Computational study of cold ions trapped in a double-well potential

We report a rigorous computational treatment of quantum dynamics of cold ions in a double-well trap using the time-dependent Schrödinger equation. Our method employs a numerically accurate approach that avoids approximations, such as assumption of weak coupling between the wells; normal mode nature of vibrations; or harmonic approximation for energy spectrum of the double-well system. Our goal is to reproduce, from first principles, the process of energy swaps between the wells observed in the experiments at NIST [Nature 471, 196 (2011)] and Innsbruck [Nature 471, 200 (2011)]. The model parameters and the initial conditions are carefully chosen to mimic experimental conditions. We obtain accurate energies and wave functions of the system numerically, and study the evolution of motional wave packets to provide new insight. This model reproduces experimental results obtained by NIST and Innsbruck in detail. We explain the energy transfer in terms of wave packet dynamics in the asymmetric potential energy well. We also show that, for a localised initial wave packet, this phenomenon can be interpreted using the terms of classical dynamics, such as trajectory of motion governed by the well-known simple principle: the angle of reflection equals the angle of incidence.     

Coupling of two asymmetric exclusion processes with open boundaries

We study the dynamics of a coupled two-channel ASEP in which intra-channel transition rates are dependent on the configuration of neighboring channel. The binding constant k$k$, which signifies the ratio of inter-channel transition rates, is introduced and the symmetric and asymmetric coupling conditions are analyzed for different values of k$k$. The vertical cluster mean-field theory is used to study the system behavior exactly in strong coupling conditions and approximately in intermediate coupling conditions. Additionally, the consequences of particular dynamics such as totally asymmetric simple exclusion process (TASEP), partially asymmetric simple exclusion process (PASEP) and symmetric simple exclusion process (SSEP) in either one or both channels are investigated. It is found that the transition rates have a significant influence on both the qualitative and quantitative nature of the phase diagrams. The mathematical computation shows how the number of phases varies from 3 via 6 to 7 under different environments. Interestingly, in the fully asymmetric coupling case, the results are found to be independent of the magnitude of non-zero vertical transition rate. Our theoretical arguments are in well agreement with extensively performed Monte-Carlo simulation results.     

Dynamics of a tunable superfluid junction

We study the population dynamics of a Bose-Einstein condensate in a double-well potential throughout the crossover from Josephson dynamics to hydrodynamics. At barriers higher than the chemical potential, we observe slow oscillations well described by a Josephson model. In the limit of low barriers, the fundamental frequency agrees with a simple hydrodynamic model, but we also observe a second, higher frequency. A full numerical simulation of the Gross-Pitaevskii equation giving the frequencies and amplitudes of the observed modes between these two limits is compared to the data and is used to understand the origin of the higher mode. Implications for trapped matter-wave interferometers are discussed.     

Modelling Foreign Exchange Interventions under Rayleigh Process: Applications to Swiss Franc Exchange Rate Dynamics

This paper models the foreign exchange intervention policy following the Rayleigh process derived from the standard flexible-price monetary framework. The exchange rate dynamics associated with the interventions are more sensitive to the change in the economic fundamental when a currency’s money supply is ample and its appreciation expectation cannot be offset by lower interest rates that have fallen to the zero lower bound, suggesting that more intensive interventions are required to counteract currency appreciation pressure and resulting in foreign reserve accumulation. The empirical results using market data during January 2015–February 2020 demonstrate that the model can describe the dynamics of the Swiss franc exchange rate. The accumulation of foreign reserves through interventions is negatively co-integrated with the exchange rate volatility and the value of the mean level of the Swiss franc exchange rate in the dynamics, to some extent indicating a reasonably high degree of effectiveness of the Swiss National Bank’s interventions. The transition between the target-zone and floating-rate regimes in 2015 caused changes in the level of exchange rate volatility but not its dynamical structure, suggesting that transitions between the floating-rate and target-zone regimes do not seem to have material consequence in this regard.     

