Feedback cooling of atomic motion in cavity QED

We consider the problem of controlling the motion of an atom trapped in an optical cavity using continuous feedback. In order to realize such a scheme experimentally, one must be able to perform state estimation of the atomic motion in real time. While in theory this estimate may be provided by a stochastic master equation describing the full dynamics of the observed system, integrating this equation in real time is impractical. Here we derive an approximate estimation equation for this purpose, and use it as a drive in a feedback algorithm designed to cool the motion of the atom. We examine the effectiveness of such a procedure using full simulations of the cavity QED system, including the quantized motion of the atom in one dimension.Comment: 22 pages, 17 figure

Lotka-Volterra predator-prey model with periodically varying carrying capacity

We study the stochastic spatial Lotka-Volterra (LV) model for predator-prey interaction subject to a periodically varying carrying capacity. The LV model with on-site lattice occupation restrictions that represent finite food resources for the prey exhibits a continuous active-to-absorbing phase transition. The active phase is sustained by spatio-temporal patterns in the form of pursuit and evasion waves. Monte Carlo simulations on a two-dimensional lattice are utilized to investigate the effect of seasonal variations of the environment on species coexistence. The results of our simulations are also compared to a mean-field analysis. We find that the parameter region of predator and prey coexistence is enlarged relative to the stationary situation when the carrying capacity varies periodically. The stationary regime of our periodically varying LV system shows qualitative agreement between the stochastic model and the mean-field approximation. However, under periodic carrying capacity switching environments, the mean-field rate equations predict period-doubling scenarios that are washed out by internal reaction noise in the stochastic lattice model. Utilizing visual representations of the lattice simulations and dynamical correlation functions, we study how the pursuit and evasion waves are affected by ensuing resonance effects. Correlation function measurements indicate a time delay in the response of the system to sudden changes in the environment. Resonance features are observed in our simulations that cause prolonged persistent spatial correlations. Different effective static environments are explored in the extreme limits of fast- and slow periodic switching. The analysis of the mean-field equations in the fast-switching regime enables a semi-quantitative description of the stationary state.Comment: 17 pages, 20 figure

Stability of positive equilibrium of a Nicholson blowflies model with stochastic perturbations

This paper is concerned with the stability problem of the positive equilibrium of a Nicholson’s blowflies model with nonlinear density-dependent mortality rate subject to stochastic perturbations. More specifically, the existence of a unique positive equilibrium of a Nicholson’s blowflies model described by the delay differential equation N 0 (t) = − a − be−N(t) + βN(t − τ)e −γN(t−τ) is first quoted. It is assumed that the underlying model in noisy environments is exposed to stochastic perturbations, which are proportional to the derivation of the state from the equilibrium point. Then, by utilizing a stability criterion formulated for linear stochastic differential delay equations, explicit stability conditions are obtained. An extension to models with multiple delays is also presented

Time- and momentum-resolved photoemission studies using time-of-flight momentum microscopy at a free-electron laser

Time-resolved photoemission with ultrafast pump and probe pulses is an emerging technique with wide application potential. Real-time recording of nonequilibrium electronic processes, transient states in chemical reactions, or the interplay of electronic and structural dynamics offers fascinating opportunities for future research. Combining valence-band and core-level spectroscopy with photoelectron diffraction for electronic, chemical, and structural analyses requires few 10 fs soft X-ray pulses with some 10 meV spectral resolution, which are currently available at high repetition rate free-electron lasers. We have constructed and optimized a versatile setup commissioned at FLASH/PG2 that combines free-electron laser capabilities together with a multidimensional recording scheme for photoemission studies. We use a full-field imaging momentum microscope with time-of-flight energy recording as the detector for mapping of 3D band structures in (kx, ky, E) parameter space with unprecedented efficiency. Our instrument can image full surface Brillouin zones with up to 7 Å−1 diameter in a binding-energy range of several eV, resolving about 2.5 × 105 data voxels simultaneously. Using the ultrafast excited state dynamics in the van der Waals semiconductor WSe2 measured at photon energies of 36.5 eV and 109.5 eV, we demonstrate an experimental energy resolution of 130 meV, a momentum resolution of 0.06 Å−1, and a system response function of 150 fs

Stability of positive equilibrium of a Nicholson blowflies model with stochastic perturbations

This paper is concerned with the stability problem of the positive equilibrium of a Nicholson's blowflies model with nonlinear density-dependent mortality rate subject to stochastic perturbations. More specifically, the existence of a unique positive equilibrium of a Nicholson's blowflies model described by the delay differential equation \begin{equation*} N'(t)=-\left(a-be^{-N(t)}\right)+\beta N(t-\tau)e^{-\gamma N(t-\tau)} \end{equation*} is first quoted. It is assumed that the underlying model in noisy environments is exposed to stochastic perturbations, which are proportional to the derivation of the state from the equilibrium point. Then, by utilizing a stability criterion formulated for linear stochastic differential delay equations, explicit stability conditions are obtained. An extension to models with multiple delays is also presented

