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arxiv: 2605.05083 · v1 · submitted 2026-05-06 · ✦ hep-th

Time-Fractional Schr\"odinger Evolution in Coupled Double Quantum Dots: Memory Effects on Quantum Resources

Abdessamie Chhieb , Mostafa Mansour , Mohamed Ouchrif This is my paper

Pith reviewed 2026-05-08 17:49 UTC · model grok-4.3

classification ✦ hep-th
keywords time-fractional Schrödinger equationquantum entanglementdouble quantum dotsmemory effectsnon-Markovian dynamicslocal quantum uncertaintyquantum coherencenegativity
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The pith

Time-fractional evolution in coupled double quantum dots shows memory effects sustain entanglement longer at higher fractional orders.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper investigates the time evolution of entanglement, local quantum uncertainty, and correlated coherence in a system of two coupled double quantum dots governed by a time-fractional Schrödinger equation. This equation incorporates memory effects through a fractional parameter τ that controls non-Markovian dynamics, while the authors also vary tunneling amplitudes and inter-dot interaction strength. They find that low τ produces rapid growth of entanglement toward maximal values near 1 along with strong non-classical correlations, whereas higher τ slows the initial rise but lets these resources persist longer due to memory, keeping negativity above roughly 0.6. A reader would care because the results suggest a route to prolonging quantum resources in nanoscale systems without altering the underlying Hamiltonian.

Core claim

The central claim is that fractional dynamics with low τ rapidly generates entanglement expecting maximal values LN≈1 and non-classical correlations quantified by local quantum uncertainty for both initial states, while higher τ leads to slower entanglement generation but memory effects allow quantum resources to remain significant longer with negativity remaining above ≈0.6; higher interaction strength accelerates correlations and stabilizes coherence, yet strong tunneling asymmetry degrades entanglement and coherence despite initial benefits.

What carries the argument

The time-fractional Schrödinger equation, which encodes memory effects via the fractional order τ in the evolution of the coupled double quantum dot Hamiltonian.

If this is right

  • Higher inter-dot interaction strength accelerates the generation of correlations and stabilizes coherence over time.
  • Strong tunneling asymmetry between the dots degrades both entanglement and coherence even when initial resource growth appears beneficial.
  • The negativity of entanglement stays above approximately 0.6 for longer durations when memory effects are stronger at higher fractional orders.
  • Both initial states exhibit qualitatively similar patterns of rapid entanglement buildup at low τ and prolonged resources at high τ.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Tuning an effective memory parameter could offer a practical way to extend coherence times in solid-state quantum devices without changing physical couplings.
  • The fractional-order approach might generalize to other open quantum systems where non-Markovian environments are engineered or measured.
  • Direct comparison of the model's predictions against time-resolved measurements in actual double-dot experiments would test whether the memory prolongation survives realistic noise.
  • Extending the two-dot model to chains or arrays could show how the memory-induced lifetime scales with the number of sites.

Load-bearing premise

The chosen time-fractional derivative accurately models the memory effects in this specific coupled double quantum dot Hamiltonian without additional validation against the ordinary Schrödinger equation.

What would settle it

An experiment on real coupled quantum dots that measures entanglement negativity as a function of a tunable memory parameter and finds identical decay rates for all values of that parameter would falsify the predicted influence of fractional memory effects.

Figures

Figures reproduced from arXiv: 2605.05083 by Abdessamie Chhieb, Mohamed Ouchrif, Mostafa Mansour.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic of two capacitively coupled double quan view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Comparative plots showing the time evolution of view at source ↗
Figure 3
Figure 3. Figure 3: illustrates the dynamics of quantum correlations in a system of two coupled double quantum dots (DQDs) under the influence of fractional dynamics. Three fun￾damental quantum resources — logarithmic negativity (LN ), local quantum uncertainty (LQU), and correlated coherence (Ccc) — are analyzed as a function of time for different values of the fractional parameter τ and for two distinct initial states (p = … view at source ↗
Figure 4
Figure 4. Figure 4: illustrates the time evolution of quantum correlations in a system of two coupled double quantum dots (DQDs), highlighting the influence of the frequency parameter (ν) on three fundamental quantum resources: logarithmic negativity (LN ), local quantum uncertainty (LQU), and correlated coherence (Ccc). The analysis is carried out for increasing values of ν = 5, 10, 15, 30, with a fixed fractional parameter … view at source ↗
Figure 5
Figure 5. Figure 5: illustrates the influence of the tunneling coupling strength (δA) on the temporal behavior of key quantum resources—logarithmic negativity (LN ), local quantum uncertainty (LQU), and correlated coherence (Ccc)—in a system of two coupled double quantum dots subject to fractional Caputo dynamics with τ = 0.8. For the initially separable state (p = 0), quantum correlations dynamically emerge and quickly reach… view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Plots illustrating view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The manuscript studies the time evolution of entanglement (logarithmic negativity), local quantum uncertainty, and correlated coherence in a coupled double quantum dot system using a time-fractional Schrödinger equation to model memory effects in the non-Markovian regime. The authors perform numerical parameter sweeps over the fractional order τ, tunneling amplitudes δ_A and δ_B, and interaction strength V, reporting that low τ produces rapid entanglement generation (reaching LN≈1) while higher τ slows generation but allows resources to persist longer (negativity remaining above ≈0.6) due to memory; higher V accelerates and stabilizes correlations, whereas tunneling asymmetry degrades them.

