Reducing mean first passage times with intermittent confining potentials: a realization of resetting processes

During a random search, resetting the searcher's position from time to starting point often reduces mean completion of process. Although many different models have been studied over past ten years, only few can be physically implemented. Here we study theoretically protocol that realised experimentally and which exhibits unusual optimization properties. A Brownian particle is subject an arbitrary confining potential $v(x)$ switched on off intermittently at fixed rates. Motion constrained between absorbing wall located origin reflective wall. When walls are sufficiently far apart, interplay free diffusion during "off" phases attraction toward minimum "on" gives rise rich behaviours, not observed in ideal models. For potentials form $v(x)=k|x-x_0|^n/n$, with $n>0$, switch-on switch-off rates minimise first passage (MFPT) undergo continuous phase transition as stiffness $k$ varied. above critical value $k_c$, intermittency enhances target encounter: minimal MFPT lower than Kramer's attained for non-vanishing pair switching We focus harmonic case $n=2$, extending previous results piecewise linear ($n=1$) unbounded domains. also non-equilibrium stationary states emerging this