The Effects of Weak Spatiotemporal Noise on a Bistable One-Dimensional System

We treat analytically a model that captures several features of the phenomenon of spatially inhomogeneous reversal of an order parameter. The model is a classical Ginzburg-Landau field theory restricted to a bounded one-dimensional spatial domain, perturbed by weak spatiotemporal noise having a flat power spectrum in time and space. Our analysis extends the Kramers theory of noise-induced transitions to the case when the system acted on by the noise has nonzero spatial extent, and the noise itself is spatially dependent. By extending the Langer-Coleman theory of the noise-induced decay of a metastable state, we determine the dependence of the activation barrier and the Kramers reversal rate prefactor on the size of the spatial domain. As this is increased from zero and passes through a certain critical value, a transition between activation regimes occurs, at which the rate prefactor diverges. Beyond the transition, reversal preferentially takes place in a spatially inhomogeneous rather than in a homogeneous way. Transitions of this sort were not discovered by Langer or Coleman, since they treated only the infinite-volume limit. Our analysis uses higher transcendental functions to handle the case of finite volume. Similar transitions between activation regimes should occur in other models of metastable systems with nonzero spatial extent, perturbed by weak noise, as the size of the spatial domain is varied.Comment: 16 page

Charge transfer statistics of a molecular quantum dot with strong electron-phonon interaction

We analyze the nonequilibrium transport properties of a quantum dot with a harmonic degree of freedom (Holstein phonon) coupled to metallic leads, and derive its full counting statistics (FCS). Using the Lang-Firsov (polaron) transformation, we construct a diagrammatic scheme to calculate the cumulant generating function. The electron-phonon interaction is taken into account exactly, and the employed approximation represents a summation of a diagram subset with respect to the tunneling amplitude. By comparison to Monte Carlo data the formalism is shown to capture the basic properties of the strong coupling regime

Noise-Activated Escape from a Sloshing Potential Well

We treat the noise-activated escape from a one-dimensional potential well of an overdamped particle, to which a periodic force of fixed frequency is applied. We determine the boundary layer behavior, and the physically relevant length scales, near the oscillating well top. We show how stochastic behavior near the well top generalizes the behavior first determined by Kramers, in the case without forcing. Both the case when the forcing dies away in the weak noise limit, and the case when it does not, are examined. We also discuss the relevance of various scaling regimes to recent optical trap experiments.Comment: 9 pages, no figures, REVTeX, expanded versio

Noisy Classical Field Theories with Two Coupled Fields: Dependence of Escape Rates on Relative Field Stiffnesses

Exit times for stochastic Ginzburg-Landau classical field theories with two or more coupled classical fields depend on the interval length on which the fields are defined, the potential in which the fields deterministically evolve, and the relative stiffness of the fields themselves. The latter is of particular importance in that physical applications will generally require different relative stiffnesses, but the effect of varying field stiffnesses has not heretofore been studied. In this paper, we explore the complete phase diagram of escape times as they depend on the various problem parameters. In addition to finding a transition in escape rates as the relative stiffness varies, we also observe a critical slowing down of the string method algorithm as criticality is approached.Comment: 16 pages, 10 figure

Asymptotic Exit Location Distributions in the Stochastic Exit Problem

Consider a two-dimensional continuous-time dynamical system, with an attracting fixed point $S$. If the deterministic dynamics are perturbed by white noise (random perturbations) of strength $\epsilon$, the system state will eventually leave the domain of attraction $\Omega$ of $S$. We analyse the case when, as $\epsilon\to0$, the exit location on the boundary $\partial\Omega$ is increasingly concentrated near a saddle point $H$ of the deterministic dynamics. We show that the asymptotic form of the exit location distribution on $\partial\Omega$ is generically non-Gaussian and asymmetric, and classify the possible limiting distributions. A key role is played by a parameter $\mu$, equal to the ratio $|\lambda_s(H)|/\lambda_u(H)$ of the stable and unstable eigenvalues of the linearized deterministic flow at $H$. If $\mu<1$ then the exit location distribution is generically asymptotic as $\epsilon\to0$ to a Weibull distribution with shape parameter $2/\mu$, on the $O(\epsilon^{\mu/2})$ length scale near $H$. If $\mu>1$ it is generically asymptotic to a distribution on the $O(\epsilon^{1/2})$ length scale, whose moments we compute. The asymmetry of the asymptotic exit location distribution is attributable to the generic presence of a `classically forbidden' region: a wedge-shaped subset of $\Omega$ with $H$ as vertex, which is reached from $S$, in the $\epsilon\to0$ limit, only via `bent' (non-smooth) fluctuational paths that first pass through the vicinity of $H$. We deduce from the presence of this forbidden region that the classical Eyring formula for the small-$\epsilon$ exponential asymptotics of the mean first exit time is generically inapplicable.Comment: This is a 72-page Postscript file, about 600K in length. Hardcopy requests to [email protected] or [email protected]