Significance. If the fractional model is shown to reduce exactly to standard unitary evolution at τ=1 and the numerical implementation is validated, the work could provide a concrete illustration of how memory encoded in τ influences the generation speed and lifetime of quantum resources in a solid-state platform. The qualitative trends from the parameter variations offer potentially useful guidance for tuning quantum-dot systems to preserve entanglement and coherence, though the lack of direct benchmarks against the Markovian limit currently limits the strength of the physical interpretation.

major comments (2)
  1. [§2] §2 (Hamiltonian and time-fractional Schrödinger equation): the central interpretation that differences in entanglement generation and resource persistence for τ<1 arise from memory effects requires an explicit check that the chosen fractional derivative reduces to the standard iħ ∂_t |ψ⟩ = H |ψ⟩ dynamics when τ=1, with identical negativity, local quantum uncertainty, and correlated coherence curves. No such benchmark (analytic or numerical) is provided, leaving open whether the reported trends reflect the physics of the double-dot Hamiltonian or properties of the fractional solver.
  2. [§3] §3 (Numerical results and figures): the quantitative claims (e.g., LN≈1, negativity remaining above ≈0.6) are presented without specification of the fractional-derivative definition employed, the numerical integrator, time-step convergence tests, or error bars on the plotted quantities. This omission is load-bearing for assessing the reliability of the memory-effect conclusions drawn from the τ sweeps.
minor comments (3)
  1. [Abstract] Abstract: the phrasing 'rapidly generates entanglement expecting maximal values' is awkward; 'reaching' or 'attaining' would be clearer.
  2. [Throughout] Notation consistency: logarithmic negativity is denoted LN in the abstract but appears as script-LN or other variants in the text and figures; adopt a single symbol throughout.
  3. [Figure captions] Figure captions and text should explicitly state the initial states used for the two cases mentioned in the abstract so that readers can reproduce the qualitative trends.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major comment below and outline the revisions that will be made to strengthen the work.

read point-by-point responses

  1. Referee: [§2] §2 (Hamiltonian and time-fractional Schrödinger equation): the central interpretation that differences in entanglement generation and resource persistence for τ<1 arise from memory effects requires an explicit check that the chosen fractional derivative reduces to the standard iħ ∂_t |ψ⟩ = H |ψ⟩ dynamics when τ=1, with identical negativity, local quantum uncertainty, and correlated coherence curves. No such benchmark (analytic or numerical) is provided, leaving open whether the reported trends reflect the physics of the double-dot Hamiltonian or properties of the fractional solver.

    Authors: We agree that an explicit benchmark is required to support the memory-effects interpretation. Although the Caputo fractional derivative reduces to the ordinary derivative by definition when τ=1, we will add a new subsection in the revised manuscript that numerically verifies this reduction for the specific observables. We will solve the system at τ=1 with our integrator and directly overlay the LN, LQU, and CC curves against those obtained from the standard (integer-order) Schrödinger equation using an independent unitary propagator. This comparison will confirm that the curves coincide at τ=1 and that the trends for τ<1 arise from the non-local memory kernel. revision: yes

  2. Referee: [§3] §3 (Numerical results and figures): the quantitative claims (e.g., LN≈1, negativity remaining above ≈0.6) are presented without specification of the fractional-derivative definition employed, the numerical integrator, time-step convergence tests, or error bars on the plotted quantities. This omission is load-bearing for assessing the reliability of the memory-effect conclusions drawn from the τ sweeps.

    Authors: We acknowledge the need for full transparency in the numerical implementation. In the revised manuscript we will explicitly state the fractional-derivative definition (Caputo), describe the numerical integrator employed, report the time-step size used, include convergence tests (by halving the step size and verifying that the plotted quantities remain stable within a small tolerance), and add error bars or shaded uncertainty regions to the figures. These additions will allow readers to evaluate the robustness of the reported quantitative trends. revision: yes

Circularity Check

0 steps flagged

No significant circularity in numerical parameter exploration

full rationale

The paper numerically integrates the time-fractional Schrödinger equation for a fixed double-quantum-dot Hamiltonian while independently varying the free parameters τ, δ_A, δ_B and V. Entanglement negativity, local quantum uncertainty and correlated coherence are computed directly from the resulting time-dependent states for two initial conditions. No equation or step reduces by construction to the input parameters, no output quantity is fitted and then relabeled as a prediction, and no load-bearing claim rests on a self-citation or imported uniqueness theorem. The reported trends are therefore ordinary consequences of the numerical solver applied to the chosen fractional model; any question of whether the fractional operator recovers ordinary unitary evolution at τ = 1 is a separate issue of model validation, not circularity.

Axiom & Free-Parameter Ledger

3 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that a time-fractional Schrödinger equation correctly encodes memory in the double-dot Hamiltonian; no new particles or forces are introduced, but the fractional derivative itself functions as an ad-hoc modeling choice whose justification is not supplied in the abstract.

free parameters (3)
  • fractional order τ
    Varied across values to control memory strength; no explicit fitting procedure described.
  • tunneling amplitudes δ_A and δ_B
    Treated as tunable parameters whose asymmetry is explored.
  • interaction strength V
    Varied to study stabilization of coherence.
axioms (1)
  • domain assumption The time-fractional Schrödinger equation governs the unitary evolution of the coupled double quantum dot system.
    Invoked as the starting dynamical law without derivation or limit check against the standard Schrödinger equation.

pith-pipeline@v0.9.0 · 5509 in / 1458 out tokens · 42140 ms · 2026-05-08T17:49:57.393686+00:00 · methodology

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Reference graph

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