Decay of a metastable state activated by non-Gaussian noise: A critical review of the generalized Kramers problem

Activated escape of periodically driven systems

We discuss activated escape from a metastable state of a system driven by a time-periodic force. We show that the escape probabilities can be changed very strongly even by a comparatively weak force. In a broad parameter range, the activation energy of escape depends linearly on the force amplitude. This dependence is described by the logarithmic susceptibility, which is analyzed theoretically and through analog and digital simulations. A closed-form explicit expression for the escape rate of an overdamped Brownian particle is presented and shown to be in quantitative agreement with the simula…

非平衡Kramers翻转在Kerr参数振荡器中

Nonequilibrium Kramers Turnover in a Kerr Parametric Oscillator

研究非平衡Kerr参数振荡器中的Kramers翻转现象，通过重新缩放旋转框架动力学和有效摩擦控制，揭示了非平衡系统中激活动力学的特征。

Thermal stability of metastable magnetic skyrmions: Entropic narrowing and significance of internal eigenmodes

We compute annihilation rates of metastable magnetic skyrmions using a form of Langer's theory in the intermediate-to-high damping (IHD) regime. For a Néel skyrmion, a Bloch skyrmion, and an antiskyrmion, we look at two possible paths to annihilation: collapse and escape through a boundary. We also study the effects of a curved vs. a flat boundary, a second skyrmion and a non-magnetic defect. We find that the skyrmion's internal modes play a dominant role in the thermally activated transitions compared to the spin-wave excitations and that the relative contribution of internal modes depends on…

Thermally Activated Transitions Between Micromagnetic States

We review work by the authors on thermal activation in nanoscopic magnetic systems. These systems present unique difficulties in analyzing noise-induced escape over a barrier, including the presence of nonlocal interactions, nongradient terms in the energy functional, and dynamical textures as initial or saddle states. We begin with a discussion of magnetic reversal between single-domain configurations of the magnetization. Here the transition (saddle) state can be either a single-domain or a spatially varying (instanton-like) configuration, and depending on the system parameters can exhibit e…

Escape dynamics of active particles in multistable potentials

Rare transitions between long-lived metastable states underlie a great variety of physical, chemical and biological processes. Our quantitative understanding of reactive mechanisms has been driven forward by the insights of transition state theory. In particular, the dynamic framework developed by Kramers marks an outstanding milestone for the field. Its predictions, however, do not apply to systems driven by non-conservative forces or correlated noise histories. An important class of such systems are active particles, prominent in both biology and nanotechnology. Here, we trap a silica nanopa…

Universality in escape from a modulated potential well

We show that the rate of activated escape $W$ from a periodically modulated potential displays scaling behavior versus modulation amplitude $A$. For adiabatic modulation of an optically trapped Brownian particle, measurements yield $\ln W\propto (A_{\rm c} - A)^μ$ with $μ= 1.5$. The theory gives $μ=3/2$ in the adiabatic limit and predicts a crossover to $μ=2$ scaling as $A$ approaches the bifurcation point where the metastable state disappears.