Dissipative Dicke Model with Collective Atomic Decay: Bistability, Noise-Driven Activation and Non-Thermal First Order Superradiance Transition

The Dicke model describes the coherent interaction of a laser-driven ensemble of two level atoms with a quantized light field. It is realized within cavity QED experiments, which in addition to the coherent Dicke dynamics feature dissipation due to e.g. atomic spontaneous emission and cavity photon loss. Spontaneous emission supports the uncorrelated decay of individual atomic excitations as well as the enhanced, collective decay of an excitation that is shared by $N$ atoms and whose strength is determined by the cavity geometry. We derive a many-body master equation for the dissipative Dicke model including both spontaneous emission channels and analyze its dynamics on the basis of Heisenberg-Langevin and stochastic Bloch equations. We find that the collective loss channel leads to a region of bistability between the empty and the superradiant state. Transitions between these states are driven by non-thermal, markovian noise. The interplay between dissipative and coherent elements leads to a genuine non-equilibrium dynamics in the bistable regime, which is expressed via a non-conservative force and a multiplicative noise kernel appearing in the stochastic Bloch equations. We present a semiclassical approach, based on stochastic nonlinear optical Bloch equations, which for the infinite-range Dicke Model become exact in the large-$N$-limit. The absence of an effective free energy functional, however, necessitates to include fluctuation corrections with $\mathcal{O}(1/N)$ for finite $N<\infty$ to locate the non-thermal first-order phase transition between the superradiant and the empty cavity.Comment: as published in Physical Review

Passengers' Airport Choice

Modelling airport choice of passengers has been a subject of interest for air transport scientists and airport managers already for a while. Wilken, Berster and Gelhausen have reported of a market segment specific model approach to airport choice in Germany in a paper entitled "Airport Choice in Germany - New Empirical Evidence of the German Air Traveller Survey 2003" presented at the Air Transport Research Society World Conference 2005 in Rio de Janeiro, Brazil. In continuation of the analysis of airport choice, based on the evidence coming from the data of the survey mentioned, this paper deals with a model of combined airport and access mode choice in Germany by market segment. The question arises why to model airport and access mode choice simultaneously. The underlying hypothesis is that airport and access mode choice are closely interrelated. Air travellers typically have a strong preference to choose the nearest airport as the aforementioned survey reveals. In Germany, 67% of the air travellers choose on average the nearest airport, however, travel time not only depends on distance covered, but also on the accessibility of fast access modes, such as for instance high speed intercity trains, to reduce travel time. Access time and access cost play a major role in airport choice, which in turn depend on access mode choice. The availability of access modes is again airport specific. Because of the strong dependence of airport and access mode choice on each other a combined model approach seems more sensible than two separate models. The combined approach allows including the aforementioned interrelations. This paper presents a combined airport and access mode choice model based on a nested logit approach, first presented at the Air Transport Research Society World Conference 2006 in Nagoya, Japan. It is called a "generalized nested logit model for airport and access mode choice" as it is not restricted to specific airports or a certain number of airport and access mode combinations, but allows to evaluate airport plans like the future Berlin-Brandenburg International Airport (BBI) in the southeast of Berlin or the introduction of new access modes, like a direct high speed intercity train access at already existing airports as this was the case between Cologne and Frankfurt airport in 2002. The case study concluding the paper is a modified excerpt of a study dealing with different future scenarios relating to airport and access mode choice in the Cologne region conducted by the author. As a means to achieve a general applicability of the model airports have been grouped into “airport categories”. Airports are categorised from a demand-oriented point of view to form clusters of homogenous airports regarding their general picture of their flight plan. The model is of particular interest for airport managers as well as high speed rail providers since it shows the dependence between the market share of an airport and access mode combination and its quality regarding their attributes, e.g. travel time, travel cost and weekly flight frequency to a given destination.Airport and access mode choice, discrete choice models, German Air Traveller Survey 2003, high speed train access, nested logit model

Many-Body Quantum Optics with Decaying Atomic Spin States: (γ\gamma, κ\kappa) Dicke model

We provide a theory for quantum-optical realizations of the open Dicke model with internal, atomic spin states subject to spontaneous emission with rate $\gamma$. This introduces a second decay channel for excitations to irreversibly dissipate into the environment, in addition to the photon loss with rate $\kappa$, which is composed of individual atomic decay processes and a collective atomic decay mechanism. The strength of the latter is determined by the cavity geometry. We compute the mean-field non-equilibrium steady states for spin and photon observables in the long-time limit, $t\rightarrow \infty$. Although $\gamma$ does not conserve the total angular momentum of the spin array, we argue that our solution is exact in the thermodynamic limit, for the number of atoms $N\rightarrow \infty$. In light of recent and upcoming experiments realizing superradiant phase transitions using internal atomic states with pinned atoms in optical lattices, our work lays the foundation for the pursuit of a new class of open quantum magnets coupled to quantum light.Comment: 17 pages, 6 figures; added appendix for the derivation of a collective atomic decay mechanism in a Lindblad formalism; version as published in Physical Review

