Time-Fractional Schrödinger Evolution in Coupled Double Quantum Dots: Memory Effects on Quantum Resources

Abstract

Our work explore the time evolution of entanglement, local quantum uncertainty, and correlated coherence, within a system modeled by two double quantum dots. The dynamics is represented using a time-fractional Schrödinger equation, which includes memory effects in a non-Markovian regime. We vary the fractional parameter $\ddot{I}„$, the tunneling amplitudes $\hat{I}{´}_A$ and $\hat{I}{´}_B$, as well as the inter-dot interaction strength $\mathcal{V}$, to investigate how these key parameters govern the generation, stabilization, and decay of quantum resources within the system. The obtained results reveal that, for both initial states, fractional dynamics with a low $\ddot{I}„$ rapidly generates entanglement expecting maximal values $\mathcal{L}\mathcal{N}\approx 1$ and non-classical correlations quantified by local quantum uncertainty. Conversely, higher values of $\ddot{I}„$ lead to slower entanglement but memory effects allow quantum resources to remain significant for a longer time, with the negativity remaining above ($\approx 0.6$). We also find that higher interaction frequencies $\mathcal{V}$ accelerate correlations and stabilize coherence, while a strong tunneling asymmetry degrades entanglement and coherence despite the initial benefits of increasing quantum resources.