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In crystalline and amorphous semiconductors, the temperature-dependent Urbach energy can be determined from the inverse slope of the logarithm of the absorption spectrum and reflects the static and dynamic energetic disorder. Using recent advances in the sensitivity of photocurrent spectroscopy methods, we elucidate the temperature-dependent Urbach energy in lead halide perovskites containing different numbers of cation components. We find Urbach energies at room temperature to be 13.0 +/- 1.0, 13.2 +/- 1.0, and 13.5 +/- 1.0 meV for single, double, and triple cation perovskite. Static, temperature-independent contributions to the Urbach energy are found to be as low as 5.1 ?+/- 0.5, 4.7 +/- 0.3, and 3.3 +/- 0.9 meV for the same systems. Our results suggest that, at a low temperature, the dominant static disorder in perovskites is derived from zero-point phonon energy rather than structural disorder. This is unusual for solution-processed semiconductors but broadens the potential application of perovskites further to quantum electronics and devices.
Statistical Analysis of Hiss Waves in Plasmaspheric Plumes Using Van Allen Probe Observations
(2019)
Plasmaspheric hiss waves commonly observed in high‐density regions in the Earth's magnetosphere are known to be one of the main contributors to the loss of radiation belt electrons. There has been a lot of effort to investigate the distributions of hiss waves in the plasmasphere, while relatively little attention has been given to those in the plasmaspheric plume. In this study, we present for the first time a statistical analysis of the occurrence and the spatial distribution of wave amplitudes and wave normal angles for hiss waves in plumes using Van Allen Probes observations during the period of October 2012 to December 2016. Statistical results show that a wide range of hiss wave amplitudes in plumes from a few picotesla to >100 pT is observed, but a modest (<20 pT) wave amplitude is more commonly observed regardless of geomagnetic activity in both the midnight‐to‐dawn and dusk sector. By contrast, stronger amplitude hiss occurs preferentially during geomagnetically active times in the dusk sector. The wave normal angles are distributed over a broad range from 0° to 90° with a bimodal distribution: a quasi‐field‐aligned population (<20°) with an occurrence rate of <60% and an oblique one (>50°) with a relative low occurrence rate of ≲20%. Therefore, from a statistical point of view, we confirm that the hiss intensity (a few tens of picotesla) and field‐aligned hiss wave adopted in previous simulation studies are a reasonable assumption but stress that the activity dependence of the wave amplitude should be considered.
We provide a detailed stochastic description of the swimming motion of an E. coli bacterium in two dimension, where we resolve tumble events in time. For this purpose, we set up two Langevin equations for the orientation angle and speed dynamics. Calculating moments, distribution and autocorrelation functions from both Langevin equations and matching them to the same quantities determined from data recorded in experiments, we infer the swimming parameters of E. coli. They are the tumble rate lambda, the tumble time r(-1), the swimming speed v(0), the strength of speed fluctuations sigma, the relative height of speed jumps eta, the thermal value for the rotational diffusion coefficient D-0, and the enhanced rotational diffusivity during tumbling D-T. Conditioning the observables on the swimming direction relative to the gradient of a chemoattractant, we infer the chemotaxis strategies of E. coli. We confirm the classical strategy of a lower tumble rate for swimming up the gradient but also a smaller mean tumble angle (angle bias). The latter is realized by shorter tumbles as well as a slower diffusive reorientation. We also find that speed fluctuations are increased by about 30% when swimming up the gradient compared to the reversed direction.
Statistical properties of a free-electron laser revealed by Hanbury Brown-Twiss interferometry
(2017)
We present a comprehensive experimental analysis of statistical properties of the self-amplified spontaneous emission free-electron laser (FEL) FLASH by means of Hanbury Brown and Twiss interferometry. The experiments were performed at FEL wavelengths of 5.5, 13.4, and 20.8 nm. We determined the second-order intensity correlation function for all wavelengths and different operation conditions of FLASH. In all experiments a high degree of spatial coherence (above 50%) was obtained. Our analysis performed in spatial and spectral domains provided us with the independent measurements of an average pulse duration of the FEL that were below 60 fs. To explain the complicated behavior of the second-order intensity correlation function we developed an advanced theoretical model that includes the presence of multiple beams and external positional jitter of the FEL pulses. By this analysis we determined that in one of the experiments external positional jitter was about 25% of the beam size. We envision that methods developed in our study will be used widely for analysis and diagnostics of FEL radiation.
Diffusive search for a static target is a common problem in statistical physics with numerous applications in chemistry and biology.
