Bond orbital description of the strain induced second order optical susceptibility in silicon

We develop a theoretical model, relying on the well established sp3 bond-orbital theory, to describe the strain-induced $\chi^{(2)}$ in tetrahedrally coordinated centrosymmetric covalent crystals, like silicon. With this approach we are able to describe every component of the $\chi^{(2)}$ tensor in terms of a linear combination of strain gradients and only two parameters $\alpha$ and $\beta$ which can be estimated theoretically. The resulting formula can be applied to the simulation of the strain distribution of a practical strained silicon device, providing an extraordinary tool for optimization of its optical nonlinear effects. By doing that, we were able not only to confirm the main valid claims known about $\chi^{(2)}$ in strained silicon, but also estimate the order of magnitude of the $\chi^{(2)}$ generated in that device

Activated escape of a self-propelled particle from a metastable state

We study the noise-driven escape of active Brownian particles (ABPs) and run-and-tumble particles (RTPs) from confining potentials. In the small noise limit, we provide an exact expression for the escape rate in term of a variational problem in any dimension. For RTPs in one dimension, we obtain an explicit solution, including the first sub-leading correction. In two dimensions we solve the escape from a quadratic well for both RTPs and ABPs. In contrast to the equilibrium problem we find that the escape rate depends explicitly on the full shape of the potential barrier, and not only on its height. This leads to a host of unusual behaviors. For example, when a particle is trapped between two barriers it may preferentially escape over the higher one. Moreover, as the self-propulsion speed is varied, the escape route may discontinuously switch from one barrier to the other, leading to a dynamical phase transition

Nonlocal stationary probability distributions and escape rates for an active Ornstein-Uhlenbeck particle

We evaluate the steady-state distribution and escape rate for an Active Ornstein-Uhlenbeck Particle (AOUP) using methods from the theory of large deviations. The calculation is carried out both for small and large memory times of the active force in one-dimension. We compare our results to those obtained in the literature about colored noise processes, and we emphasize their relevance for the field of active matter. In particular, we stress that contrary to equilibrium particles, the invariant measure of such an active particle is a non-local function of the potential. This fact has many interesting consequences, which we illustrate through two phenomena. First, active particles in the presence of an asymmetric barrier tend to accumulate on one side of the potential -a ratchet effect that was missing is previous treatments. Second, an active particle can escape over a deep metastable state without spending any time at its bottom

Effective driven dynamics for one-dimensional conditioned Langevin processes in the weak-noise limit

In this work we focus on fluctuations of time-integrated observables for a particle diffusing in a one-dimensional periodic potential in the weak-noise asymptotics. Our interest goes to rare trajectories presenting an atypical value of the observable, that we study through a biased dynamics in a large-deviation framework. We determine explicitly the effective probability-conserving dynamics which makes rare trajectories of the original dynamics become typical trajectories of the effective one. Our approach makes use of a weak-noise path-integral description in which the action is minimised by the rare trajectories of interest. For `current-type' additive observables, we find the emergence of a propagative trajectory minimising the action for large enough deviations, revealing the existence of a dynamical phase transition at a fluctuating level. In addition, we provide a new method to determine the scaled cumulant generating function of the observable without having to optimise the action. It allows one to show that the weak-noise and the large-time limits commute in this problem. Finally, we show how the biased dynamics can be mapped in practice to an effective driven dynamics, which takes the form of a driven Langevin dynamics in an effective potential. The non-trivial shape of this effective potential is key to understand the link between the dynamical phase transition in the large deviations of current and the standard depinning transition of a particle in a tilted potential

Encouraging self-reflection in social work students: Using Personal Construct methods

We report on a research study in which we introduced undergraduate social work students in England to two methods originating in Personal Construct Theory (PCT) as a way of encouraging in-depth self-reflection. The methods were first piloted with four students and subsequently used with two large classes of second year students. The students often found the methods challenging, but many felt that these enabled them to reflect upon social work practice and upon their own assumptions, values and behaviour in a fresh and thought-provoking way. We argue that such methods could usefully be added to existing methods for encouraging reflexivity in social work students. Teaching materials and instructions for delivering our teaching session using these methods are available online at http://www.hud.ac.uk/research/researchcentres/capr/projects/personal-construct-methods-in-reflective-practice

Optical Gain in Carbon Nanotubes

Semiconducting single-wall carbon nanotubes (s-SWNTs) have proved to be promising material for nanophotonics and optoelectronics. Due to the possibility of tuning their direct band gap and controlling excitonic recombinations in the near-infrared wavelength range, s-SWNT can be used as efficient light emitters. We report the first experimental demonstration of room temperature intrinsic optical gain as high as 190 cm-1 at a wavelength of 1.3 {\mu}m in a thin film doped with s-SWNT. These results constitute a significant milestone toward the development of laser sources based on carbon nanotubes for future high performance integrated circuits.Comment: 4 figure