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arxiv: 2605.26223 · v1 · pith:JNODKA4Tnew · submitted 2026-05-25 · ❄️ cond-mat.str-el

Quantum Interference Corrections in Electron Hydrodynamics

Alberto Cortijo This is my paper

Pith reviewed 2026-06-29 20:24 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords electron hydrodynamicsquantum interferenceweak localizationviscosityWard identitiesCooperonchannel flowstress tensor
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The pith

Quantum interference corrections in electron fluids are forced by conservation laws into the stress sector, lowering viscous resistivity in channel flow with the opposite sign to weak localization.

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

The paper claims that hydrodynamic Ward identities tightly constrain quantum-interference corrections in an electron fluid. Charge and momentum conservation shield the m=0 and m=±1 sectors, so the leading correction appears only in the m=±2 stress sector. The resulting hydrodynamic Cooperon renormalizes stress relaxation and therefore viscosity. In channel flow the effect lowers viscous resistivity, producing a signature opposite in sign to ordinary weak localization. A reader would care because it identifies a concrete, measurable way quantum coherence can modify hydrodynamic transport without violating conservation laws.

Core claim

Quantum-interference corrections in an electron fluid are tightly constrained by hydrodynamic Ward identities: charge and momentum conservation protect the m=0,±1 sectors, so the leading correction first appears in the spin-two m=±2 stress sector. The resulting hydrodynamic Cooperon has a robust infrared structure that renormalizes stress relaxation, and hence the viscosity. In channel flow this lowers the viscous resistivity, producing a hydrodynamic interference signature with the opposite sign to ordinary weak localization.

What carries the argument

The hydrodynamic Cooperon in the m=±2 stress sector, whose infrared structure is protected by charge and momentum conservation Ward identities and which renormalizes stress relaxation time and viscosity.

If this is right

  • Viscosity receives a quantum-interference renormalization from the m=±2 Cooperon.
  • Viscous resistivity decreases in channel flow geometries.
  • The correction carries the opposite sign from conventional weak localization.
  • The m=0 and m=±1 hydrodynamic sectors remain protected from leading interference corrections.

Where Pith is reading between the lines

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

  • The same protection mechanism may suppress interference corrections in other conserved hydrodynamic modes such as heat current.
  • The effect could be searched for in graphene or other two-dimensional systems that realize electron hydrodynamics at accessible temperatures.
  • Higher-order multipole sectors beyond m=±2 may receive further interference corrections once the m=±2 channel is renormalized.

Load-bearing premise

The electron system remains inside a hydrodynamic regime in which Ward identities from charge and momentum conservation continue to protect the m=0 and m=±1 sectors while allowing a well-defined hydrodynamic Cooperon in the m=±2 sector.

What would settle it

An experiment that measures an increase (rather than a decrease) in viscous resistivity inside a narrow channel under hydrodynamic conditions where quantum interference should be present would falsify the predicted sign of the correction.

Figures

Figures reproduced from arXiv: 2605.26223 by Alberto Cortijo.

Figure 1
Figure 1. Figure 1: FIG. 1. Diffusive versus hydrodynamic interference. In [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Representative Fermi-liquid Gurzhi response. The [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
read the original abstract

We show that quantum-interference corrections in an electron fluid are tightly constrained by hydrodynamic Ward identities: charge and momentum conservation protect the $m=0,\pm1$ sectors, so the leading correction first appears in the spin-two $m=\pm2$ stress sector. The resulting hydrodynamic Cooperon has a robust infrared structure that renormalizes stress relaxation, and hence the viscosity. In channel flow this lowers the viscous resistivity, producing a hydrodynamic interference signature with the opposite sign to ordinary weak localization.

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 / 1 minor

Summary. The manuscript claims that quantum-interference corrections in an electron fluid are tightly constrained by hydrodynamic Ward identities arising from charge and momentum conservation. These identities protect the m=0, ±1 sectors, so the leading correction appears in the spin-two m=±2 stress sector. The resulting hydrodynamic Cooperon possesses a robust infrared structure that renormalizes stress relaxation and hence the viscosity; in channel flow this produces a reduction in viscous resistivity whose sign is opposite to that of ordinary weak localization.

Significance. If substantiated by the derivation, the result would supply a conservation-law-protected prediction for quantum corrections inside the hydrodynamic regime of electron fluids. The opposite-sign signature relative to weak localization offers a potentially falsifiable experimental distinction in transport measurements on clean 2D systems, and the absence of free parameters in the Ward-identity argument is a notable strength.

major comments (1)
  1. [Abstract] Abstract, first sentence: the claim that charge and momentum conservation protect the m=0, ±1 sectors while permitting a well-defined hydrodynamic Cooperon only in the m=±2 sector is load-bearing, yet the manuscript supplies no explicit statement of the hydrodynamic regime boundaries (e.g., length or temperature scales) under which the Ward identities remain operative and the Cooperon remains inside the hydrodynamic description.
minor comments (1)
  1. [Abstract] The abstract introduces the term 'hydrodynamic Cooperon' without a preceding definition or reference to its construction; a one-sentence clarification of its relation to the standard Cooperon would improve accessibility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive comment and positive assessment of the work. We address the major comment below and will incorporate a revision to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract, first sentence: the claim that charge and momentum conservation protect the m=0, ±1 sectors while permitting a well-defined hydrodynamic Cooperon only in the m=±2 sector is load-bearing, yet the manuscript supplies no explicit statement of the hydrodynamic regime boundaries (e.g., length or temperature scales) under which the Ward identities remain operative and the Cooperon remains inside the hydrodynamic description.

    Authors: We agree that an explicit statement of the hydrodynamic regime boundaries would improve clarity. The Ward identities follow directly from charge and momentum conservation and are operative throughout the hydrodynamic regime, defined by the standard scale separation l_ee ≪ l_mr, L (where l_ee is the electron-electron scattering length, l_mr the momentum-relaxation length, and L the system size), together with temperatures where quantum interference corrections remain relevant but the fluid description holds. The hydrodynamic Cooperon is constructed and its infrared structure analyzed strictly inside this regime. We will revise the abstract (and add a brief clarifying paragraph in the introduction) to state these boundaries explicitly. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The provided abstract and claims rely on standard hydrodynamic Ward identities arising from charge and momentum conservation, which are external physical principles rather than results derived or fitted within the paper itself. No equations, self-citations, or load-bearing steps are exhibited that reduce any prediction to a fitted input, self-definition, or prior author work by construction. The central claim follows directly from conservation constraints on angular momentum sectors without internal reduction to the paper's own inputs, making the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Only the abstract is available, so the ledger is necessarily incomplete and based solely on terms mentioned in the abstract.

axioms (1)
  • domain assumption Hydrodynamic Ward identities arising from charge and momentum conservation protect the m=0, ±1 sectors
    Invoked in the first sentence of the abstract to constrain where corrections can appear
invented entities (1)
  • hydrodynamic Cooperon no independent evidence
    purpose: To encode the quantum interference correction that renormalizes stress relaxation in the m=±2 sector
    Introduced in the abstract as having a robust infrared structure

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Reference graph

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