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arxiv: 2606.30521 · v1 · pith:IBOTXT4Fnew · submitted 2026-06-29 · ⚛️ nucl-th · astro-ph.HE· cond-mat.supr-con

Nonequilibrium Andreev transport at the QGP-2SC interface

Tingyu Zhang , Honoka Hoshino , Hiroyuki Tajima , Motoi Tachibana , Mariusz Sadzikowski This is my paper

Pith reviewed 2026-06-30 03:16 UTC · model grok-4.3

classification ⚛️ nucl-th astro-ph.HEcond-mat.supr-con
keywords Andreev reflectionquark-gluon plasmacolor superconductivitynonequilibrium transporttunneling currentcompact starsSchwinger-Keldysh2SC phase
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The pith

Andreev reflection occurs at fourth order in tunneling strength at the QGP-2SC interface, converting an incident quark to a reflected hole while injecting a Cooper pair.

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

The paper establishes that nonequilibrium Andreev reflection arises at the interface between quark-gluon plasma and two-flavor color superconducting quark matter when a chemical-potential bias drives tunneling. Using the Schwinger-Keldysh framework with a relativistic tunneling model, the work calculates the momentum-resolved current and isolates the reflection process at fourth order in tunneling strength. This produces an incident quark converting to a reflected hole accompanied by Cooper-pair injection into the condensate. The effect strengthens when the bias matches the gap size and weakens above the gap, reproducing the pattern seen in ordinary superconductors. The formulation supplies a field-theoretic route to transport across dense-matter boundaries that appear in compact-star interiors.

Core claim

Based on the Schwinger-Keldysh framework and a relativistic tunneling model, the momentum-resolved tunneling current generated by a chemical-potential bias shows that the Andreev reflection appears at the fourth order of the tunneling strength, in which an incident quark in QGP is converted into a reflected hole, while a Cooper pair is injected into the 2SC condensate. The Andreev reflection is enhanced when the bias becomes comparable to the gap and is suppressed in the supergap region.

What carries the argument

The fourth-order Andreev reflection process within the relativistic tunneling model, which maps an incident quark to a reflected hole while adding a Cooper pair to the 2SC condensate.

If this is right

  • The tunneling current is momentum-resolved and set by the size of the chemical-potential bias.
  • Andreev reflection strengthens when the bias reaches the magnitude of the superconducting gap and weakens in the supergap regime.
  • The same bias-driven mechanism supplies a field-theoretic description of transport across QGP-2SC boundaries.
  • The process reproduces the bias dependence familiar from conventional superconducting junctions.

Where Pith is reading between the lines

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

  • The same fourth-order channel could be inserted into hydrodynamic simulations of quark-matter regions inside neutron stars to track charge and flavor transport during mergers.
  • Extensions that add magnetic fields or color-magnetic fluxes at the interface would test whether the reflection survives under realistic stellar conditions.
  • The formulation opens a route to compute nonequilibrium conductivities that could later be compared with cooling curves or gravitational-wave signals from compact objects.

Load-bearing premise

The Schwinger-Keldysh framework combined with the relativistic tunneling model captures the essential interface dynamics without requiring additional strong-interaction corrections or explicit treatment of other phases.

What would settle it

A calculation that retains higher-order strong-interaction corrections and finds the Andreev signature appearing at lower than fourth order or disappearing entirely would falsify the central claim.

Figures

Figures reproduced from arXiv: 2606.30521 by Hiroyuki Tajima, Honoka Hoshino, Mariusz Sadzikowski, Motoi Tachibana, Tingyu Zhang.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: shows the k-dependence of Iint and IA, where we take ∆µ/ϵF = |∆|/ϵF = 0.2. The peaks in panels (a) and (b) come from resonances between the QGP spectral function and the anomalous 2SC spectral branches. Ac￾cording to form of the Green’s functions, we know that the QGP spectral function peaks at ω−∆µ+µQGP−k ≃ 0 and the 2SC anomalous spectral function peaks at (a) (b) FIG. 4. Total anomalous tunneling curren… view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
read the original abstract

We discuss a nonequilibrium Andreev reflection at an interface between quark-gluon plasma (QGP) and two-flavor color superconducting (2SC) quark matter. Based on the Schwinger-Keldysh framework and a relativistic tunneling model, we evaluate the momentum-resolved tunneling current generated by a chemical-potential bias between the QGP and 2SC phases. We find that the Andreev reflection appears as at the fourth order of the tunneling strength, in which an incident quark in QGP is converted into a reflected hole, while a Cooper pair is injected into the 2SC condensate. We show that the Andreev reflection is enhanced when the bias becomes comparable to the gap and is suppressed in the supergap region, which is similar to that in superconducting materials. The present formulation provides a field-theoretical pathway to strongly-correlated transport across dense-matter interfaces relevant to nonequilibrium dynamics in compact stars.