The one-dimensional kinetic Ising model: A series expansion study

Exact power series expansions (through eight terms) in the time are derived for relaxation in the one-dimensional Ising model with nearest-neighbor interactions for a general rate parameter where the activation energy is a variable fraction of the energy required to break nearest-neighbor bonds. It is found that the qualitative nature of the relaxation is very dependent on this parameter, varying from nearly simple exponential decay (as with Glauber dynamics) for an intermediate value of this parameter, to an initial rate of change that is either much slower or faster than a simple exponential at the extremes of the range of variation of the parameter. The rate equations for the limit of rapid internal diffusion (internal equilibration) are integrated for several special values of the rate parameter. In general the internal equilibration approximation is not a good representation of the relaxation except when the relaxation is similar to Glauber dynamics.     

Stochastic ferroelectric switching of lead zirconate titanate thin films

We investigate the repolarization phenomenon in a ferroelectric film. Our ferroelectric sample was lead zirconate titanate (PZT) obtained by sol-gel synthesis and deposited by spin coating on ITO/glass substrate. A series of repolarizations were induced in the ferroelectric film by applying a triangular wave and the current peaks related to the switchings of the ferroelectric domains were acquired for statistical analyses. It is shown that the dynamics and statistics of polarization switchings are well simulated by a simple mean-field model in which a double-well, asymmetric potential is included to describe the asymmetry at the PZT-ITO interface.     

Noise induced stability in fluctuating, bistable potentials

The overdamped motion of a Brownian particle in an asymmetric, bistable, fluctuating potential shows noise induced stability: For intermediate fluctuation rates the mean occupancy of minima with an energy above the absolute minimum is enhanced. The model works as a detector for potential fluctuations being not too fast and not too slow. This effect occurs due to the different time scales in the problem. We present a detailed analysis of this effect using the exact solution of the Fokker-Planck equation for a simple model. Further we show that for not too fast fluctuations the system can be well described by effective rate equations. The results of the rate equations agree quantitatively with the exact results.     

Longitudinal mode competition in semiconductor lasers under optical feedback: Regime of short-external cavity

This paper introduces a theoretical study of longitudinal mode competition in semiconductor lasers subject to optical feedback. The study is based on a model of time-delay multimode rate equations taking into account both symmetric and asymmetric suppressions of modal gain. The model is numerically solved and applied to the case of a short-external cavity. Mode competition is characterized along the feedback-induced period-doubling route to chaos as well as under chaotic dynamics. Contributions of symmetric and asymmetric gain suppressions to both mode dynamics and modal operation under OFB are clarified. The results show that under chaotic dynamics, mode competition induces multimode hopping giving rise to asymmetric multimode output spectra. In regimes of continuous-wave operation, mode competition supports single-mode oscillation, and the side-mode suppression ratio improves with the increase of feedback. In the regime of strong feedback, the lasing mode moves to either long- or short-wavelength side in a seemingly random fashion, which is strongly related to asymmetric gain suppression.     

Ultrafast spin dynamics in magnetic semiconductor quantum wells studied by magnetization modulation spectroscopy

1-x Mn_xTe quantum well structures at room temperature using time-resolved magnetization modulation spectroscopy. Access to the different electron and hole spin dynamics is obtained by carefully measuring the spectroscopic changes of the magneto-optical response during the first hundreds of femtoseconds after excitation. Experimental results are discussed in the framework of a simple model for a two-dimensional band structure. The spectroscopy is shown to be intimately related to the spectral band width of the applied ultrashort laser pulses. The general potential of the method for fundamental studies on other materials and systems is addressed. Received: 20 September 1998     

Use of recurrence plot and recurrence quantification analysis in Taiwan unemployment rate time series

The aim of the article is to answer the question if the Taiwan unemployment rate dynamics is generated by a non-linear deterministic dynamic process. This paper applies a recurrence plot and recurrence quantification approach based on the analysis of non-stationary hidden transition patterns of the unemployment rate of Taiwan. The case study uses the time series data of the Taiwan’s unemployment rate during the period from 1978/01 to 2010/06. The results show that recurrence techniques are able to identify various phases in the evolution of unemployment transition in Taiwan.     