The Effect of Focusing and Caustics on Exit Phenomena in Systems Lacking Detailed Balance

We study the trajectories followed by a particle subjected to weak noise when escaping from the domain of attraction of a stable fixed point. If detailed balance is absent, a _focus_ may occur along the most probable exit path, leading to a breakdown of symmetry (if present). The exit trajectory bifurcates, and the exit location distribution may become `skewed' (non-Gaussian). The weak-noise asymptotics of the mean escape time are strongly affected. Our methods extend to the study of skewed exit location distributions in stochastic models without symmetry.Comment: REVTEX macros (latest version). Two accompanying PS figures, one of which is large (over 600K unpacked

Uncertainty-Aware Organ Classification for Surgical Data Science Applications in Laparoscopy

Objective: Surgical data science is evolving into a research field that aims to observe everything occurring within and around the treatment process to provide situation-aware data-driven assistance. In the context of endoscopic video analysis, the accurate classification of organs in the field of view of the camera proffers a technical challenge. Herein, we propose a new approach to anatomical structure classification and image tagging that features an intrinsic measure of confidence to estimate its own performance with high reliability and which can be applied to both RGB and multispectral imaging (MI) data. Methods: Organ recognition is performed using a superpixel classification strategy based on textural and reflectance information. Classification confidence is estimated by analyzing the dispersion of class probabilities. Assessment of the proposed technology is performed through a comprehensive in vivo study with seven pigs. Results: When applied to image tagging, mean accuracy in our experiments increased from 65% (RGB) and 80% (MI) to 90% (RGB) and 96% (MI) with the confidence measure. Conclusion: Results showed that the confidence measure had a significant influence on the classification accuracy, and MI data are better suited for anatomical structure labeling than RGB data. Significance: This work significantly enhances the state of art in automatic labeling of endoscopic videos by introducing the use of the confidence metric, and by being the first study to use MI data for in vivo laparoscopic tissue classification. The data of our experiments will be released as the first in vivo MI dataset upon publication of this paper.Comment: 7 pages, 6 images, 2 table

Quantum plasmonics: second-order coherence of surface plasmons launched by quantum emitters into a metallic film

We address the issue of the second-order coherence of single surface plasmons launched by a quantum source of light into extended gold films. The quantum source of light is made of a scanning fluorescent nanodiamond hosting five nitrogen-vacancy (NV) color centers. By using a specially designed microscopy that combines near-field optics with far-field leakage-radiation microscopy in the Fourier space and adapted spatial filtering, we find that the quantum statistics of the initial source of light is preserved after conversion to surface plasmons and propagation along the polycrystalline gold film.Comment: Second version with minor changes made to comply with Referees' comments. Editorially approved for publication in Phys. Rev. B on 22 June 201

Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles

Linear arrays of very small Ag nanoparticles (diameter ~10 nm, spacing 0–4 nm) were fabricated in sodalime glass using an ion irradiation technique. Optical extinction spectroscopy of the arrays reveals a large polarization-dependent splitting of the collective plasmon extinction band. Depending on the preparation condition, a redshift of the longitudinal resonance as large as 1.5 eV is observed. Simulations of the three-dimensional electromagnetic field evolution are used to determine the resonance energy of idealized nanoparticle arrays with different interparticle spacings and array lengths. Using these data, the experimentally observed redshift is attributed to collective plasmon coupling in touching particles and/or in long arrays of strongly coupled particles. The simulations also indicate that for closely coupled nanoparticles (1–2 nm spacing) the electromagnetic field is concentrated in nanoscale regions (10 dB radius: 3 nm) between the particles, with a 5000-fold local field intensity enhancement. In arrays of 1-nm-spaced particles the dipolar particle interaction extends to over 10 particles, while for larger spacing the interaction length decreases. Spatial images of the local field distribution in 12-particle arrays of touching particles reveal a particlelike coupled mode with a resonance at 1.8 eV and a wirelike mode at 0.4 eV