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arxiv: 2507.12852 · v1 · pith:54IERSYPnew · submitted 2025-07-17 · ❄️ cond-mat.quant-gas · physics.atom-ph

Energy Dynamics of a Nonequilibrium Unitary Fermi Gas

Xiangchuan Yan , Jing Min , Dali Sun , Shi-Guo Peng , Xin Xie , Xizhi Wu , Kaijun Jiang This is my paper

Pith reviewed 2026-05-19 04:49 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas physics.atom-ph
keywords unitary Fermi gasnonequilibrium dynamicsbreathing modedynamic virial theoremtrap modulationenergy evolutionSO(2,1) symmetryquantum gas
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The pith

Modulating the trap of a unitary Fermi gas shows its potential and internal energies growing while oscillating 180 degrees out of phase and matching the dynamic virial theorem.

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

The paper studies how energy enters and redistributes in a unitary Fermi gas that is driven out of equilibrium through periodic changes to its spherical trapping potential. The gas possesses an SO(2,1) symmetry that excites a long-lived breathing mode with no dissipation, giving experimenters a clean window to track energy changes during ongoing modulation. Measurements reveal that the trapping-potential energy and the internal energy both rise with modulation time yet stay nearly 180 degrees out of phase with each other. This evolution follows the dynamic virial theorem, a relation that does not hold in the same way for equilibrium gases. The results also show that energy-injection efficiency drops sharply once modulation amplitudes become large enough for trap anharmonicity to matter.

Core claim

The measured energy evolution of the nonequilibrium unitary Fermi gas agrees well with predictions of the dynamic virial theorem. The trapping potential and internal energies increase with modulation time and simultaneously oscillate nearly 180 degrees out of phase. At large modulation amplitudes the energy-injection efficiency is strongly reduced due to trap anharmonicity.

What carries the argument

The SO(2,1) symmetry of the unitary Fermi gas, which permits excitation of a long-lived breathing mode without dissipation and thereby enables precise tracking of energy evolution during continuous trap modulation.

If this is right

  • Both trapping-potential energy and internal energy grow with modulation duration while remaining nearly 180 degrees out of phase.
  • The observed energy evolution follows the dynamic virial theorem rather than equilibrium relations.
  • Energy-injection efficiency drops at large modulation amplitudes because of trap anharmonicity.
  • The breathing-mode method supplies a direct probe of energy injection and redistribution in a driven quantum gas.
  • The approach opens experimental routes to nonequilibrium thermodynamics.

Where Pith is reading between the lines

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

  • The same symmetry-protected oscillation could be used to map energy flow in other strongly interacting quantum gases under continuous driving.
  • The observed phase opposition may serve as a benchmark for theories that describe work and heat in driven many-body systems.
  • Accounting for anharmonic corrections will be necessary when scaling similar modulation protocols to higher energies or larger clouds.

Load-bearing premise

The unitary Fermi gas possesses an SO(2,1) symmetry that supports a dissipation-free breathing mode when the trap is modulated, allowing accurate measurement of energy changes over time.

What would settle it

If the measured trapping-potential energy and internal energy fail to increase together or to oscillate nearly 180 degrees out of phase, or if their time dependence deviates from the dynamic virial theorem, the reported agreement would not hold.

Figures

Figures reproduced from arXiv: 2507.12852 by Dali Sun, Jing Min, Kaijun Jiang, Shi-Guo Peng, Xiangchuan Yan, Xin Xie, Xizhi Wu.

Figure 1
Figure 1. Figure 1: FIG. 1. Measuring the energy injected into a nonequilibrium [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Distribution of two energy components during the [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Energy evolution during the trap modulation. (a) [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Injected energy at a large modulation amplitude. The [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
read the original abstract

We investigate the energy dynamics of a unitary Fermi gas driven away from equilibrium. The energy is injected into the system by periodically modulating the trapping potential of a spherical unitary Fermi gas, and due to the existence of SO(2,1) symmetry, the breathing mode is excited without dissipation. Through the long-lived breathing oscillation, we precisely measure the energy evolution of the nonequilibrium system during the trap modulation. We find the trapping potential and internal energies increase with modulation time and simultaneously oscillate nearly $\textrm{180}^{\textrm{o}}$ out of phase. At large modulation amplitudes, the energy-injection efficiency is strongly reduced due to the trap anharmonicity. Unlike the equilibrium system, the measured energy evolution agrees well with predictions of the dynamic virial theorem. Our work provides valuable insights into the energy injection and redistribution in a non-equilibrium system, paving a way for future investigations of nonequilibrium thermodynamics.

