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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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Gamma rhythms are known to contribute to the process of memory encoding. However, little is known about the underlying mechanisms at the molecular, cellular and network levels. Using local field potential recording in awake behaving mice and concomitant field potential and whole-cell recordings in slice preparations we found that gamma rhythms lead to activity-dependent modification of hippocampal networks, including alterations in sharp wave- ripple complexes. Network plasticity, expressed as long-lasting increases in sharp wave-associated synaptic currents, exhibits enhanced excitatory synaptic strength in pyramidal cells that is induced postsynaptically and depends on metabotropic glutamate receptor-5 activation. In sharp contrast, alteration of inhibitory synaptic strength is independent of postsynaptic activation and less pronounced. Further, we found a cell type-specific, directionally biased synaptic plasticity of two major types of GABAergic cells, parvalbumin- and cholecystokinin-expressing interneurons. Thus, we propose that gamma frequency oscillations represent a network state that introduces long-lasting synaptic plasticity in a cell-specific manner.
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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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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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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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