Photon BEC with Thermo-Optic Interaction at Dimensional Crossover

Since the advent of experiments with photon Bose-Einstein condensates in dye-filled microcavities in 2010, many investigations have focused upon the emerging effective photon-photon interaction. Despite its smallness, it can be identified to stem from two physically distinct mechanisms. On the one hand, a Kerr nonlinearity of the dye medium yields a photon-photon contact interaction. On the other hand, a heating of the dye medium leads to an additional thermo-optic interaction, which is both delayed and non-local. The latter turns out to represent the leading contribution to the effective interaction for the current 2D experiments. Here we analyse theoretically how the effective photon-photon interaction increases when the system dimension is reduced from 2D to 1D. To this end, we consider an anisotropic harmonic trapping potential and determine via a variational approach how the properties of the photon Bose-Einstein condensate in general, and both aforementioned interaction mechanisms in particular, change with increasing anisotropy. We find that the thermo-optic interaction strength increases at first linearly with the trap aspect ratio and lateron saturates at a certain value of the trap aspect ratio. Furthermore, in the strong 1D limit the roles of both interactions get reversed as the thermo-optic interaction remains saturated and the contact Kerr interaction becomes the leading interaction mechanism. Finally, we discuss how the predicted effects can be measured experimentally.Comment: 16 pages, 4 figure

Thermodynamics of Trapped Photon Gases at Dimensional Crossover from 2D to 1D

Photon Bose-Einstein condensates are characterised by a quite weak interaction, so they behave nearly as an ideal Bose gas. Moreover, since the current experiments are conducted in a microcavity, the longitudinal motion is frozen out and the photon gas represents effectively a two-dimensional trapped gas of massive bosons. In this paper we therefore focus on a harmonically confined ideal Bose gas in two dimensions, where the anisotropy of the confinement allows for a dimensional crossover. If the anisotropy is even large enough so that the squeezed direction is frozen out, then only one degree of freedom survives and the system can be considered to be quasi-one dimensional. We work out the thermodynamic properties for such a system analytically and examine, in particular, the dimensional information which is contained in the respective thermodynamic quantities. With this our results are useful for future experiments of photon gases at the dimensional crossover from 2D to 1D in view of determining their effective dimensionality from thermodynamic quantities.Comment: 21 pages, 7 figures, submission to New Journal of Physic

Online mechanism design for electric vehicle charging

The rapid increase in the popularity of electric vehicles (EVs) and plug-in hybrid electric vehicles (PHEVs) is expected to place a considerable strain on the existing electricity grids, due to the high charging rates these vehicles require. In many places, the limited capacity of the local electricity distribution network will be exceeded if many such vehicles are plugged in and left to charge their batteries simultaneously. Thus, it will become increasingly important to schedule the charging of these vehicles, taking into account the vehicle owners’ preferences, and the local constraints on the network. In this paper, we address this setting using online mechanism design and develop a mechanism that incentivises agents (representing vehicle owners) to truthfully reveal their preferences, as well as when the vehicle is available for charging. Existing related online mechanisms assume that agent preferences can be described by a single parameter. However, this is not appropriate for our setting since agents are interested in acquiring multiple units of electricity and can have different preferences for these units, depending on factors such as their expected travel distance. To this end, we extend the state of the art in online mechanism design to multi-valued domains, where agents have non-increasing marginal valuations for each subsequent unit of electricity. Interestingly, we show that, in these domains, the mechanism occasionally requires leaving electricity unallocated to ensure truthfulness. We formally prove that the proposed mechanism is dominant-strategy incentive compatible, and furthermore, we empirically evaluate our mechanism using data from a real-world trial of electric vehicles in the UK. We show that our approach outperforms any fixed price mechanism in terms of allocation efficiency, while performing only slightly worse than a standard scheduling heuristic, which assumes non-strategic agents

Spin-orbit effects on the Larmor dispersion relation in GaAs quantum wells

We have studied the relevance of spin-orbit coupling to the dispersion 00009 relation of the Larmor resonance observed in inelastic light scattering and electron-spin resonance experiments on GaAs quantum wells. We show that the spin-orbit interaction, here described by a sum of Dresselhaus and Bychkov-Rashba terms, couples Zeeman and spin-density excitations. We have evaluated its contribution to the spin splitting as a function of the magnetic field $B$, and have found that in the small $B$ limit, the spin-orbit interaction does not contribute to the spin splitting, whereas at high magnetic fields it yields a $B$ independent contribution to the spin splitting given by $2(\lambda_R^2-\lambda_D^2)$, with $\lambda_{R,D}$ being the intensity of the Bychkov-Rashba and Dresselhaus spin-orbit terms.Comment: To be published in Physical Review

