Memories of initial states and density imbalance in dynamics of interacting disordered systems

Ahana Chakraborty; Pranay Gorantla; Rajdeep Sensarma

doi:10.1103/PhysRevB.102.224306

paper

Memories of initial states and density imbalance in dynamics of interacting disordered systems

arXiv:1906.02205 · doi:10.1103/PhysRevB.102.224306

Abstract

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 $A ˉ$ sites. For non-interacting systems we establish a universal relation between the long time density imbalance between $A$ and $A ˉ$ 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 $ξ ~_{l}$ 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.

arXiv comment5+4 pages, 2+5 figures

Memories of initial states and density imbalance in dynamics of interacting disordered systems

Abstract

References in corpus (34)

Cited by in corpus (5)