2026/07/23 by Xiangyu Cao, Jorge Kurchan
#quant-ph #cond-mat.stat-mech #hep-th
We study three definitions of large deviation in many-body quantum dynamics: (i) via the full distribution of an extensive observable, (ii) via the distribution of measurement outcomes (from a continuous monitoring of the observable) over a time interval t ≤ tmax, and (iii) via the distribution of expectation values over t ≤ tmax. In generic systems without conservation laws, the large deviation function (i) reaches its longtime limit at t ∼ O(1), independently of system size N. (ii) and (iii) reach their longtime limit at t ∼ e N and t ∼ exp(eN), respectively. Before that, there is a \it sharp frontier between the explored and unexplored outcomes/expectation values; their distribution equals the longtime limit truncated at values that drift with tmax. We propose that the evolution of these values with tmax provides a measure of quantum complexity.