Motion of a droplet for the mass-conserving stochastic Allen-Cahn equation

We study the stochastic mass-conserving Allen-Cahn equation posed on a bounded two-dimensional domain with additive spatially smooth space-time noise. This equation associated with a small positive parameter describes the stochastic motion of a small almost semicircular droplet attached to domain's boundary and moving towards a point of locally maximum curvature. We apply It\^o calculus to derive the stochastic dynamics of the droplet by utilizing the approximately invariant manifold introduced by Alikakos, Chen and Fusco for the deterministic problem. In the stochastic case depending on the scaling, the motion is driven by the change in the curvature of the boundary and the stochastic forcing. Moreover, under the assumption of a sufficiently small noise strength, we establish stochastic stability of a neighborhood of the manifold of droplets in $L^2$ and $H^1$, which means that with overwhelming probability the solution stays close to the manifold for very long time-scales

Nonlinear Temporal Dynamics of Strongly Coupled Quantum Dot-Cavity System

We theoretically analyze and simulate the temporal dynamics of strongly coupled quantum dot-cavity system driven by a resonant laser pulse. We observe the signature of Rabi oscillation in the time resolved response of the system (i.e., in the numerically calculated cavity output), derive simplified linear and non-linear semi-classical models that approximate well the system's behavior in the limits of high and low power drive pulse, and describe the role of quantum coherence in the exact dynamics of the system. Finally, we also present experimental data showing the signature of the Rabi oscillation in time domain

Efficiency of tunable band-gap structures for single-photon emission

The efficiency of recently proposed single-photon emitting sources based on tunable planar band-gap structures is examined. The analysis is based on the study of the total and ``radiative'' decay rates, the expectation value of emitted radiation energy and its collimating cone. It is shown that the scheme operating in the frequency range near the defect resonance of a defect band-gap structure is more efficient than the one operating near the band edge of a perfect band-gap structure.Comment: 9 pages, 7 figure

How continuous quantum measurements in finite dimension are actually discrete

We show that in finite dimension a quantum measurement with continuous set of outcomes is always equivalent to a continuous random choice of measurements with only finite outcomes.Comment: 4 pages, 1 figur

Adaptive State Space Partitioning for Dynamic Decision Processes

With the rise of newbusiness processes that require real-time decision making, anticipatory decision making becomes necessary to use the available resources wisely. Dynamic real-time problems occur in many business fields, for example in vehicle routing applications with stochastic customer service requests expecting a fast response. For anticipatory decision making, offline simulation-based optimization methods like value function approximation are promising solution approaches. However, these methods require a suitable approximation architecture to store the value information for the problem states. In this paper, an approach is proposed that finds and adapts this architecture iteratively during the approximation process. A computational proof of concept is presented for a dynamic vehicle routing problem. In comparison to conventional architectures, the proposed method is able to improve the solution quality and reduces the required architecture size significantly

The multi-vehicle stochastic-dynamic inventory routing problem for bike sharing systems

We address the operational management of station-based bike sharing systems (BSSs). In BSSs, users can spontaneously rent and return bikes at any stations in the system. Demand is driven by commuter, shopping, and leisure activities. This demand constitutes a regular pattern of bike usage over the course of the day but also shows a significant short-term uncertainty. Due to the heterogeneity and the uncertainty in demand, stations may run out of bikes or congest during the day. At empty stations, no rental demand can be served. At full stations, no return demand can be served. To avoid unsatisfied demand, providers dynamically relocate bikes between stations in reaction of current shortages or congestion, but also in anticipation of potential future demand. For this real-time decision problem, we present a method that anticipates potential future demands based on historical observations and that coordinates the fleet of vehicles accordingly. We apply our method for two case studies based on real-world data of the BSSs in Minneapolis and San Francisco. We show that our policy outperforms benchmark policies from the literature. Moreover, we analyze how the interplay between anticipation and coordination is essential for the successful operational management of BSSs. Finally, we reveal that the value of coordination and anticipation based on the demand-structure of the BSS under consideration

Relativistic Iron Line Emission from the Neutron Star Low-mass X-ray Binary 4U 1636-536

We present an analysis of XMM-Newton and RXTE data from three observations of the neutron star LMXB 4U 1636-536. The X-ray spectra show clear evidence of a broad, asymmetric iron emission line extending over the energy range 4-9 keV. The line profile is consistent with relativistically broadened Fe K-alpha emission from the inner accretion disk. The Fe K-alpha line in 4U 1636-536 is considerably broader than the asymmetric iron lines recently found in other neutron star LMXBs, which indicates a high disk inclination. We find evidence that the broad iron line feature is a combination of several K-alpha lines from iron in different ionization states.Comment: 7 pages, 2 figures, Published in the Astrophysical Journa

Experimental investigation of quantum key distribution with position and momentum of photon pairs

We investigate the utility of Einstein-Podolsky-Rosen correlations of the position and momentum of photon pairs from parametric down-conversion in the implementation of a secure quantum key distribution protocol. We show that security is guaranteed by the entanglement between downconverted pairs, and can be checked by either direct comparison of Alice and Bob's measurement results or evaluation of an inequality of the sort proposed by Mancini et al. (Phys. Rev. Lett. 88, 120401 (2002)).Comment: 6 pages, 6 figures, subimitted for publicatio