Time-Fractional Schr\"odinger 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 Schr\"odinger equation, which includes memory effects in a non-Markovian regime. We vary the fractional parameter $\tau$, the tunneling amplitudes $\delta_A$ and $\delta_B$, 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 $\tau$ rapidly generates entanglement expecting maximal values $\mathcal{LN}\approx 1$ and non-classical correlations quantified by local quantum uncertainty. Conversely, higher values of $\tau$ 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.