Conditional no-jump dynamics of noninteracting quantum chains

Lindbladian dissipative processes can be determined by stochastic samplings of individual trajectories, whose non-Hermitian evolution is perturbed by quantum jumps. The conditional dynamics of the jump events is fundamental to access many relevant statistical quantities of the dissipative dynamics. In this work, we mostly focus on the conditional no-jump evolution of noninteracting chains, including partial missed detection of jumps. As a main result, for Gaussian-preserving Lindblad operators, the conditional dynamics is captured by a nonlinear Riccati-type differential equation for the correlation matrix. As an application, we study the no-jump probability and the waiting-time distributions for chains of hopping particles and double quantum dots.