We consider quantum dynamics on a graph, with repeated strong measurements performed locally at a fixed time interval $\tau$. For example a particle starting on node $x$ and measurements performed on another node $x'$. From the basic postulates of quantum mechanics the string of measurements yields a sequence no,no,no, $\cdots$ and finally in the $n$-th attempt a yes, i.e. the particle is...
Evolving stochastic process, when interrupted at random epochs and reset to its initial condition, reaches a new nonequilibrium stationary state. The approach to the stationary state is accompanied by an unusual `dynamical phase transition'. Moreever, the mean first-passage time to a fixed target becomes a minimum at an optimal value of the resetting rate. This makes the diffusive search...
