# Quantification of the memory effect of steady-state currents from interaction-induced transport in quantum systems

## TL;DR

This paper demonstrates that isolated quantum many-body systems can retain long-term memory effects in steady-state currents induced by interactions, revealing non-trivial dependence on initial states and ramping protocols.

## Contribution

It uncovers long-time memory effects in steady states of isolated quantum systems driven by interaction imbalances, highlighting the role of initial states and ramping protocols.

## Key findings

- Quasi-steady state currents form in finite systems and become steady in the thermodynamic limit.
- Memory effects depend on initial states and ramping protocols.
- Systems exhibit a generalized Fick's law with memory-dependent diffusion coefficients.

## Abstract

Dynamics of a system in general depends on its initial state and how the system is driven, but in many-body systems the memory is usually averaged out during evolution. Here, interacting quantum systems without external relaxations are shown to retain long-time memory effects in steady states. To identify memory effects, we first show quasi-steady state currents form in finite, isolated Bose and Fermi Hubbard models driven by interaction imbalance and they become steady-state currents in the thermodynamic limit. By comparing the steady state currents from different initial states or ramping rates of the imbalance, long-time memory effects can be quantified. While the memory effects of initial states are more ubiquitous, the memory effects of switching protocols are mostly visible in interaction-induced transport in lattices. Our simulations suggest the systems enter a regime governed by a generalized Fick's law and memory effects lead to initial-state dependent diffusion coefficients. We also identify conditions for enhancing memory effects and discuss possible experimental implications.