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 / 1 minor

Summary. The paper claims that nonequilibrium Andreev reflection occurs at the QGP-2SC interface, appearing at fourth order in the tunneling strength within the Schwinger-Keldysh formalism combined with a relativistic tunneling Hamiltonian. An incident quark from the QGP is converted to a reflected hole while a Cooper pair is injected into the 2SC condensate; the process is enhanced for biases comparable to the gap and suppressed in the supergap regime, analogous to conventional superconductors. The formulation is positioned as a field-theoretic route to transport across dense-matter interfaces relevant to compact-star dynamics.

Significance. If the fourth-order identification and bias dependence survive scrutiny, the work supplies a concrete perturbative pathway linking relativistic transport calculations to Andreev processes in color-superconducting matter, potentially informing nonequilibrium modeling of neutron-star interfaces. The absence of free parameters in the order-counting argument and the explicit momentum-resolved current would constitute a technical strength.

major comments (2)
  1. [Abstract / method description] The central identification of Andreev reflection at precisely fourth order in the tunneling amplitude rests on the assumption that the relativistic tunneling Hamiltonian plus Schwinger-Keldysh contour captures the leading interface process without strong-interaction corrections (e.g., gluon exchange) entering at the same or lower order. No explicit check against such corrections is described in the abstract or method outline; if those channels contribute at O(t^4) or below, the reported order counting would not hold.
  2. [Abstract] The bias dependence (enhancement near the gap, suppression in the supergap region) is stated to mirror conventional superconductors, yet the manuscript supplies no derivation steps, error estimates, or numerical checks in the abstract; the full calculation must demonstrate that this dependence survives the relativistic kinematics and color structure of the 2SC phase.
minor comments (1)
  1. Notation for the tunneling amplitude and the precise definition of the chemical-potential bias should be introduced with an equation number in the main text to allow direct comparison with the fourth-order diagrams.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment below and indicate planned revisions.

read point-by-point responses

  1. Referee: [Abstract / method description] The central identification of Andreev reflection at precisely fourth order in the tunneling amplitude rests on the assumption that the relativistic tunneling Hamiltonian plus Schwinger-Keldysh contour captures the leading interface process without strong-interaction corrections (e.g., gluon exchange) entering at the same or lower order. No explicit check against such corrections is described in the abstract or method outline; if those channels contribute at O(t^4) or below, the reported order counting would not hold.

    Authors: Our model treats the QGP and 2SC phases as separate bulk systems whose strong interactions are already encoded in the respective propagators and gap structure within the Schwinger-Keldysh formalism. The interface is introduced perturbatively via the relativistic tunneling Hamiltonian, which is the standard effective description for transport across such interfaces. Processes involving gluon exchange across the interface lie outside this tunneling approximation and are not captured at leading order in the tunneling amplitude. We agree that an explicit discussion of this separation of scales is missing from the method outline. We will add a clarifying paragraph in the methods section explaining why gluon-mediated corrections across the interface do not enter at O(t^4) or lower within the adopted framework. revision: yes

  2. Referee: [Abstract] The bias dependence (enhancement near the gap, suppression in the supergap region) is stated to mirror conventional superconductors, yet the manuscript supplies no derivation steps, error estimates, or numerical checks in the abstract; the full calculation must demonstrate that this dependence survives the relativistic kinematics and color structure of the 2SC phase.

    Authors: The abstract provides a concise summary of the results. The explicit momentum-resolved current calculation, which incorporates the relativistic dispersion relations, the color-flavor locked structure of the 2SC gap matrix, and the resulting phase-space factors, is carried out in the body of the paper. There the enhancement for biases comparable to the gap (arising from the opening of Andreev channels) and the suppression in the supergap regime are demonstrated analytically and numerically. We will revise the abstract to state that this bias dependence has been verified by the full relativistic computation, thereby making the connection clearer without embedding derivation steps in the abstract itself. revision: partial

Circularity Check

0 steps flagged

No circularity: derivation rests on external frameworks without self-referential reduction

full rationale

The abstract presents the fourth-order Andreev reflection as a computed outcome from the Schwinger-Keldysh formalism combined with a relativistic tunneling Hamiltonian under chemical-potential bias. No equations, fitted parameters, or self-citations appear in the provided text that would make the reported order or process equivalent to the inputs by construction. The method is treated as an independent calculational tool whose results (order counting, bias dependence) are derived rather than presupposed. This is the most common honest outcome when no load-bearing self-definition or renamed fit is exhibited.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Based on abstract only. The central claim rests on the applicability of the Schwinger-Keldysh formalism and the relativistic tunneling model to the QGP-2SC interface.

axioms (2)
  • standard math Schwinger-Keldysh framework for nonequilibrium quantum systems
    Used to evaluate the momentum-resolved tunneling current generated by chemical-potential bias.
  • domain assumption Relativistic tunneling model for the interface
    Basis for computing the current and identifying the order of Andreev reflection.

pith-pipeline@v0.9.1-grok · 5711 in / 1296 out tokens · 58196 ms · 2026-06-30T03:16:47.899280+00:00 · methodology

discussion (0)

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Reference graph

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