Large deviations in quantum dynamics and complexity

• URL: http://arxiv.org/abs/2607.20959v1
• Date: Thu, 23 Jul 2026 06:36:47 GMT
• Title: Large deviations in quantum dynamics and complexity
• Abstract summary: In generic systems without conservation laws, the large deviation function reaches its longtime limit at $t sim mathcalO(1)$.<n>We propose that the evolution of these values with $t_max$ provides a measure of quantum complexity.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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