We study the dynamics of one and two dimensional disordered lattice bosons/fermions initialized to a Fock state with a pattern of $1$ and $0$ particles on $A$ and ${\bar A}$ sites. For non-interacting systems we establish a universal relation between the long time density imbalance between $A$ and ${\bar A}$ site, $I(\infty)$, the localization length $ξ_l$, and the geometry of the initial pattern. For alternating initial pattern of $1$ and $0$ particles in 1 dimension, $I(\infty)=\tanh[a/ξ_l]$, where $a$ is the lattice spacing. For systems with mobility edge, we find analytic relations between $I(\infty)$, the effective localization length $\tildeξ_l$ and the fraction of localized states $f_l$. The imbalance as a function of disorder shows non-analytic behaviour when the mobility edge passes through a band edge. For interacting bosonic systems, we show that dissipative processes lead to a decay of the memory of initial conditions. However, the excitations created in the process act as a bath, whose noise correlators retain information of the initial pattern. This sustains a finite imbalance at long times in strongly disordered interacting systems.
Information dynamics of our brains in dynamically driven disordered superconducting loop networks
Department of Physics, University of California San Diego（加州大学圣地亚哥分校物理系）；Department of Electrical and Computer Engineering, University of California, Riverside（加州大学河滨分校电气与计算机工程系）
