details 4.2 Nutation and Selectivity 4.3 Nutation of P@C60 (solution) 4.4 Nutation of P@C60 (powder) 4.5 Conclusions 5 Towards a Fullerene Quantum Computer 5.1 A Fullerene-based Quantum Cellular Automaton 5.2 Alignment of N@C60 and N@C70 in a Liquid-Crystal Matrix 5.3 Towards a two Qubit System 5.4 Conclusions 6 Conclusions and Perspectives 6.1 Conclusions 6.2 Perspectives 7 References 7.1 References in chapter 1 7.2 References in chapter 2 7.3 References in chapter 3 7.4 References in chapter 4 7.5 References in chapter 5 7.6 References of chapter 6 Appendix A N@PCBM Publications Acknowledgements Curriculum Vitae 1 1 2 4 6 8 11 12 14 14 16 19 19 20 20 21 26 26 28 29 31 31 32 40 41 45 45 47 50 51 58 61 61 68 72 74 77 77 79 81 81 84 85 86 86 87 89 91 93 95,This work investigates the properties of nitrogen and phosphorous encapsulated in the Buckminster?fullerene C60 for an application as qubits in a quantum computer. Previous works proved the existence of group V endohedral fullerenes. The (cw) ESR spectra showed sharp resonance lines even for chemical modifications of N@C60. First relaxation measurements of N@C60 indicated that these endohedral fullerenes might be good candidates for qubits in a quantum computer. This idea has been developed systematically in this thesis. In this work, it has been shown for the first time that the separation and enrichment via HPLC is possible for P@C60. The first intensive investigation of the spectroscopic properties of P@C60 has been done and consequences of the results for quantum computing with endohedral fullerenes have been discussed. The relaxation properties of P@C60 have been examined in detail. It has been shown that they are similar to those of N@C60. The model for relaxation has been reviewed and improved evaluating the limits of the harmonic oscillator model. The relaxation properties remain mainly molecular even if the spin concentration increases. This means that a quantum computer using endohedral fullerenes might be scalable towards numerous qubits if the dipolar coupling between them is controlled. More spectroscopic properties of P@C60, especially the zero?field splitting that could not be resolved so far, have been investigated using transient nutation experiments. This method has been applied to endohedral fullerenes for the first time. For a quantum computer, transient nutation reveals the behaviour of the spin system under single qubit operations. It has been shown for N@C60 and P@C60 that numerous operations can been done at room temperature. Low temperature measurements showed that the nutation of a S = 3/2 system is complicated under special conditions. The experiments reveal nutation frequencies as predicted by theory. It seems to be possible to implement two qubits in one spin with S = 3/2. However, an alignment of the molecules would be necessary in this case. At the same time, such an alignment would provide control over the dipolar interaction. Therefore, in the last part of this thesis the orientation of endohedral fullerenes in a liquid crystal matrix has been investigated. It has been shown that the alignment of the endohedral monomers N@C60 and N@C70 is possible. However, the alignment of larger molecules like dimers is more difficult although initial steps could be demonstrated. If full orientation of endohedral fullerenes can be achieved while keeping a well?defined distance between them, quantum computing with group V endohedral fullerenes seems to be feasible.,Die vorliegende Arbeit untersucht die Eigenschaften von Stickstoff- und Phosphoratomen im Buckminsterfulleren C60 für die Anwendung als Qubits in einem Quantencomputer. Vorangegangene Arbeiten haben die Existenz der endohedralen Fullerene N@C60 und P@C60 bewiesen. Die (cw) ESR Spektren zeigten scharfe Resonanzlinien - sogar für chemische Modifikationen von N@C60. Erste Messungen der Relaxation von N@C60 deuteten an, dass diese endohedralen Fullerene gute Kandidaten für Qubits in einem Quantencomputer sein könnten. Diese Idee wurde in dieser Dissertation systematisch entwickelt. Zum ersten Mal wird in dieser Arbeit die Trennung und Anreicherung von P@C60 mittels