arxiv: 2605.06701 · v1 · submitted 2026-05-05 · ❄️ cond-mat.mes-hall · cond-mat.dis-nn· cond-mat.quant-gas

Recognition: no theorem link

Diffusive transport from spatially correlated random phase kicks

Pei Wang

Authors on Pith no claims yet

Pith reviewed 2026-05-11 01:17 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.dis-nncond-mat.quant-gas

keywords diffusive transportrandom phase kicksspatial correlationswave-packet spreadingquantum latticedephasingdriven systemscold atoms

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The pith

Spatially correlated random phase kicks on a lattice suppress ballistic spreading and produce diffusion whose coefficient is given by an explicit formula in the correlation length.

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

The paper examines a wave packet on a one-dimensional lattice that receives periodic random phase kicks whose values are correlated over a controllable spatial distance. It demonstrates that these kicks eliminate the usual ballistic expansion and replace it with ordinary diffusion at long times. By shifting to a momentum-space description, the authors obtain a closed-form expression for the diffusion constant that depends only on the correlation length of the kicks. The formula matches direct numerical simulations of the wave-packet evolution. The result supplies a simple, testable rule for how controlled dephasing can regulate quantum transport in periodically driven systems.

Core claim

We study the dynamics of a single-particle wave packet on a one-dimensional lattice subject to periodic random phase kicks with finite spatial correlation length. This stroboscopic setting provides a controllable model of dephasing in driven quantum systems. Using a momentum-space formulation, we show that the evolution is governed by an accumulated phase whose structure determines the spreading of the wave packet. We find that the phase kicks strongly suppress ballistic transport and induce diffusion at long times. We derive an explicit analytical expression for the diffusion coefficient as a function of the correlation length, in excellent agreement with numerical simulations.

What carries the argument

The accumulated phase in the momentum-space stroboscopic map, whose spatial correlations set the long-time spreading rate of the wave packet.

If this is right

Ballistic transport is replaced by diffusion once the kicks are present.
The diffusion coefficient is an explicit, monotonic function of the kick correlation length.
The same phase-kick mechanism supplies a quantitative prediction for transport in any periodically driven lattice system.
Cold-atom realizations can directly test the predicted dependence on correlation length.

Where Pith is reading between the lines

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

The same accumulated-phase construction may be used to analyze dephasing in higher-dimensional or multi-particle driven systems.
Tuning the correlation length offers an experimental knob for switching between ballistic and diffusive regimes without changing kick strength.
The analytical route could be extended to non-periodic or non-random kick sequences that still possess finite spatial correlations.

Load-bearing premise

The entire dynamics reduces to the structure of an accumulated phase that is applied stroboscopically and whose correlations alone fix the asymptotic spreading.

What would settle it

Numerical or experimental data in which the measured long-time diffusion coefficient deviates systematically from the closed-form expression when the spatial correlation length of the kicks is varied.

Figures

Figures reproduced from arXiv: 2605.06701 by Pei Wang.

**Figure 2.** Figure 2: FIG. 2. Squared width of the wave packet, [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Di [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

read the original abstract

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.

Desk Editor's Note private letter to a colleague

The paper derives a closed-form diffusion constant from the spatial correlation length of periodic random phase kicks on a 1D lattice, with claimed numerical agreement.

read the letter

The core result here is a new analytical expression for the long-time diffusion coefficient that depends directly on the correlation length of the phase kicks. The momentum-space formulation ties the accumulated phase structure to the suppression of ballistic spreading, turning it into diffusion in a controllable way. That link is the fresh piece, and it looks like a clean derivation rather than a rehash of existing dephasing models. The stroboscopic setup makes the numerics straightforward to run and compare, which is a practical strength for this kind of driven-system work. It gives a testable prediction for how noise correlations control transport, useful in cold-atom contexts where you can engineer the kicks. The model stays simple enough that the mechanism is easy to follow without extra machinery. On the soft side, the abstract states excellent agreement but does not include the derivation steps, error bars, or details on averaging and system sizes, so the robustness is hard to judge from what's visible. The result is tied to this specific periodic-kick protocol, which may limit how far it generalizes without further checks. This is aimed at people working on quantum transport in lattices or open driven systems who need an analytically tractable dephasing model. A reader already thinking about noise correlations would find the formula worth looking at. It deserves a serious referee to verify the algebra and the numerics. I would send it for review rather than desk-reject.

Referee Report

0 major / 3 minor

Summary. The manuscript studies the dynamics of a single-particle wave packet on a one-dimensional lattice subject to periodic random phase kicks with finite spatial correlation length. Using a momentum-space formulation, it shows that the evolution is governed by an accumulated phase that determines the spreading of the wave packet. The phase kicks suppress ballistic transport and induce diffusion at long times. An explicit analytical expression for the diffusion coefficient is derived as a function of the correlation length, reported to be in excellent agreement with numerical simulations. Possible experimental realizations in cold-atom platforms are discussed.

Significance. If the central derivation holds, the work supplies a controllable, analytically tractable model of dephasing in driven quantum systems, yielding an explicit, parameter-free formula for the diffusion coefficient together with direct numerical confirmation. This constitutes a quantitatively testable prediction for transport in periodically driven lattices and could guide experiments in cold-atom platforms.

minor comments (3)

Abstract: the phrase 'excellent numerical agreement' would be strengthened by a brief statement of the correlation-length range, system sizes, and time scales over which the comparison was performed.
The momentum-space formulation section would benefit from an explicit statement of the stroboscopic map and the definition of the accumulated phase before the diffusion-coefficient derivation.
Discussion of experimental realizations: quantitative estimates of achievable correlation lengths and kick strengths in cold-atom setups would make the proposed test more concrete.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading and positive evaluation of our manuscript. The referee's summary accurately captures the central results: the momentum-space formulation showing that accumulated phases from spatially correlated kicks suppress ballistic spreading and induce diffusion, together with the explicit analytical formula for the diffusion coefficient and its numerical confirmation. We are pleased that the work is viewed as supplying a controllable, analytically tractable model with quantitatively testable predictions for cold-atom experiments. No specific major comments were raised in the report, so we address the recommendation for minor revision below by noting that we will incorporate any editorial clarifications requested by the editor.

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper derives an explicit analytical expression for the diffusion coefficient directly from the structure of the accumulated phase in the momentum-space stroboscopic formulation, with the correlation length treated as an independent controllable parameter. This is validated against separate numerical simulations rather than fitted to them. No self-definitional steps, fitted inputs renamed as predictions, or load-bearing self-citations appear in the provided abstract or description; the central result is presented as a first-principles consequence of the phase-kick model and remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete. The model rests on standard single-particle quantum mechanics on a lattice plus the assumption that kicks are applied stroboscopically and can be represented by an accumulated phase in momentum space.

axioms (2)

domain assumption Single-particle wave packet on a one-dimensional lattice subject to periodic random phase kicks with finite spatial correlation length
Stated directly as the system under study in the abstract.
domain assumption Evolution is governed by an accumulated phase whose structure determines the spreading
Central modeling step announced in the abstract.

pith-pipeline@v0.9.0 · 5424 in / 1481 out tokens · 62110 ms · 2026-05-11T01:17:45.230417+00:00 · methodology

discussion (0)

Reference graph

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