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arxiv: 2509.18255 · v2 · pith:KW2YTN2Dnew · submitted 2025-09-22 · ✦ hep-th · cond-mat.str-el

Bootstrapping transport in the Drude-Kadanoff-Martin model

Subham Dutta Chowdhury , Sean A. Hartnoll , Aditya Hebbar , Ruby Khondaker This is my paper

Pith reviewed 2026-05-18 14:16 UTC · model grok-4.3

classification ✦ hep-th cond-mat.str-el
keywords charge transportDrude modelKadanoff-MartinMott-Ioffe-Regel boundGreen's function boundslattice modelsmean free pathdiffusivity
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The pith

The Drude-Kadanoff-Martin model cannot hold at microscopic scales in lattice systems and produces a lower bound on collective mean free path that enforces a Mott-Ioffe-Regel limit.

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

The paper derives constraints on the parameters of the Drude-Kadanoff-Martin model for charge transport, which is parameterized by current relaxation time τ, diffusivity D, and compressibility χ. Using upper bounds on the retarded Green's function for charge density, it demonstrates that this effective model is inconsistent with the exponential suppression of spectral weight at the highest frequencies present in any lattice model with local and bounded interactions. Assuming the model captures the low-energy dynamics, the analysis yields a lower bound on the collective mean free path ℓ defined as the square root of τ times D, which directly implies that conventional Drude peaks are impossible when this length scale is much smaller than the underlying lattice spacing.

Core claim

Under the assumption that the low energy dynamics is captured by the Drude-Kadanoff-Martin model, we obtain a lower bound on the collective mean free path ℓ ≡ √(τ D). This bound is shown to imply a version of the Mott-Ioffe-Regel bound: systems with ℓ much shorter than the lattice length scale cannot have conventional Drude peaks. The Drude-Kadanoff-Martin model cannot pertain at microscopic energy scales because it is inconsistent with the exponential suppression of spectral weight at the highest frequencies in a lattice model.

What carries the argument

Upper bounds on the retarded Green's function for the charge density, which convert into constraints on the Drude-Kadanoff-Martin parameters τ, D and χ in lattice models with local and bounded interactions.

If this is right

  • The Drude-Kadanoff-Martin model is ruled out at microscopic energy scales due to mismatch with high-frequency spectral weight suppression.
  • A lower bound holds on the collective mean free path ℓ ≡ √(τ D) whenever the model applies at low energies.
  • Conventional Drude peaks are forbidden when ℓ is much smaller than the lattice length scale, giving a version of the Mott-Ioffe-Regel bound.

Where Pith is reading between the lines

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

  • The Green's function bounds could be applied to other low-energy transport descriptions to obtain analogous microscopic limits.
  • Numerical studies of interacting lattice models could directly test whether the extracted lower bound on ℓ is saturated.
  • Experimental transport data in materials near the Mott-Ioffe-Regel limit might be reinterpreted through this effective-model constraint.

Load-bearing premise

The low energy dynamics of the underlying lattice model with local and bounded interactions is captured by the Drude-Kadanoff-Martin model.

What would settle it

A material or numerical simulation exhibiting a conventional Drude peak while having collective mean free path much shorter than the lattice spacing would contradict the derived bound.

Figures

Figures reproduced from arXiv: 2509.18255 by Aditya Hebbar, Ruby Khondaker, Sean A. Hartnoll, Subham Dutta Chowdhury.

Figure 1
Figure 1. Figure 1: The integrated spectral weight (solid curve) must lie within the shaded region, allowed [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The two solid curves are the integrated spectral weight ( [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Schematic evolution of the collective mean free path [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
read the original abstract

The Drude-Kadanoff-Martin model is a simple low energy and long wavelength description of charge transport, parameterised by the current relaxation timescale $\tau$, charge diffusivity $D$ and charge compressibility $\chi$. We obtain sharp constraints on these parameters in terms of the microscopic energy and length scales of any underlying lattice model with local and bounded interactions. Our primary tools are upper bounds on the retarded Green's function for the charge density in such a setting. We first note that the Drude-Kadanoff-Martin model cannot pertain at microscopic energy scales because it is inconsistent with the exponential suppression of spectral weight at the highest frequencies in a lattice model. Secondly, under the assumption that the low energy dynamics is captured by the model, we obtain a lower bound on the collective mean free path $\ell \equiv \sqrt{\tau D}$. This bound is shown to imply a version of the Mott-Ioffe-Regel bound: systems with $\ell$ much shorter than the lattice length scale cannot have conventional Drude peaks.

