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arxiv: 2605.22966 · v1 · pith:CR3UWASTnew · submitted 2026-05-21 · 🪐 quant-ph · cond-mat.quant-gas· cond-mat.stat-mech· cond-mat.str-el

Phase-dependent role of dissipation across the Aubry-Andr\'e-Harper transition

Gerardo Su\'arez , Baptiste Debecker , Francesco Cosco , Francesco Plastina , Fran\c{c}ois Damanet , Nicola Lo Gullo , Francesco Perciavalle This is my paper

Pith reviewed 2026-05-25 05:36 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.quant-gascond-mat.stat-mechcond-mat.str-el
keywords Aubry-André-Harper modelnon-Markovian dissipationlocalization transitionquantum transportopen quantum systemsAubry-André-Harper transition
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The pith

Bath memory reshapes transport in the extended phase of the Aubry-André-Harper model but only renormalizes timescales in the localized phase

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

The paper shows that non-Markovian dissipation affects single-particle transport differently on either side of the Aubry-André-Harper localization transition. In the extended phase, finite bath correlation time changes the form of the dynamical generator itself and produces transport that cannot be recovered by rescaling time. In the localized phase, the bath induces motion between otherwise static states while memory effects act mainly as a rescaling of the relevant timescales. The work therefore presents localization as a mechanism that filters non-Markovian signatures, preserving their qualitative impact only when states are delocalized.

Core claim

For a single particle initialized at the chain center, bath memory qualitatively reshapes the dynamical generator in the extended phase, producing transport patterns that cannot be reduced to a simple rescaling of time; by contrast, in the localized phase the bath activates motion between localized states and bath memory mainly renormalizes dynamical timescales, so that localization functions as a simple filter of non-Markovian effects.

What carries the argument

The Aubry-André-Harper localization transition acting as a phase-dependent filter on non-Markovian bath memory in the open-system dynamical generator

Load-bearing premise

The chosen non-Markovian bath model with finite correlation decay time together with a single-particle initial condition at the chain center are sufficient to expose the essential difference in how memory affects the two phases.

What would settle it

Numerical or experimental comparison, in the extended phase, between the full non-Markovian evolution and a time-rescaled Markovian counterpart, checking whether the spatial transport profiles coincide or deviate qualitatively.

Figures

Figures reproduced from arXiv: 2605.22966 by Baptiste Debecker, Fran\c{c}ois Damanet, Francesco Cosco, Francesco Perciavalle, Francesco Plastina, Gerardo Su\'arez, Nicola Lo Gullo.

Figure 1
Figure 1. Figure 1: Cartoon of the setup: a fermionic quasiperiodic [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Dynamics of a single particle in a dissipative AAH chain across the extended–localized transition. Panels (a) and [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Features of the HEOM spectrum across the [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

We study transport across the Aubry-Andr\'e-Harper localization transition in the presence of non-Markovian dissipation. For a single particle initially at the center of the chain, we show that bath memory (i.e., finite decay time of bath correlations) plays distinct roles in the two phases. In the extended phase, bath memory qualitatively reshapes the dynamical generator, thereby producing transport patterns that cannot be reduced to a simple rescaling of time. By contrast, in the localized phase, the bath activates motion between localized states and bath memory mainly renormalizes the dynamical timescales. Our results identify localization as a simple filter of non-Markovian effects: memory restructures transport in the extended regime, but survives mainly as a timescale renormalization in the deeply localized regime.

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 / 2 minor

Summary. The manuscript examines transport of a single particle initially at the chain center in the Aubry-André-Harper model subject to non-Markovian dissipation. It reports that bath memory (finite correlation decay time) plays qualitatively distinct roles across the localization transition: in the extended phase it reshapes the dynamical generator to produce transport patterns irreducible to time rescaling, whereas in the localized phase the bath enables inter-site motion and memory effects act primarily as timescale renormalization. Localization is thereby positioned as a filter that converts non-Markovian structure into simple renormalization only in the deeply localized regime.

