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We show that a thermally isolated system driven across a quantum phase transition by a noisy control field exhibits anti-Kibble-Zurek behavior, whereby slower driving results in higher excitations. We characterize the density of excitations as a function of the ramping rate and the noise strength. The optimal driving time to minimize excitations is shown to scale as a universal power law of the noise strength. Our findings reveal the limitations of adiabatic protocols such as quantum annealing and demonstrate the universality of the optimal ramping rate., 5 pages, 3 figures, 2 pages of supplemental material

Bidirectional motion is an example of collective behavior of molecular motors. It occurs at finite noise level in a nonequilibrium system. We consider this problem as a first exit problem. We identify the noise strength by doing an expansion of a master equation and apply the Wentzell-Freidlin theory to define an effective nonequilibrium potential and provide analytical estimates of the reversal time. Our results match very well with the results of stochastic simulations.

Time--delayed feedback is exploited for controlling noise--induced motion in coherence resonance oscillators. Namely, under the proper choice of time delay, one can either increase or decrease the regularity of motion. It is shown that in an excitable system, delayed feedback can stabilize the frequency of oscillations against variation of noise strength. Also, for fixed noise intensity, the phenomenon of entrainment of the basic oscillation period by the delayed feedback occurs. This allows one to steer the timescales of noise-induced motion by changing the time delay., 4 pages, 4 figures. In the replacement file Fig. 2 and Fig. 4(b),(d) were amended. The reason is numerical error found, that affected the quantitative estimates of correlation time, but did not affect the main message

We investigate experimentally the scaling of the average time \ensuremath{\tau} between intermittent, noise-induced bursts for a chaotic mechanical system near a crisis. The system studied is a periodically driven (frequency f) magnetoelastic ribbon. Theory predicts that for deterministic crises where \ensuremath{\tau} scales as \ensuremath{\tau}\ensuremath{\sim}\ensuremath{\Vert}f-${\mathit{f}}_{\mathit{c}}$${\mathrm{\ensuremath{\Vert}}}^{\mathrm{\ensuremath{-}}\ensuremath{\gamma}}$ (f${\mathit{f}}_{\mathit{c}}$, f=${\mathit{f}}_{\mathit{c}}$ at crisis), the characteristic time between noise-induced bursts (f\ensuremath{\ge}${\mathit{f}}_{\mathit{c}}$) should scale as \ensuremath{\tau}\ensuremath{\sim}${\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{-}}\ensuremath{\gamma}}$g(\ensuremath{\Vert}f-${\mathit{f}}_{\mathit{c}}$\ensuremath{\Vert}/\ensuremath{\sigma}), where \ensuremath{\sigma} is the noise strength and \ensuremath{\gamma} is the same in both cases. We determine \ensuremath{\gamma} for the low-noise (``deterministic'') system, then add noise and observe that the scaling for \ensuremath{\tau} is as predicted.