A Polynomial-time, Truthful, Individually Rational and Budget Balanced Ridesharing Mechanism

Ridesharing has great potential to improve transportation efficiency while reducing congestion and pollution. To realize this potential, mechanisms are needed that allocate vehicles optimally and provide the right incentives to riders. However, many existing approaches consider restricted settings (e.g., only one rider per vehicle or a common origin for all riders). Moreover, naive applications of standard approaches, such as the Vickrey-Clarke-Groves or greedy mechanisms, cannot achieve a polynomial-time, truthful, individually rational and budget balanced mechanism. To address this, we formulate a general ridesharing problem and apply mechanism design to develop a novel mechanism which satisfies all four properties and whose social cost is within 8.6% of the optimal on average

A multi-scale flood monitoring system based on fully automatic MODIS and TerraSAR-X processing chains

A two-component fully automated flood monitoring system is described and evaluated. This is a result of combining two individual flood services that are currently under development at DLR’s (German Aerospace Center) Center for Satellite based Crisis Information (ZKI) to rapidly support disaster management activities. A first-phase monitoring component of the system systematically detects potential flood events on a continental scale using daily-acquired medium spatial resolution optical data from the Moderate Resolution Imaging Spectroradiometer (MODIS). A threshold set controls the activation of the second-phase crisis component of the system, which derives flood information at higher spatial detail using a Synthetic Aperture Radar (SAR) based satellite mission (TerraSAR-X). The proposed activation procedure finds use in the identification of flood situations in different spatial resolutions and in the time-critical and on demand programming of SAR satellite acquisitions at an early stage of an evolving flood situation. The automated processing chains of the MODIS (MFS) and the TerraSAR-X Flood Service (TFS) include data pre-processing, the computation and adaptation of global auxiliary data, thematic classification, and the subsequent dissemination of flood maps using an interactive web-client. The system is operationally demonstrated and evaluated via the monitoring two recent flood events in Russia 2013 and Albania/Montenegro 2013

Quantum Mechanical Description of Thermo-Optic Interaction

Thermo-optic interaction significantly differs from the usual particle-particle interactions in physics, as it is retarded in time. A prominent platform for realising this kind of interaction are photon Bose-Einstein condensates, which are created in dye-filled microcavities. The dye solution continually absorbs and re-emits these photons, causing the photon gas to thermalise and to form a Bose-Einstein condensate. Because of a non-ideal quantum efficiency, these cycles heat the dye solution, creating a medium that provides an effective thermo-optic photon-photon interaction. So far, only a mean-field description of this process exists. This paper goes beyond by working out a quantum mechanical description of the effective thermo-optic photon-photon interaction. To this end, the self-consistent modelling of the temperature diffusion builds the backbone of the modelling. Furthermore, the manyfold experimental timescales allow for deriving an approximate Hamiltonian. The resulting quantum theory is applied in the perturbative regime to both a harmonic and a box potential for investigating its prospect for precise measurements of the effective photon-photon interaction strength

Two-sided online markets for electric vehicle charging

With the growing popularity of electric vehicles (EVs), the number of public charging stations is increasing rapidly, allowing drivers to charge their cars while parked away from home or en-route to their destination. However, as a full charge can take a significant amount of time, drivers may face queues and uncertainty over availability of charging facilities at different stations and times. In this paper, we address this problem by proposing a novel, two-sided market for advance reservations, in which agents, representing EV owners, report their preferences for time slots and charging locations, while charging stations report their availability and costs. In our model, both parties are rational, profit-maximising entities, and buyers enter the market dynamically over time. Given this, we apply techniques from online mechanism design to develop a pricing mechanism which is truthful on the buyer side (i.e., drivers have no incentive to misreport their preferences or to delay their reservations). For the seller side, we adapt three well-known pricing mechanisms and compare them both theoretically and empirically. Using realistic simulations, we demonstrate that two of our proposed mechanisms consistently achieve a high efficiency (90–95% of optimal), while offering a trade-off between stability and budget balance. Surprisingly, the third mechanism, a common payment mechanism that is truthful in simpler settings, achieves a significantly lower efficiency and runs a high deficit