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

1 major / 3 minor

Summary. The paper studies the Drude-Kadanoff-Martin (DKM) effective model for charge transport, parameterized by relaxation time τ, diffusivity D, and compressibility χ. It derives sharp upper bounds on the retarded charge-density Green's function from locality and bounded interactions in an underlying lattice model. These bounds are used first to show that the DKM form is inconsistent with the exponential decay of spectral weight at high frequencies, and second (under the assumption that DKM captures the low-energy regime) to obtain a lower bound on the collective mean free path ℓ ≡ √(τ D). The bound is shown to imply a version of the Mott-Ioffe-Regel criterion: conventional Drude peaks cannot exist when ℓ is much smaller than the lattice spacing.

Significance. If the central derivation holds, the work supplies a model-independent, locality-based constraint on effective transport parameters that directly limits the applicability of the DKM description. This strengthens the theoretical foundation for the Mott-Ioffe-Regel bound in lattice systems and provides a concrete criterion for when hydrodynamic or Drude-like peaks are admissible. The use of analytic properties of retarded Green's functions and exponential high-frequency suppression is a strength; the result is falsifiable once the low-energy assumption is tested in a concrete microscopic model.

major comments (1)
  1. §3.2, around Eq. (12): the conversion from the Green's-function upper bound to the inequality ℓ ≳ a (lattice spacing) appears to rely on a specific choice of the frequency window in which the DKM form is assumed to hold. Clarify how the window is chosen without circularity and whether the bound remains uniform when the window is varied within the regime where the exponential suppression is still negligible.
minor comments (3)
  1. Abstract and §1: the phrase 'sharp constraints' is used; replace with 'rigorous upper bounds' or quantify the sharpness (e.g., by the prefactor in the ℓ bound) to avoid overstatement.
  2. Figure 1: the caption should explicitly state the values of τ, D, χ used in the plotted DKM spectral function and the lattice scale a against which ℓ is compared.
  3. §4: add a short remark on whether the same Green's-function bounds can be applied to other effective models (e.g., with momentum relaxation) or whether the argument is specific to the DKM form.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment and the helpful request for clarification on the frequency window. We address the point below and have revised the manuscript accordingly.

read point-by-point responses

  1. Referee: [—] §3.2, around Eq. (12): the conversion from the Green's-function upper bound to the inequality ℓ ≳ a (lattice spacing) appears to rely on a specific choice of the frequency window in which the DKM form is assumed to hold. Clarify how the window is chosen without circularity and whether the bound remains uniform when the window is varied within the regime where the exponential suppression is still negligible.

    Authors: We thank the referee for highlighting this point. The frequency window is fixed by the microscopic scales of the lattice model: it extends up to a cutoff ω_max ≪ Λ, where Λ is set by the bandwidth or interaction strength at which the exponential suppression of spectral weight becomes appreciable. This cutoff is determined entirely from the underlying lattice Hamiltonian and is independent of the transport parameters τ and D, eliminating circularity. In the revised manuscript we have added an explicit statement of this choice together with a short argument showing that the resulting lower bound ℓ ≳ a is uniform for any window whose upper edge lies in the regime where the exponential suppression remains negligible (i.e., for any fixed fraction of Λ). The Green's-function bound itself supplies a window-independent constraint once the DKM form is assumed to hold throughout that interval, so the numerical prefactor in ℓ ≳ a changes only by O(1) factors under such variations. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The derivation begins from general properties of retarded Green's functions (analyticity in the upper half-plane, locality of interactions, and boundedness on a lattice) that are independent of the Drude-Kadanoff-Martin parameters. These properties yield upper bounds on the charge-density correlator at high frequencies and short distances. Under the explicit assumption that the low-energy sector is described by the DKM form, the bounds are converted into a lower limit on ℓ ≡ √(τ D). No equation equates the target bound to a fitted quantity by construction, no load-bearing step reduces to a self-citation whose content is itself unverified, and the central claim remains conditional on the stated effective-theory premise rather than being smuggled in by definition or renaming.

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 0 invented entities

The central claim rests on analytic properties of retarded Green's functions and the assumption that the effective model applies at low energies. No new particles or forces are introduced. The parameters τ, D, χ are inputs to the effective model rather than fitted outputs of this derivation.

axioms (3)
  • standard math Retarded Green's functions for charge density satisfy standard analyticity and causality properties in local quantum systems.
    Invoked to obtain upper bounds on the spectral weight at high frequencies.
  • domain assumption The underlying model has local and bounded interactions on a lattice.
    Used to guarantee exponential suppression of spectral weight at microscopic energy scales.
  • domain assumption Low-energy dynamics is captured by the Drude-Kadanoff-Martin model.
    Required to translate Green's function bounds into constraints on τ and D.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Bootstrapping Euclidean Two-point Correlators

    hep-th 2025-11 unverdicted novelty 7.0

    A semidefinite programming bootstrap is formulated for Euclidean two-point correlators in quantum mechanics, yielding rigorous bounds and low-lying spectrum extraction in the ungauged one-matrix model.

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