Comparative Analysis of Different Univariate Forecasting Methods in Modelling and Predicting the Romanian Unemployment Rate for the Period 2021–2022

Unemployment has risen as the economy has shrunk. The coronavirus crisis has affected many sectors in Romania, some companies diminishing or even ceasing their activity. Making forecasts of the unemployment rate has a fundamental impact and importance on future social policy strategies. The aim of the paper is to comparatively analyze the forecast performances of different univariate time series methods with the purpose of providing future predictions of unemployment rate. In order to do that, several forecasting models (seasonal model autoregressive integrated moving average (SARIMA), self-exciting threshold autoregressive (SETAR), Holt–Winters, ETS (error, trend, seasonal), and NNAR (neural network autoregression)) have been applied, and their forecast performances have been evaluated on both the in-sample data covering the period January 2000–December 2017 used for the model identification and estimation and the out-of-sample data covering the last three years, 2018–2020. The forecast of unemployment rate relies on the next two years, 2021–2022. Based on the in-sample forecast assessment of different methods, the forecast measures root mean squared error (RMSE), mean absolute error (MAE), and mean absolute percent error (MAPE) suggested that the multiplicative Holt–Winters model outperforms the other models. For the out-of-sample forecasting performance of models, RMSE and MAE values revealed that the NNAR model has better forecasting performance, while according to MAPE, the SARIMA model registers higher forecast accuracy. The empirical results of the Diebold–Mariano test at one forecast horizon for out-of-sample methods revealed differences in the forecasting performance between SARIMA and NNAR, of which the best model of modeling and forecasting unemployment rate was considered to be the NNAR model.     

Symmetry breaking,bifurcations, quasiperiodicity,and chaos due to electric fields in a coupled cell model

A model for the asymmetric coupling of two oscillatory cells is considered. The coupling between the cells is both through diffusional exchange (symmetric) and through the electromigration of ionic reactant species from one cell to the other (asymmetric) in applied electric fields. The kinetics in each cell are the same and based on the Gray-Scott scheme. Without the electric field, only simple, stable dynamics are seen. The effect of the asymmetry (applying electric fields) is to create a wide variety of stable dynamics, multistability, multiperiodic oscillations, quasiperiodicity and chaos being observed, this complexity in response being more prevalent at weaker coupling rates and at weaker field strengths. The results are obtained using a standard dynamical systems continuation program, though asymptotic results are obtained for strong coupling rates and strong electric fields. These are seen to agree well with the numerically determined values in the appropriate parameter regimes. (c) 2002 American Institute of Physics.     

The hot fermi gas model

Ample production of fast particles has been observed in intermediate heavy ion reactions [1]. These particles have often been related to sources having velocities close to half that of the beam and temperatures ranging between a few and several tens MeV. For such temperatures neither the low temperature Fermi gas model nor the Boltzmann gas model are valid. A more correct treatment is necessary in order to understand the relationship between the incident energy per nucleon, the excitation energy of the source and its temperature. In this short paper we give simple closed expressions allowing to interpolate between the Fermi and the Boltzmann regimes. In the following we consider a gas of fermions (Nucleons) at a temperatureT trapped in a square potential well of depthU. We shall not deal with the dynamics of the expansion of the gas except through the calculation of the particle evaporation rate. Likewise we do not consider the implications of a possible liquid gas transition [2]. We first approximate the variation of the chemical potential as a function of the temperature. Using that, we are able to compute and find approximations to the variations of the excitation energy with temperature and vice-versa. Finally we give expressions for the particle evaporation rate of a hot Fermi gas and compare them to the Weisskopf formula.     