We look at this problem from a different perspective and investigate the statistics of encounters between the diffusing particle and the target. While an exact solution of this problem was recently derived in the form of a spectral expansion over the eigenbasis of the Dirichlet-to-Neumann operator, the latter is generally difficult to access for an arbitrary target.
In this paper, we present three complementary approaches to approximate the probability density of the rescaled number of encounters with a small target in a bounded confining domain. In particular, we derive a simple fully explicit approximation, which depends only on a few geometric characteristics such as the surface area and the harmonic capacity of the target, and the volume of the confining domain.
We discuss the advantages and limitations of three approaches and check their accuracy.
We also deduce an explicit approximation for the distribution of the first-crossing time, at which the number of encounters exceeds a prescribed threshold. Its relations to common first-passage time problems are discussed.
We present a feasibility study with several magnetic field configurations for creating spin-dependent forces that can split a low-energy ion beam by the Stern-Gerlach (SG) effect. To the best of our knowledge, coherent spin-splittings of charged particles have yet to be realised. Our proposal is based on ion source parameters taken from a recent experiment that demonstrated single-ion implantation from a high-brightness ion source combined with a radio-frequency Paul trap. The inhomogeneous magnetic fields can be created by permanently magnetised microstructures or from current-carrying wires with sizes in the micron range, such as those recently used in a successful implementation of the SG effect with neutral atoms. All relevant forces (Lorentz force and image charges) are taken into account, and measurable splittings are found by analytical and numerical calculations.
We show that "stochastic bursting" is observed in a ring of unidirectional delay-coupled noisy excitable systems, thanks to the combinational action of time-delayed coupling and noise. Under the approximation of timescale separation, i.e., when the time delays in each connection are much larger than the characteristic duration of the spikes, the observed rather coherent spike pattern can be described by an idealized coupled point processwith a leader-follower relationship. We derive analytically the statistics of the spikes in each unit, the pairwise correlations between any two units, and the spectrum of the total output from the network. Theory is in good agreement with the simulations with a network of theta-neurons. Published under license by AIP Publishing.
We develop a model of stochastic radiation pressure for rotating non-spherical particles and apply the model to circumplanetary dynamics of dust grains. The stochastic properties of the radiation pressure are related to the ensemble-averaged characteristics of the rotating particles, which are given in terms of the rotational time-correlation function of a grain. We investigate the model analytically and show that an ensemble of particle trajectories demonstrates a diffusion-like behaviour. The analytical results are compared with numerical simulations, performed for the motion of the dusty ejecta from Deimos in orbit around Mars. We find that the theoretical predictions are in a good agreement with the simulation results. The agreement however deteriorates at later time, when the impact of non-linear terms, neglected in the analytic approach, becomes significant. Our results indicate that the stochastic modulation of the radiation pressure can play an important role in the circumplanetary dynamics of dust and may in case of some dusty systems noticeably alter an optical depth. (c) 2006 Elsevier Ltd. All rights reserved.
We introduce and study a Lévy walk (LW) model of particle spreading with a finite propagation speed combined with soft resets, stochastically occurring periods in which an harmonic external potential is switched on and forces the particle towards a specific position. Soft resets avoid instantaneous relocation of particles that in certain physical settings may be considered unphysical. Moreover, soft resets do not have a specific resetting point but lead the particle towards a resetting point by a restoring Hookean force. Depending on the exact choice for the LW waiting time density and the probability density of the periods when the harmonic potential is switched on, we demonstrate a rich emerging response behaviour including ballistic motion and superdiffusion. When the confinement periods of the soft-reset events are dominant, we observe a particle localisation with an associated non-equilibrium steady state. In this case the stationary particle probability density function turns out to acquire multimodal states. Our derivations are based on Markov chain ideas and LWs with multiple internal states, an approach that may be useful and flexible for the investigation of other generalised random walks with soft and hard resets. The spreading efficiency of soft-rest LWs is characterised by the first-passage time statistic.
Stochastic resetting, a diffusive process whose amplitude is reset to the origin at random times, is a vividly studied strategy to optimize encounter dynamics, e.g., in chemical reactions. Here we generalize the resetting step by introducing a random resetting amplitude such that the diffusing particle may be only partially reset towards the trajectory origin or even overshoot the origin in a resetting step. We introduce different scenarios for the random-amplitude stochastic resetting process and discuss the resulting dynamics. Direct applications are geophysical layering (stratigraphy) and population dynamics or financial markets, as well as generic search processes.