Signal detection via residence times statistics: Noise-mediated minimization of the measurement error

Abstract

We study the problem of detecting a small dc signal by quantifying its effect on the mean difference DeltaT in residence times in the stable steady states of a bistable dynamical measurement device, in the presence of a noise floor and a known time-sinusoidal bias signal. Errors in the measurement process occur due to a finite observation time that is present in most practical scenarios. The error is found to have a nonmonotonic dependence on the noise intensity; at a critical noise intensity, the error is minimized. This phenomenon, reminiscent of the well-known stochastic resonance effect, can also be obtained by adjusting the device tuning parameters for a given noise floor. The effect appears to be most pronounced for subthreshold bias signals in the strongly nonlinear response regime.

Stochastic resonance in an asymmetric bistable system driven by correlated multiplicative and additive noise

“…Li [13] investigated the effect of asymmetry of the potential on stochastic resonance for a bistable model driven by additive noise and found the asymmetry weakening the stochastic resonance. Nikitin et al [14] presented the theoretical results of switching time distributions of an asymmetric bistable system driven by periodic and stochastic force.…”

High-Flux Beam Source for Cold, Slow Atoms or Molecules

“…Under the conditions described here, this beam source could be used to load a peak flux of up to 2 10 11 s ÿ1 Na atoms into a simple permanent magnet guide such as the type described in Ref. [7]. An electrostatic guide such as that described in Ref.…”

“…Because the number of trapped particles is typically limited by the characteristics of the initial beam (flux, forward velocity, temperature, etc. ), significant effort has been put into developing improved atomic beam sources [1][2][3][4][5][6][7]. Work on developing cold molecular sources has recently been a particularly active field of research [8][9][10][11][12][13].…”

Escape rates in periodically driven Markov processes

“…Our main objective is to develop an accurate analytical approximation that avoids certain restrictive assumptions of prior attempts. All these, in fact, involve the use of either of the following limiting approximation schemes such as the limit of linear response theory (i.e., a weak stimulus A51) [7,9] or the limit of asymptotically weak noise [10][11][12][13][14]. Our scheme detailed below yields analytic and tractable expressions beyond the linear response and weak-noise limits; as will be demonstrated, this novel scheme indeed provides analytical formulae that compare very favorably with precise numerical results of the full dynamics in Eqs.…”