Hadronic matrix elements with heavy-light mesons from QCD sum rules

Die Suche nach neuer Physik in schwachen Zerfällen ist ein wichtiges Forschungsgebiet der modernen Teilchenphysik. Viele Experimente an großen Teilchenbeschleunigern, zum Beispiel dem Large Hadron Collider (LHC) am CERN, beschäftigen sich intensiv mit der Untersuchung verschiedener exklusiver Zerfälle von schweren Hadronen. In der Theorie werden solche Zerfälle mit hadronischen Matrixelementen parametrisiert, welche die nichtperturbative Quark-Gluon-Dynamik eines Prozesses beschreiben. Die Berechnung solcher Matrixelemente mit der Technik der QCD-Summenregeln ist zentraler Gegenstand dieser Arbeit. Nach einer allgemeinen Einführung und der Erläuterung der Summenregelmethodik beschäftigt sich der erste Teil dieser Arbeit mit der Herleitung und Auswertung von verschiedenen Summenregeln für eine bestimmte Klasse von hadronischen Matrixelementen, den Zerfallskonstanten. Eine besondere Rolle spielen dabei die erstmals für Vektorströme einbezogenen Korrekturen für das Quarkkondensat in nächstführender Ordnung. Neben einer ausführlichen Diskussion der Unsicherheiten umfasst die Analyse auch einen Vergleich mit Gitter-QCD-Resultaten. Die Ergebnisse dieser Arbeit weisen mit diesen eine gute Übereinstimmung auf. Im Anschluss werden die hergeleiteten QCD-Summenregeln modifiziert, um die Zerfallskonstanten für die ersten radialen Anregungen der zuvor untersuchten Mesonen zu bestimmen. Dabei wird die hadronische Darstellung der Korrelationsfunktion in der modifizierten Summenregel um die entsprechende Resonanz erweitert. Zur Fixierung des Grenzparameters wird eine neue Anpassungsprozedur verwendet, welche trotz einer vergleichsweise großen Unsicherheit in den Mesonmassen der radialen Anregungen eine gute und für einige Kanäle erstmalige Abschätzung der Zerfallskonstanten ermöglicht. Im letzten Abschnitt werden QCD-Lichtkegelsummenregeln zur Bestimmung der starken Kopplung zwischen zwei schweren Mesonen mit pseudoskalarer bzw. vektorieller Spinparität und einem Pion hergeleitet. Der Fokus liegt dabei auf der Aktualisierung und Reorganisation der Beiträge in führender Ordnung, so dass diese für eine geplante Analyse unter Einbeziehung der nächstführenden Ordnung verwendet werden können. Zusätzlich werden die Ergebnisse der vorherigen Abschnitte genutzt, um erstmals starke Kopplungen mit radial angeregten Mesonzuständen abzuschätzen.The search for new physics in weak decays is an important subject of modern Particle Physics. At accelerators, e.g. at the Large Hadron Collider (LHC) at CERN, exclusive decays of heavy hadrons with various final states are extensively studied. In theory, these decays are parameterized by hadronic matrix elements which involve nonperturbative quark-gluon dynamics. The calculation of these matrix elements using the technique of QCD sum rules is the main subject of this thesis. After a general introduction and a discussion of the sum rule technique, the first part of this work is focussed on the derivation and evaluation of various sum rules for a certain kind of hadronic matrix elements called decay constants. In this analysis, for the first time next to leading order corrections to the quark condensate contributions for vector currents are taken into account. In addition to a detailed discussion of uncertainties, the results obtained using the sum rule technique are found to be in good agreement with lattice QCD results. Furthermore, the previously used QCD sum rules are modified to calculate the decay constants for the first radial excitation of the considered mesons. In the modified sum rule, the hadronic representation of the correlation function is extended to also include the corresponding resonance. Notably, a new fitting procedure is adopted to fix the duality threshold parameter. Despite large uncertainties in the meson masses for the radial excitations, this new procedure provides a satisfactory, and for some channels the first, estimate of the decay constants. In the last part of the thesis, QCD light-cone sum rules for the calculation of the strong coupling between three mesons, two heavy ones with vector and pseudoscalar spin parity and a pion, are derived. The major purpose of this section is the update and reorganization of the leading order contributions for a smooth implementation in the future next to leading order analysis. Furthermore, the results from the previous sections are used, to provide a first estimate for strong couplings with radial excitations

Airport Choice in Germany - New Empirical Evidence of the German Air Traveller Survey 2003

The paper deals with the quantitative relationship between the number of air travellers in any region and the airports chosen in Germany in 2003. The purpose of the paper is to present results of an analysis of airport choice behaviour of total air passenger demand in Germany, based on data of the German air traveller survey conducted at 17 international and 5 regional airports. About 210 000 passengers were interviewed about their trip origin, destination, choice of travel mode to the airport, purpose of their journey and further journey and person related attributes. As a result of the analysis so far, the distribution of airports chosen by all passengers coming from any region in Germany can be shown in relation to the journey purpose and destination. Based on these data, logit models have been calibrated for each market segment to forecast airport choice in relation to the accessibility and attractiveness of airports. As a further methodological step the outline of a combined neural and nested logit model of access mode and airport choice is given, which will be calibrated on the basis of the data of the German air traveller survey. Typically, the nearest airport will be chosen by most travellers, there are, however, on average eight airports serving one region (defined as a Spatial Planning Region, of which there are 97 in Germany). If there is an international airport in a region about two thirds of the demand coming from that region will choose that airport, and about one third will choose to depart from one of seven other airports. Vice versa, each airport attracts passengers coming from almost 40 regions. There is thus an intense interaction between an airport and a large influential area.Regional air travel demand; airport choice; air traveller survey; catchment areas of airports; travel route from origin via departing airport to destination area; logit model on airport choice; neural networks