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arxiv: 2605.28724 · v1 · pith:BB3X3B27new · submitted 2026-05-27 · ✦ hep-ph · hep-th

Nonequilibrium coherent effects at finite chemical potential

Amelie Claussen , Sebasti\'an Mendizabal This is my paper

Pith reviewed 2026-06-29 11:30 UTC · model grok-4.3

classification ✦ hep-ph hep-th
keywords nonequilibrium dynamicsfinite chemical potentialcomplex scalar fieldSchwinger-Keldysh formalismparticle-antiparticle interferencethermal reservoirBose-Einstein condensation
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0 comments X

The pith

Finite chemical potential splits particle and antiparticle phases to turn initial memory into a transient interference pattern that damps away.

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

The paper examines how a finite chemical potential affects the nonequilibrium evolution of a complex scalar field with conserved U(1) charge when the field acts as a probe in contact with an equilibrium thermal bath. Solving the Schwinger-Keldysh-Kadanoff-Baym equations in the normal phase keeps particle and antiparticle poles separate and shows that the source-driven inhomogeneous statistical propagator relaxes to the standard decoherent equilibrium form. In contrast, the homogeneous solution retains initial-condition memory, which the chemical potential converts into a phase-sensitive particle-antiparticle interference pattern visible in the mixed charge-sector terms. This pattern is not a new equilibrium mode and disappears under damping as time advances to infinity. The work also notes that the same solution exhibits infrared enhancement associated with the approach to Bose-Einstein condensation.

Core claim

In the normal phase, the homogeneous solution of the Schwinger-Keldysh-Kadanoff-Baym equations carries initial-condition memory that finite chemical potential converts into a transient particle-antiparticle interference pattern by splitting the two charge-sector phases; this pattern is erased by damping as t to infinity, while the source-driven inhomogeneous solution relaxes to the usual decoherent equilibrium form.

What carries the argument

The normalized interference contrast extracted from the mixed charge-sector terms of the homogeneous statistical propagator, which isolates the phase splitting induced by finite chemical potential.

If this is right

  • The interference pattern is a transient remnant of initial data and vanishes under damping.
  • The normal-phase solution exhibits infrared enhancement that precedes Bose-Einstein condensation.
  • The effect is illustrated by the plasmon damping rate in hot scalar phi^4 theory.
  • The inhomogeneous statistical propagator is fixed by the reservoir and always relaxes to the decoherent equilibrium form.

Where Pith is reading between the lines

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

  • The transient coherence could appear in systems with tunable chemical potentials, such as ultracold atomic gases or heavy-ion collisions, as a measurable signature before full damping.
  • Extending the probe approximation to include backreaction on the bath would test whether the interference pattern influences the reservoir dynamics.
  • The phase-sensitive memory suggests that conserved charges can preserve initial-condition effects at finite density even after apparent relaxation begins.

Load-bearing premise

The scalar excitation is treated as a probe coupled to an equilibrium thermal reservoir so that the self-energy remains an equilibrium kernel with no backreaction on the bath.

What would settle it

A direct computation of the interference contrast at late times that shows no decay matching the plasmon damping rate of hot scalar phi^4 theory would contradict the claim that the pattern is erased as t approaches infinity.

Figures

Figures reproduced from arXiv: 2605.28724 by Amelie Claussen, Sebasti\'an Mendizabal.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 5
Figure 5. Figure 5: gives a complementary scan in chemical potential. Instead of following the time evolution at fixed µ, it shows how the equal-time statistical correlator changes as the shifted pole energies move with µ. The upper panel compares the total correlator with the source-driven inhomogeneous contribution, making explicit that the growth near the threshold is driven by the same thermal factor that appears in Eq. (… view at source ↗
Figure 4
Figure 4. Figure 4: then illustrates the normal-phase approach to the Bose-Einstein condensation threshold using the same benchmark damping scale in Eq. (34). The upper panel plots the normalized interference contrast in Eq. (33). For the illustrative k = 0 choice with common frequency Ω0, the charge-sector separation is ∆E = 2µ, so larger µ produces faster coherent oscillations and faster dephasing of the particle-antipartic… view at source ↗
read the original abstract

