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REVIEW 2 major objections 1 minor 58 references

Current partition in a five-terminal geometry diagnoses ballistic-hydrodynamic-Ohmic crossover and extracts the two scattering rates.

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2026-06-30 23:55 UTC pith:XDXUZ5TI

load-bearing objection Five-terminal current partition is a concrete idea for mapping scattering rates, but the linearized BTE needs explicit checks against hydrodynamic limits. the 2 major comments →

arxiv 2605.03030 v3 pith:XDXUZ5TI submitted 2026-05-04 cond-mat.mes-hall cond-mat.str-el

Characterizing electronic scattering rates with transport in multiterminal devices

Jack H. Farrell , Andrew Lucas This is my paper
classification cond-mat.mes-hall cond-mat.str-el
keywords electron transportBoltzmann transport equationmultiterminal deviceshydrodynamic transportballistic transportscattering ratestomographic regimemesoscopic physics
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper establishes that a single multiterminal measurement can identify which transport regime governs electron flow in a 2D device and quantify the underlying momentum-relaxing and momentum-conserving scattering rates. A linearized Boltzmann calculation in a five-terminal layout predicts distinct patterns of how injected current divides among the drain contacts, each pattern tied to a different regime. These patterns remain usable even when the device sits in the crossover between idealized ballistic, hydrodynamic, and Ohmic limits. The same layout produces additional signatures that could separate viscous flow from tomographic flow. The approach therefore offers a route to regime diagnosis that avoids the need for spatially resolved imaging.

Core claim

Using a linearized Boltzmann model in a five-terminal geometry, current partition among the drain contacts diagnoses the ballistic-hydrodynamic-Ohmic crossover and allows extraction of momentum-relaxing and momentum-conserving scattering rates in the crossover regime. The same geometry also exhibits clear signatures of the tomographic regime, potentially allowing for a quantitative discrimination between viscous and tomographic flow in experiments.

What carries the argument

Current partition among the drain contacts in a five-terminal geometry, which maps the relative strengths of momentum-relaxing and momentum-conserving scattering onto measurable current ratios.

Load-bearing premise

The linearized Boltzmann transport equation remains quantitatively accurate for the five-terminal geometry across the ballistic-hydrodynamic-Ohmic crossover and tomographic regimes.

What would settle it

A fabricated five-terminal device whose measured current-partition ratios deviate systematically from the Boltzmann predictions once the two scattering rates are independently constrained by other means would falsify the claimed diagnostic power.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Current-partition ratios distinguish ballistic, hydrodynamic, and Ohmic regimes without spatial imaging.
  • The same ratios yield quantitative values for both scattering rates inside the crossover window.
  • Distinct partition patterns appear in the tomographic regime, separating it from ordinary viscous flow.
  • Multiterminal devices become a practical experimental alternative to imaging-based transport studies.

Where Pith is reading between the lines

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

  • The diagnostic could be ported to other multiterminal layouts once the Boltzmann solver is rerun for the new contact geometry.
  • Combining the partition measurement with a local probe of one scattering rate would over-constrain the second rate and test internal consistency.
  • The method assumes steady-state linear response; time-resolved or nonlinear extensions would require separate modeling.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 1 minor

Summary. The paper claims that current partition ratios among the drain terminals in a five-terminal multiterminal device, computed from a linearized Boltzmann transport equation, can diagnose the ballistic-hydrodynamic-Ohmic crossover, extract the momentum-relaxing and momentum-conserving scattering rates in the crossover regime, and exhibit distinct signatures of the tomographic regime, thereby providing a simpler experimental alternative to spatially resolved imaging for characterizing transport in 2D electron liquids.

Significance. If the central mapping from current partitions to scattering rates is robust, the work would offer a practical, non-imaging route to quantify scattering rates in crossover regimes, which is of clear value for experiments on clean 2D devices where hydrodynamic and tomographic effects are expected.

major comments (2)
  1. [Abstract] Abstract and main text: the central claim that the linearized BTE yields quantitative current-partition signatures across the ballistic-hydrodynamic-Ohmic and tomographic regimes rests on an unvalidated forward model; no comparison is shown to the Navier-Stokes limit (or to known analytic results for viscosity and slip length) in the five-terminal geometry, leaving the hydrodynamic accuracy of the relaxation-time treatment unverified.
  2. The extraction procedure is presented without reported error bars, convergence tests with respect to discretization or relaxation-time parameters, or sensitivity analysis, so the robustness of the claimed signatures cannot be assessed from the given information.
minor comments (1)
  1. Notation for the two scattering rates and the precise definition of the tomographic regime should be stated explicitly in the abstract or introduction for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We respond to each major comment below, indicating planned revisions where appropriate.