On a new hyperchaotic system

A new hyperchaotic system is presented, which has two large positive and one small negative Lyapunov exponent over a large range of parameters. As a consequence, system orbits strongly expand in some directions but rapidly shrink in some other directions. These strong expansions and shrinking lead the system orbits to be more disordered and random. Bifurcation and Poincaré-map analyses further show that the system has very rich bifurcations in different directions and extremely complicated dynamics overall. Spectral analysis shows that the system in the hyperchaotic mode has an extremely broad frequency bandwidth of high magnitudes, verifying its unusual random nature and indicating its great potential for some relevant engineering applications such as secure communications.     

Kink dynamics in one-dimensional coupled map lattices

We examine the problem of the dynamics of interfaces in a one-dimensional space-time discrete dynamical system. Two different regimes are studied: the non-propagating and the propagating one. In the first case, after proving the existence of such solutions, we show how they can be described using Taylor expansions. The second situation deals with the assumption of a travelling wave to follow the kink propagation. Then a comparison with the corresponding continuous model is proposed. We find that these methods are useful in simple dynamical situations but their application to complex dynamical behaviour is not yet understood. (c) 1995 American Institute of Physics.     

On the motion control of microparticles by means of an electromagnetic field increasing with time for spectroscopic applications

The possibility of controlling the motion of microparticles by means of external electromagnetic fields (nonresonance laser radiation, in particular) that induce potential wells for such particles, which are characterized by fixed spatial distribution but deepen over time to a certain level, are analyzed. It is assumed that the particles are located in high vacuum and are affected by nondissipative external forces. Slowing down of relatively fast particles when they pass through the discussed potential wells is shown. Such slowing down of particles is demonstrated using a nonresonance laser beam with intensity increasing over time as an example. Specific features of particle dynamics in the electromagnetic fields under consideration in the case of a one-dimensional rectangular potential well are studied in detail based on simple analytical relations derived from the fundamental equations of classical mechanics. The methods of particle cooling and localization demonstrated in the present work can substantially increase spectroscopy resolution of various microparticles, including, under certain conditions, atoms and molecules.     

Fundamental modes in waveguide pipe twisted by saturated double-well potential

We study fundamental modes trapped in a rotating ring with a saturated nonlinear double-well potential. This model, which is based on the nonlinear Schrödinger equation, can be constructed in a twisted waveguide pipe in terms of light propagation, or in a Bose–Einstein condensate (BEC) loaded into a toroidal trap under a combination of a rotating π-out-of-phase linear potential and nonlinear pseudopotential induced by means of a rotating optical field and the Feshbach resonance. Three types of fundamental modes are identified in this model, one symmetric and the other two asymmetric. The shape and stability of the modes and the transitions between different modes are investigated in the first rotational Brillouin zone. A similar model used a Kerr medium to build its nonlinear potential, but we replace it with a saturated nonlinear medium. The model exhibits not only symmetry breaking, but also symmetry recovery. A specific type of unstable asymmetric mode is also found, and the evolution of the unstable asymmetric mode features Josephson oscillation between two linear wells. By considering the model as a configuration of a BEC system, the ground state mode is identified among these three types, which characterize a specific distribution of the BEC atoms around the trap.     

Irregular vocal-fold vibration--high-speed observation and modeling

Direct observations of nonstationary asymmetric vocal-fold oscillations are reported. Complex time series of the left and the right vocal-fold vibrations are extracted from digital high-speed image sequences separately. The dynamics of the corresponding high-speed glottograms reveals transitions between low-dimensional attractors such as subharmonic and quasiperiodic oscillations. The spectral components of either oscillation are given by positive linear combinations of two fundamental frequencies. Their ratio is determined from the high-speed sequences and is used as a parameter of laryngeal asymmetry in model calculations. The parameters of a simplified asymmetric two-mass model of the larynx are preset by using experimental data. Its bifurcation structure is explored in order to fit simulations to the observed time series. Appropriate parameter settings allow the reproduction of time series and differentiated amplitude contours with quantitative agreement. In particular, several phase-locked episodes ranging from 4:5 to 2:3 rhythms are generated realistically with the model.