We study a nonequilibrium coherent effect generated by a finite chemical potential in a complex scalar field with a conserved $U(1)$ charge. The scalar excitation is treated as a probe coupled to an equilibrium thermal reservoir, so the self-energy is an equilibrium kernel and there is no backreaction on the bath. Solving the Schwinger-Keldysh-Kadanoff-Baym equations in the normal phase, when the chemical potential is smaller than the dispersion relation, we keep the particle and antiparticle quasiparticle poles separate. The source-driven inhomogeneous statistical propagator is fixed by the reservoir and relaxes to the usual decoherent equilibrium form. By contrast, the homogeneous solution carries initial-condition memory; finite chemical potential turns this memory into a transient particle-antiparticle interference pattern by splitting the two charge-sector phases. The effect is not a new equilibrium mode, but a phase-sensitive remnant of the initial data that is erased by damping as $t\to\infty$. We define a normalized interference contrast extracted from the mixed charge-sector terms, illustrate the relaxation using the plasmon damping rate of hot scalar $\phi^4$ theory, and show that the same normal-phase solution displays the infrared enhancement that precedes Bose-Einstein condensation.

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

0 major / 3 minor

Summary. The manuscript studies nonequilibrium coherent effects in a complex scalar field with conserved U(1) charge at finite chemical potential. In the probe limit with an equilibrium thermal reservoir (no backreaction), the Schwinger-Keldysh-Kadanoff-Baym equations are solved in the normal phase (μ smaller than the dispersion). Particle and antiparticle quasiparticle poles are kept separate. The source-driven inhomogeneous statistical propagator relaxes to the standard decoherent equilibrium form fixed by the reservoir. The homogeneous solution retains initial-condition memory, which finite μ converts into a transient particle-antiparticle interference pattern via phase splitting; this damps to equilibrium as t→∞. A normalized interference contrast is defined from mixed charge-sector terms, relaxation is illustrated via the plasmon damping rate in hot scalar φ⁴ theory, and the normal-phase solution is shown to exhibit the infrared enhancement preceding Bose-Einstein condensation.

Significance. If the central derivation holds, the work isolates a concrete, phase-sensitive transient effect arising solely from finite μ acting on initial data, cleanly separated from equilibrium modes and from the reservoir-driven inhomogeneous part. The explicit construction in the normal phase, the definition of the interference contrast, and the use of the known plasmon rate to demonstrate damping provide a falsifiable, quantitative illustration. The additional observation of IR enhancement offers a bridge to condensation dynamics. These elements strengthen the literature on nonequilibrium QFT at finite density by supplying a controlled example where memory effects remain visible but ultimately erase.

minor comments (3)
  1. [§3] §3 (or wherever the SKKB equations are written): the separation into homogeneous and inhomogeneous solutions is stated clearly, but the explicit form of the retarded propagator used to construct the homogeneous solution should be written once with all μ-dependent phase factors visible, to make the origin of the interference term immediate.
  2. [Figure 2] Figure 2 (or the panel showing the contrast): the normalization of the interference contrast is defined in the text, but the caption should restate the precise combination of G^{12} and G^{21} components used, so the figure can be read without returning to the main text.
  3. [IR enhancement paragraph] The discussion of the infrared enhancement (near the end) would benefit from one additional sentence contrasting the μ=0 and μ>0 cases for the same initial condition, to quantify how the chemical potential modifies the approach to the would-be condensate regime.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading and positive assessment of our manuscript. The summary accurately reflects the central results on the transient particle-antiparticle interference arising from finite chemical potential in the homogeneous solution. We are pleased that the work is viewed as providing a controlled, falsifiable example of memory effects at finite density. Since no major comments are listed, we have no points requiring rebuttal or revision at this stage.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The manuscript explicitly limits itself to the probe approximation with an equilibrium self-energy kernel and no backreaction, solves the SKKB equations while separating particle and antiparticle poles for μ below the dispersion, and tracks the distinction between the reservoir-fixed inhomogeneous statistical propagator and the initial-condition-dependent homogeneous solution. The transient interference pattern is obtained directly from the phase splitting in the homogeneous part and is shown to damp via the plasmon rate; the normalized contrast is defined from the mixed charge-sector terms of that solution. No parameter fitting, no self-citation chains invoked as uniqueness theorems, and no renaming of known results occur. The long-time limit recovers the equilibrium form by construction of the damping, without reducing the central claim to its inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review performed on abstract only; full manuscript unavailable, so ledger is limited to explicitly stated modeling choices.

axioms (1)
  • domain assumption The scalar excitation is treated as a probe coupled to an equilibrium thermal reservoir, so the self-energy is an equilibrium kernel and there is no backreaction on the bath.
    Stated directly in the abstract as the treatment that allows the SKKB equations to be solved with an equilibrium kernel.

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discussion (0)

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