Large deviations in quantum dynamics and complexity

Abstract: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 $t \le t_{\max}$, and (iii) via the distribution of expectation values over $t \le t_{\max}$. In generic systems without conservation laws, the large deviation function (i) reaches its longtime limit at $t \sim \mathcal{O}(1)$, independently of system size $N$. (ii) and (iii) reach their longtime limit at $t \sim e^{ N}$ and $t \sim \exp(e^{N})$, 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 $t_{\max}$. We propose that the evolution of these values with $t_{\max}$ provides a measure of quantum complexity.

17 pages, 6 figures, comments welcome!

Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th)

arXiv:2607.20959 [quant-ph]

(or arXiv:2607.20959v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.20959 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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