HPLC gezeigt. Nach einer eingehenden Untersuchung der spektroskopischen Eigenschaften von P@C60 werden Konsequenzen im Hinblick auf die Anwendung der endohedralen Fullerene als Bausteine in einem Quantencomputer diskutiert. Experimente zur Relaxation von P@C60 zeigten, dass die Ursachen dieselben wie bei N@C60 sind. Das bisher für die Relaxation verwendete Modell des Harmonischen Oszillators wurde überarbeitet und erweitert. Auch bei steigender Spinkonzentration ändern sich die Relaxationseigenschaften vom Prinzip her nicht. Das bedeutet, dass ein Quantencomputer mit endohedralen Fullerenen auf viele Qubits skalierbar sein könnte. Die Voraussetzung dafür ist jedoch, dass die Dipolkopplung der Qubits kontrolliert wird. Weitere spektroskopische Eigenschaften von P@C60, insbesondere die bisher nicht auflösbare Nullfeld?Aufspaltung, wurden mit Experimenten zur transienten Nutation untersucht. Diese Methode, die auch dem Verhalten des Spinsystems bei Ein?Qubit Operationen entspricht, wurde zum ersten Mal auf endohedrale Fullerene angewendet. Für P@C60 und N@C60 wurde gezeigt, dass eine Vielzahl von Operationen, sogar bei Raumtemperatur, ausgeführt werden kann. Messungen bei tiefer Temperatur zeigten, dass das komplizierte Nutationsverhalten des S = 3/2 Spinsystems genau der Vorhersage der Theorie folgt. Es scheint damit möglich zu sein, zwei Qubits in einem S = 3/2 Spin zu implementieren. In diesem Fall wäre jedoch eine Ausrichtung der Fullerene notwendig. Diese würde zur gleichen auch die Kontrolle über die Dipolkopplung bieten. Im letzten Teil dieser Dissertation wurde daher die Ausrichtung von endohedralen Fullerenen in einer Flüssigkristallmatrix untersucht. Es wurde gezeigt, dass die Ausrichtung der endohedralen Monomere N@C60 und N@C70 möglich ist. Es ist jedoch schwieriger, größere Moleküle, z.B. Dimere, auzurichten, obwohl auch hier erste Schritte demonstriert werden konnten. Quantencomputing mit P@C60 und N@C60 scheint unter der Voraussetzung möglich zu sein, dass eine vollständige Ausrichtung bei gleichmäßigem Abstand zwischen den Fullerenen erreicht wird.,
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Transcranial alternating current stimulation (tACS) is a form of noninvasive brain stimulation and is capable of influencing brain oscillations and cortical networks. In humans, the endogenous oscillation frequency in sensorimotor areas peaks at 20 Hz. This beta-band typically occurs during maintenance of tonic motor output and seems to play a role in interhemispheric coordination of movements. Previous studies showed that tACS applied in specific frequency bands over primary motor cortex (M1) or the visual cortex modulates cortical excitability within the stimulated hemisphere. However, the particular impact remains controversial because effects of tACS were shown to be frequency, duration and location specific. Furthermore, the potential of tACS to modulate cortical interhemispheric processing, like interhemispheric inhibition (IHI), remains elusive. Transcranial magnetic stimulation (TMS) is a noninvasive and well-tolerated method of directly activating neurons in superficial areas of the human brain and thereby a useful tool for evaluating the functional state of motor pathways. The aim of the present study was to elucidate the immediate effect of 10 min tACS in the β-frequency band (20 Hz) over left M1 on IHI between M1s in 19 young, healthy, right-handed participants. A series of TMS measurements (motor evoked potential (MEP) size, resting motor threshold (RMT), IHI from left to right M1 and vice versa) was performed before and immediately after tACS or sham using a double-blinded, cross-over design. We did not find any significant tACS-induced modulations of intracortical excitation (as assessed by MEP size and RMT) and/or IHI. These results indicate that 10 min of 20 Hz tACS over left M1 seems incapable of modulating immediate brain activity or inhibition. Further studies are needed to elucidate potential aftereffects of 20 Hz tACS as well as frequency- specific effects of tACS on intracortical excitation and IHI.
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