Significance. If the reported distinction is robust, the work supplies a concrete illustration of how localization can selectively filter non-Markovian bath effects, separating qualitative dynamical restructuring from mere rate renormalization. This supplies a useful diagnostic for open quantum dynamics in disordered systems and may inform studies of environment-assisted transport. No machine-checked proofs or parameter-free derivations are present; the result rests on numerical evolution under a specific exponential memory kernel and central initial condition.

major comments (2)
  1. [extended-phase results] § on extended-phase transport (likely the main results figure comparing different memory times): the central assertion that memory 'qualitatively reshapes the dynamical generator' such that transport 'cannot be reduced to a simple rescaling of time' is load-bearing yet unsupported by an explicit test. No attempt is shown to collapse the extended-phase curves onto a single master curve via a single fitted time-rescaling factor (matched e.g. to short-time or long-time asymptotics). Without this check the claimed qualitative distinction from the localized-phase renormalization behavior remains unanchored.
  2. [Methods] Methods section defining the non-Markovian generator and the single-particle central initial condition: the phase-dependent filtering conclusion is demonstrated only for this narrow setup (exponential memory kernel, particle starting at chain center). No additional initial conditions or memory kernels are reported to test whether the reported distinction is generic or specific to the chosen protocol.
minor comments (2)
  1. [Methods] Notation for the memory kernel and the effective dynamical generator should be introduced with an explicit equation number in the methods section to allow direct comparison with the rescaling test requested above.
  2. [Figures] Figure captions for the transport data should state the precise observable (e.g., mean-squared displacement or participation ratio) and the range of memory times shown.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive suggestions. We address the two major comments below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [extended-phase results] § on extended-phase transport (likely the main results figure comparing different memory times): the central assertion that memory 'qualitatively reshapes the dynamical generator' such that transport 'cannot be reduced to a simple rescaling of time' is load-bearing yet unsupported by an explicit test. No attempt is shown to collapse the extended-phase curves onto a single master curve via a single fitted time-rescaling factor (matched e.g. to short-time or long-time asymptotics). Without this check the claimed qualitative distinction from the localized-phase renormalization behavior remains unanchored.

    Authors: The referee is correct that an explicit collapse test was not included. In the revised manuscript we will add a supplementary analysis that attempts to rescale the extended-phase transport curves for different memory times onto a single master curve using a fitted factor (anchored to both short-time ballistic regime and long-time asymptotics). We anticipate that no single factor will achieve collapse, thereby anchoring the claim that memory effects cannot be reduced to timescale renormalization in the extended phase. This will be presented alongside the existing data. revision: yes

  2. Referee: [Methods] Methods section defining the non-Markovian generator and the single-particle central initial condition: the phase-dependent filtering conclusion is demonstrated only for this narrow setup (exponential memory kernel, particle starting at chain center). No additional initial conditions or memory kernels are reported to test whether the reported distinction is generic or specific to the chosen protocol.

    Authors: We chose the central initial condition because it directly measures unbiased transport across the full chain and the exponential kernel because it is the minimal model with a single tunable memory time. The manuscript already notes that the distinction is demonstrated for this protocol. We will expand the discussion section to explicitly state the scope of the present numerics and to indicate that testing other kernels and initial conditions is a natural direction for follow-up work. No new simulations will be added in this revision. revision: partial

Circularity Check

0 steps flagged

No circularity: central phase-dependent distinction derived from model dynamics, not reduced to input definitions or self-citations

full rationale

The abstract and provided text present the core claim—that bath memory qualitatively reshapes transport in the extended phase (cannot be reduced to time rescaling) while only renormalizing timescales in the localized phase—as a direct consequence of studying the non-Markovian model on the AAH chain with central initial condition. No equations, parameters, or results are shown to be fitted to subsets and then relabeled as predictions; no self-citations are invoked as load-bearing uniqueness theorems; the distinction is not defined in terms of itself. The derivation chain therefore remains self-contained against external benchmarks (numerical evolution of the open-system dynamics), consistent with a normal non-circular finding.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no information on free parameters, background axioms, or new entities; ledger left empty.

pith-pipeline@v0.9.0 · 5701 in / 1053 out tokens · 19490 ms · 2026-05-25T05:36:47.452097+00:00 · methodology

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Constants.lean phi_golden_ratio echoes
    ?
    echoes

    ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

    beta = (sqrt(5)-1)/2 is the inverse golden ratio... Vj = h cos(2 pi beta j + phi)

  • IndisputableMonolith/Cost/FunctionalEquation.lean Jcost_pos_of_ne_one echoes
    ?
    echoes

    ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

    in the localized phase... bath memory mainly renormalizes the dynamical timescales... time rescaled as t-tilde = Gamma_eff t

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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