Limiting dynamics in large quantum systems

Alexey Vyacheslavovich Gorshkov

Xiangyu Cao, Jorge Kurchan

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.

Victor Gurarie

We study the large time dynamics of quantum systems under a sudden quench. We show that, first of all, for a generic system in the thermodynamic limit the Gibbs distribution correctly captures its large time dynamics. For an integrable system, the generalized Gibbs ensemble captures its large time dynamics only if the system can be thought of as a number of noninteracting uncorrelated fermionic degrees of freedom.

V. M. Akulin

Keith H. Hughes

V Gurarie

We study the large time dynamics of a macroscopically large quantum system under a sudden quench. We show, first of all, that for a generic system in the thermodynamic limit the Gibbs distribution correctly captures the large time dynamics of its global observables. In contrast, for an integrable system, the generalized Gibbs ensemble captures its global large time dynamics only if the system can be thought of as a number of noninteracting uncorrelated fermionic degrees of freedom. The conditions for the generalized Gibbs ensemble to capture the large time dynamics of local quantities are likely to be far less restrictive, but this question is not systematically addressed here.