read point-by-point responses

  1. Referee: [Abstract] Abstract and main text: the central claim that the linearized BTE yields quantitative current-partition signatures across the ballistic-hydrodynamic-Ohmic and tomographic regimes rests on an unvalidated forward model; no comparison is shown to the Navier-Stokes limit (or to known analytic results for viscosity and slip length) in the five-terminal geometry, leaving the hydrodynamic accuracy of the relaxation-time treatment unverified.

    Authors: We agree that a direct validation against the Navier-Stokes limit in the five-terminal geometry would strengthen the presentation. The relaxation-time treatment of the linearized BTE is the standard forward model employed in this and related works on electron hydrodynamics, and it is known to recover the hydrodynamic regime when momentum-conserving scattering dominates. To address the concern explicitly, we will add a discussion of this limit, including references to known analytic results for viscosity and slip length, in the revised manuscript. revision: yes

  2. Referee: The extraction procedure is presented without reported error bars, convergence tests with respect to discretization or relaxation-time parameters, or sensitivity analysis, so the robustness of the claimed signatures cannot be assessed from the given information.

    Authors: The referee is correct that these quantitative checks are not reported in the current version. We will incorporate error bars on the extracted rates, convergence tests with respect to discretization and relaxation-time parameters, and a sensitivity analysis in the revised manuscript to allow assessment of robustness. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper solves the linearized Boltzmann transport equation numerically in a fixed five-terminal geometry, treating momentum-relaxing and momentum-conserving scattering rates as independent input parameters. The outputs are the resulting current-partition ratios across regimes; these ratios are then proposed as experimental diagnostics. No equation reduces a claimed prediction to a fitted quantity by construction, no uniqueness theorem is imported from self-citation, and no ansatz is smuggled via prior work. The derivation chain is a standard forward transport calculation whose central results remain independent of the target observables.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on the applicability of the linearized Boltzmann equation to the multiterminal geometry and on the assumption that scattering rates can be treated as spatially uniform parameters that are extracted by fitting the model to measured currents. No new particles or forces are postulated.

free parameters (2)
  • momentum-relaxing scattering rate
    Treated as an adjustable input to the Boltzmann model whose value is inferred from measured current partition.
  • momentum-conserving scattering rate
    Treated as a second adjustable input whose value is likewise inferred from the same data.
axioms (1)
  • domain assumption Linearized Boltzmann transport equation accurately describes electron flow in the five-terminal geometry for the regimes of interest
    The entire set of signatures is obtained by solving this equation; the abstract states the authors use this model.

pith-pipeline@v0.9.1-grok · 5669 in / 1462 out tokens · 30640 ms · 2026-06-30T23:55:20.997895+00:00 · methodology

0 comments
read the original abstract

Strongly interacting electrons in clean two-dimensional devices are theorized to exhibit many distinct transport regimes, such as ballistic, hydrodynamic, or diffusive. Realistic samples often lie in crossover regimes between these idealized limits. We show how a single experiment on a multiterminal device can distinguish these regimes and constrain the relevant scattering rates without space-resolved imaging. Using a linearized Boltzmann model in a five-terminal geometry, we find that current partition among the drain contacts diagnoses the ballistic-hydrodynamic-Ohmic crossover and allows extraction of momentum-relaxing and momentum-conserving scattering rates in the crossover regime. The same geometry also exhibits clear signatures of the tomographic regime, potentially allowing for a quantitative discrimination between viscous and tomographic flow in experiments. Our results demonstrate that multiterminal devices are a simpler experimental route to characterize transport regimes in electron liquids, relative to space-resolved imaging experiments.

Figures

Figures reproduced from arXiv: 2605.03030 by Andrew Lucas, Jack H. Farrell.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic of the five-terminal ‘fan’ geometry stud view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Current partition in the five-terminal fan geometry as a function of momentum-relaxing and momentum-conserving view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Emergence of tomographic physics. We set view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Nonlocal resistance in the fan geometry as a function of momentum-relaxing and momentum-conserving scattering. In view at source ↗

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