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Mesoscopic wave phenomena in electronic and optical ring structuresHentschel, Martina 29 October 2001 (has links)
Gegenstand dieser Arbeit sind Wellenphänomene in mesoskopischen Ringstrukturen. In Teil I der Arbeit befassen wir uns mit spinabhängigem Transport von Elektronen in effektiv eindimensionalen Ringen in Gegenwart inhomogener Magnetfelder. Wir benutzen die exakten Lösungen der Schrödinger-Gleichung im allgemeinen nicht-adiabatischen Fall in einem Transfer-Matrix-Formalismus und untersuchen Auswirkungen von geometrischen Phasen auf den Magnetwiderstand. Für den Spezialfall eines Magnetfeldes in der Ringebene sagen wir einen interessanten Spin-Flip-Effekt vorher, der die Steuerung der Polarisationsrichtung von Elektronen über einen externen Aharonov-Bohm-Fluß erlaubt. Optische mesoskopische Systeme sind Thema von Teil II dieser Arbeit. Wir betrachten zweidimensionale annulare Strukturen, charakterisiert durch unterschiedliche Brechungsindizes, sowohl im klassischen Bild der geometrischen Optik als auch mit Wellenmethoden auf der Grundlage der Maxwellschen Gleichungen. Insbesondere diskutieren wir erstmals eine Streumatrixbeschreibung optischer Mikroresonatoren und wenden sie auf das dielektrische annulare Billard an. Ein Vergleich der Ergebnisse des Wellen- und Strahlenbildes liefert eine gute Übereinstimmung, jedoch sind im Grenzfall großer Wellenlängen von der Ordnung der Systemabmessungen Korrekturen zum Strahlenbild nötig. Wir zeigen am Beispiel von Fresnel-Gesetzen für gekrümmte Oberflächen erstmals, daß der Goos-Hänchen-Effekt diese Korrekturen quantitativ erfaßt. Ausgehend von der Wellenbeschreibung leiten wir neue analytische Formeln für verallgemeinerte Fresnel-Gesetze für beide möglichen Polarisationsrichtungen ab. Die Anwendung des Strahlenbildes erlaubt eine schlüssige Interpretation eines Experiments mit einer quadrupolaren Glasfaser, außerdem schlagen wir Strahlenkonzepte als Grundlage der Konstruktion von Mikrolasern mit maßgeschneiderten Charakteristika vor. / In this work we investigate wave phenomena in mesoscopic systems using different theoretical approaches. In Part I, we focus on effectively one-dimensional electronic ring structures and address the phenomenon of geometric phases in spin-dependent electronic transport in the presence of non-uniform magnetic fields. In the general non-adiabatic case, exact solutions of the Schrödinger equation are used in a transfer matrix formalism to compute the transmission probability through the ring. In the magneto-conductance we identify clear signatures of interference effects due to geometric phases, for example in rings where the non-uniform field is created by a central micromagnet. For the special case of an in-plane magnetic field we predict an interesting spin-flip effect that allows one to control the spin polarization of electrons by applying an external Aharonov-Bohm flux. Optical mesoscopic systems are the subject of Part II. We consider two-dimensional annular structures characterized by different refractive indices, and apply classical methods from geometric optics as well as wave concepts based on Maxwell's equations. For the first time, an S-matrix approach is successfully employed in the description of resonances in optical microresonators; in particular we propose the dielectric annular billiard as an attractive model system. Comparing ray and wave pictures, we find general agreement, except for large wavelengths of the order of the system size, where corrections to the ray model are necessary. The Goos-Hänchen effect as an extension of the ray picture is shown to quantitatively account for wave modifications of Fresnel's laws due to curved interfaces. We derive novel analytical expressions for the corrected Fresnel formulas for both polarizations of light. Motivated by the successful ray description, we give a conclusive interpretation of a recent filter experiment on a quadrupolar glass fibre, and suggest novel concepts for microresonator-based lasers.
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Spacetime Symmetries from Quantum ErgodicityShoy Ouseph (18086125) 16 April 2024 (has links)
<p dir="ltr">In holographic quantum field theories, a bulk geometric semiclassical spacetime emerges from strongly coupled interacting conformal field theories in one less spatial dimension. This is the celebrated AdS/CFT correspondence. The entanglement entropy of a boundary spatial subregion can be calculated as the area of a codimension two bulk surface homologous to the boundary subregion known as the RT surface. The bulk region contained within the RT surface is known as the entanglement wedge and bulk reconstruction tells us that any operator in the entanglement wedge can be reconstructed as a non-local operator on the corresponding boundary subregion. This notion that entanglement creates geometry is dubbed "ER=EPR'' and has been the driving force behind recent progress in quantum gravity research. In this thesis, we put together two results that use Tomita-Takesaki modular theory and quantum ergodic theory to make progress on contemporary problems in quantum gravity.</p><p dir="ltr">A version of the black hole information loss paradox is the inconsistency between the decay of two-point functions of probe operators in large AdS black holes and the dual boundary CFT calculation where it is an almost periodic function of time. We show that any von Neumann algebra in a faithful normal state that is quantum strong mixing (two-point functions decay) with respect to its modular flow is a type III<sub>1</sub> factor and the state has a trivial centralizer. In particular, for Generalized Free Fields (GFF) in a thermofield double (KMS) state, we show that if the two-point functions are strong mixing, then the entire algebra is strong mixing and a type III<sub>1</sub> factor settling a recent conjecture of Liu and Leutheusser.</p><p dir="ltr">The semiclassical bulk geometry that emerges in the holographic description is a pseudo-Riemannian manifold and we expect a local approximate Poincaré algebra. Near a bifurcate Killing horizon, such a local two-dimensional Poincaré algebra is generated by the Killing flow and the outward null translations along the horizon. We show the emergence of such a Poincaré algebra in any quantum system with modular future and past subalgebras in a limit analogous to the near-horizon limit. These are known as quantum K-systems and they saturate the modular chaos bound. We also prove that the existence of (modular) future/past von Neumann subalgebras also implies a second law of (modular) thermodynamics.</p>
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