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arxiv: 2605.00679 · v1 · submitted 2026-05-01 · ❄️ cond-mat.quant-gas · cond-mat.mes-hall

Recognition: unknown

Entropy transport through a superfluid quantum point contact: A Keldysh field-theory approach

C.J. Bolech, Davide Bertolusso, Thierry Giamarchi

Pith reviewed 2026-05-09 14:34 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas cond-mat.mes-hall
keywords entropy transportquantum point contactsuperfluid Fermi gasKeldysh formalismBCS mean-fieldballistic junctionAndreev reflection
0
0 comments X

The pith

Entropy current through a superfluid quantum point contact oscillates at low voltage in the ballistic limit.

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

The paper computes particle and entropy currents between two BCS superfluid Fermi-gas reservoirs connected by a quantum point contact under chemical-potential bias. It employs the Keldysh formalism to obtain the steady-state currents, confirming standard particle-current steps from Andreev processes and extending the calculation to entropy flow. The central result is that entropy current develops oscillations with voltage at low bias when the junction is fully transparent. This matters because entropy transport encodes information about quasiparticle excitations and pairing that particle current alone does not capture. The analysis spans tunnel to ballistic transparencies and is compared with cold-atom data in the unitary regime.

Core claim

In the ballistic junction limit the entropy current exhibits an oscillatory voltage dependence at low bias, while the particle current retains its known step-like features characteristic of superfluid transport.

What carries the argument

Keldysh contour integration of the tunneling Hamiltonian between two BCS mean-field leads, yielding steady-state expectation values of both particle-number and entropy operators.

Load-bearing premise

The reservoirs are accurately modeled by a simple BCS mean-field theory that remains valid out of equilibrium.

What would settle it

An experiment that measures the entropy current in a ballistic superfluid quantum point contact at low voltage and finds no oscillations would contradict the central prediction.

Figures

Figures reproduced from arXiv: 2605.00679 by C.J. Bolech, Davide Bertolusso, Thierry Giamarchi.

Figure 1
Figure 1. Figure 1: FIG. 1. Illustration of a two-reservoir system coupled at a view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Depiction of a view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Graphical representation of the non-equilibrium view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Depiction of a view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The local density of states (LDoS) as a function of view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Current-voltage behavior for the particle (left panel) and entropy (right panel) transport under a chemical potential view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Particle and entropy currents as a function of voltage for a SN junction under an applied chemical potential bias at view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Particle current as a function of chemical potential bias for intermediate junction transparencies. Solid lines correspond view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Entropy current as a function of bias for different values of the junction transparency view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Description of the contributions to entropy and par view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. The local density of state (LDoS) for the truncated view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Entropy current behavior of the truncated SS junc view at source ↗
read the original abstract

We study the matter and entropy transport between two ultra-cold neutral Fermi-gas reservoirs linked by a quantum point contact under a chemical-potential gradient. We describe the two leads with a BCS mean-field model and derive the current-bias characteristics for both particle and entropy transport. We compute the out of equilibrium steady-state currents by using the Keldysh formalism. In accordance with previous works in the literature, we confirm the well-known behavior for the particle current and extend the computation to the entropy current in the BCS regime. The entropy current shows an oscillatory behavior at low voltage in the ballistic junction limit. We analyze the results for a wide range of values of the junction's transparency. We also compare our findings with experimental results in cold atomic gases in the unitary 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

1 major / 0 minor

Summary. The manuscript develops a Keldysh contour calculation of steady-state particle and entropy currents through a quantum point contact linking two BCS mean-field superfluid Fermi-gas reservoirs driven by a chemical-potential bias. It recovers the known particle-current characteristics and reports an additional oscillatory entropy current at low bias in the ballistic limit, examines the dependence on junction transparency, and compares the results to cold-atom experiments performed in the unitary regime.

Significance. If the oscillatory entropy current survives beyond the mean-field approximation, the work supplies a controlled Keldysh framework for entropy transport in out-of-equilibrium superfluid junctions. The explicit confirmation of established particle-current results and the parameter-free character of the derivation within the BCS model are positive features that strengthen the technical contribution.

major comments (1)
  1. [Abstract] Abstract: the headline claim of oscillatory entropy current at low voltage in the ballistic limit is obtained from the same BCS mean-field Green's functions used for the particle current. The manuscript then compares these oscillations directly to unitary-regime cold-atom experiments. Because BCS mean-field is controlled only in the weak-coupling limit while unitary gases are dominated by pairing fluctuations that modify the low-energy density of states and Andreev processes, the oscillations may be an artifact of the approximation. A concrete test (e.g., comparison with a fluctuation-corrected self-energy or a non-mean-field method) is required to establish whether the low-bias feature is robust.

Simulated Author's Rebuttal

1 responses · 1 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comment on the scope of the BCS mean-field approximation. We address the concern in detail below and outline the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the headline claim of oscillatory entropy current at low voltage in the ballistic limit is obtained from the same BCS mean-field Green's functions used for the particle current. The manuscript then compares these oscillations directly to unitary-regime cold-atom experiments. Because BCS mean-field is controlled only in the weak-coupling limit while unitary gases are dominated by pairing fluctuations that modify the low-energy density of states and Andreev processes, the oscillations may be an artifact of the approximation. A concrete test (e.g., comparison with a fluctuation-corrected self-energy or a non-mean-field method) is required to establish whether the low-bias feature is robust.

    Authors: We agree that the BCS mean-field description is controlled only in the weak-coupling limit, while the cited cold-atom experiments operate in the unitary regime where pairing fluctuations are important and can alter the low-energy density of states and Andreev processes. Our calculation employs the same mean-field Green's functions for both the particle and entropy currents, thereby recovering the established particle-current characteristics reported in the literature. The low-bias oscillatory entropy current is a direct consequence of the Keldysh contour evaluation within this controlled approximation. We will revise the abstract and add a dedicated paragraph in the discussion section to state explicitly that the oscillatory feature is a prediction of the BCS mean-field theory and that the comparison with unitary-regime data is intended to be qualitative. We note that a concrete test against a fluctuation-corrected self-energy or a non-mean-field method lies outside the present scope. revision: partial

standing simulated objections not resolved
  • A concrete test with a fluctuation-corrected self-energy or a non-mean-field method cannot be provided within the current manuscript, as it would require an entirely different theoretical framework.

Circularity Check

0 steps flagged

Keldysh-BCS derivation of entropy current is self-contained with no circular reductions

full rationale

The paper applies the standard Keldysh formalism to BCS mean-field Green's functions for the leads to compute both particle and entropy currents under a chemical potential bias. The low-voltage oscillatory entropy current in the ballistic limit emerges directly from the contour-ordered integrals over the non-equilibrium distribution functions and the junction transparency parameter; it is not obtained by fitting or redefining any input quantity. Confirmation of the particle current against prior literature is used only for validation and does not carry the entropy result. No self-definitional loops, fitted-input predictions, or load-bearing self-citations appear in the derivation chain. The calculation remains independent of the unitary-regime experiments mentioned for comparison.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The ledger is based on the abstract only. No free parameters are mentioned, and no new entities are introduced. The assumptions are standard in the field but their validity for the entropy current extension needs verification in the full paper.

axioms (2)
  • domain assumption BCS mean-field model for the leads
    The two ultra-cold neutral Fermi-gas reservoirs are described using this model.
  • domain assumption Keldysh formalism computes out-of-equilibrium steady-state currents
    Used to derive the current-bias characteristics for particle and entropy transport.

pith-pipeline@v0.9.0 · 5436 in / 1306 out tokens · 36237 ms · 2026-05-09T14:34:57.626598+00:00 · methodology

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