An Uncertain Volatility Explanation for Delayed Calls of Convertible Bonds

Arbitrage-free price bounds for convertible bonds are obtained assuming a stochastic volatility process for the common stock that lies within a band but makes few other assumptions about volatility dynamics. Equity-linked hazard rates, stochastic interest rates and different assumptions about default and recovery behavior are accommodated within this approach. A non-linear multi-factor reduced-form equity-linked default model leads to a set of non-linear partial differential complementarity equations that are governed by the volatility path. Empirical results focus on call notice period effects, showing that uncertain volatility can capture the call premia so often observed in issuer’s call policies. Increasingly pessimistic values for the issuer’s substitution asset obtain as we introduce more uncertainty during the notice period. Volatility uncertainty is thus a useful mechanism to explain issuers delayed call policies.call notice period, call premium, convertible bond, delayed calls, equity-linked default, stochastic interest rates, volatility uncertainty

Understanding the behavior of Prometheus and Pandora

We revisit the dynamics of Prometheus and Pandora, two small moons flanking Saturn's F ring. Departures of their orbits from freely precessing ellipses result from mutual interactions via their 121:118 mean motion resonance. Motions are chaotic because the resonance is split into four overlapping components. Orbital longitudes were observed to drift away from Voyager predictions, and a sudden jump in mean motions took place close to the time at which the orbits' apses were antialigned in 2000. Numerical integrations reproduce both the longitude drifts and the jumps. The latter have been attributed to the greater strength of interactions near apse antialignment (every 6.2 years), and it has been assumed that this drift-jump behavior will continue indefinitely. We re-examine the dynamics by analogy with that of a nearly adiabatic, parametric pendulum. In terms of this analogy, the current value of the action of the satellite system is close to its maximum in the chaotic zone. Consequently, at present, the two separatrix crossings per precessional cycle occur close to apse antialignment. In this state libration only occurs when the potential's amplitude is nearly maximal, and the 'jumps' in mean motion arise during the short intervals of libration that separate long stretches of circulation. Because chaotic systems explore the entire region of phase space available to them, we expect that at other times the system would be found in states of medium or low action. In a low action state it would spend most of the time in libration, and separatrix crossings would occur near apse alignment. We predict that transitions between these different states can happen in as little as a decade. Therefore, it is incorrect to assume that sudden changes in the orbits only happen near apse antialignment.Comment: 22 pages, 13 figs, Icarus accepte

Valuation of timberland under price uncertainty

In the first essay, a critical examination of three commonly used stochastic price processes is presented. Each process is described and rejected as a possible model of lumber futures prices. A mean reverting generalized autoregressive conditional heteroskedasticity (GARCH) model, developed by Bollerslev (1986), is proposed as a stochastic process for lumber futures prices. The essay provides the steps that should be taken to ensure that a proper price process is used in each application. In the second essay, a flexible harvesting strategy known as the reservation price strategy is presented. When the current price is below the reservation price, the forest owner delays the harvest. An optimal stopping model is used to derive an expression for the optimal sequence of reservation prices under price uncertainty. A solution method using a Monte Carlo backward recursion algorithm is presented. The Monte Carlo simulation procedure may be applied when analytical solutions are difficult or intractable. In the third essay, a simulation model is used to estimate the per acre value of land devoted to timber production under different harvesting strategies, stumpage price processes, and site qualities. By following the reservation price strategy, forest owners can increase the expected prots from timber harvesting and reduce the variability in profits from timber harvesting relative to a fixed rotation strategy. For an estimated mean reverting GARCH process, the reservation price strategy increases the value of timberland by 33.0 percent for a site index of 90 and by 22.1 percent for a site index of 60 relative to a fixed rotation strategy

Dynamic Bayesian smooth transition autoregressive (DBSTAR) models for non-stationary nonlinear time series

In this thesis, Dynamic Bayesian Smooth Transition Autoregressive (DBSTAR) models are proposed for nonlinear time series, as an alternative to both the classical Smooth Transition Autoregressive (STAR) models and Computational Bayesian STAR (CBSTAR) models. DBSTAR models are autoregressive formulations of dynamic linear models based on polynomial approximations of transition functions of STAR models. Unlike classical STAR and CBSTAR models, their parameters vary in time, being suitable for modelling both global and local non-stationary processes. Since DBSTAR models are Bayesian, the models do not require extensive historical data for parametric estimation and allow expert intervention via prior distribution assessment of model parameters. Because they are analytical and sequential, DBSTAR models, respectively, avoid potential computational problems associated with CBSTAR models, such as convergence issues, and allow fast estimation of dynamic parameters sequentially in time, being thus suitable for real time applications. Proposed DBSTAR models have been applied to two data sets: the much used Canadian Lynx data set, in which the aim is to validate DBSTAR models by comparing their fitting performances with existing approaches in the literature, and a Brazilian electricity load data set, for which existing models are not suitable