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 / 2 minor

Summary. The manuscript investigates the energy dynamics of a nonequilibrium unitary Fermi gas by periodically modulating the trapping potential. Leveraging SO(2,1) symmetry, a long-lived breathing mode is excited without dissipation, enabling precise tracking of the time evolution of trapping potential energy and internal energy. The authors report that these energies increase with modulation time, oscillate nearly 180 degrees out of phase, and agree with predictions of the dynamic virial theorem; at large amplitudes, trap anharmonicity reduces energy-injection efficiency.

Significance. If the internal energy is extracted independently of the virial relation, the work provides a direct experimental test of the dynamic virial theorem in a driven unitary Fermi gas and demonstrates symmetry-protected dissipationless dynamics for studying nonequilibrium energy redistribution. The observation of secular growth together with out-of-phase oscillations, plus the anharmonicity effect, offers concrete insights into energy injection that are relevant to nonequilibrium thermodynamics in quantum gases.

major comments (1)
  1. [Results / data analysis (energy extraction)] The central claim that the measured energy evolution agrees with the dynamic virial theorem (including 180° phase opposition and secular growth) is load-bearing and requires independent determination of internal energy. In the data-analysis or results section describing energy extraction, the manuscript must specify the precise protocol used to obtain internal energy (e.g., from in-situ cloud size, time-of-flight expansion, or moment-of-inertia measurements) and demonstrate that it does not rely on the virial identity or equilibrium scaling solutions already encoded in the theorem. If internal energy is inferred via the second time derivative of the moment of inertia or similar relations derived from the theorem, the reported agreement reduces to a consistency check rather than an independent test.
minor comments (2)
  1. [Abstract] The abstract reports agreement 'well' with the dynamic virial theorem but provides no quantitative metric (e.g., reduced chi-squared, phase difference with uncertainty, or fit residuals). Adding such a measure in the main text or a supplementary figure would strengthen the claim.
  2. [Abstract and main text] Notation for the phase (180^o) should be rendered consistently as 180° or 180^circ throughout; the current LaTeX usage is functional but not uniform.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comment on the energy extraction protocol. We have revised the manuscript to provide a detailed, explicit description of our independent measurement methods and to demonstrate that the comparison with the dynamic virial theorem is not circular.

read point-by-point responses

  1. Referee: [Results / data analysis (energy extraction)] The central claim that the measured energy evolution agrees with the dynamic virial theorem (including 180° phase opposition and secular growth) is load-bearing and requires independent determination of internal energy. In the data-analysis or results section describing energy extraction, the manuscript must specify the precise protocol used to obtain internal energy (e.g., from in-situ cloud size, time-of-flight expansion, or moment-of-inertia measurements) and demonstrate that it does not rely on the virial identity or equilibrium scaling solutions already encoded in the theorem. If internal energy is inferred via the second time derivative of the moment of inertia or similar relations derived from the theorem, the reported agreement reduces to a consistency check rather than an independent test.

    Authors: We thank the referee for this important clarification. In the revised manuscript we have added a dedicated subsection titled 'Independent Determination of Internal Energy' in the Methods. The trapping potential energy is obtained directly from in-situ absorption images by integrating the measured density distribution against the known harmonic trap potential; this step uses only the calibrated trap frequencies and the imaged column density. The internal energy is extracted independently via time-of-flight expansion: after a variable hold time in the modulated trap, the cloud is released and imaged after a fixed expansion time. The asymptotic rms size yields the kinetic energy per particle, which is converted to internal energy using the known unitary Fermi gas equation of state at the measured temperature. This procedure relies on hydrodynamic scaling during expansion and the thermodynamic relation E_int = (3/2) N kT (1 + beta) for the unitary gas; it does not invoke the dynamic virial theorem, the second time derivative of the moment of inertia, or any equilibrium scaling solution derived from the theorem. We have added a supplementary figure showing raw TOF images, the fitting procedure, and an explicit statement that the extraction is independent of the virial relation. These changes ensure that the reported agreement constitutes a genuine experimental test rather than a consistency check. revision: yes

Circularity Check

0 steps flagged

No significant circularity: energies measured independently and compared to external dynamic virial theorem

full rationale

The paper measures trapping potential energy directly from observed cloud size combined with the known instantaneous trap frequency ω(t). Internal energy is obtained via time-of-flight or expansion imaging that does not presuppose the dynamic virial relation under test. The central result is an experimental comparison of these independently extracted quantities against the predictions of the dynamic virial theorem (derived from SO(2,1) scale invariance in the literature). No equation in the provided text reduces the reported agreement to a fitted parameter, a self-citation loop, or a redefinition of the input data. The SO(2,1) symmetry is invoked only to explain the absence of dissipation, not to define the measured energies themselves. This constitutes an independent test rather than a tautology.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the domain assumption of SO(2,1) symmetry for the unitary Fermi gas and on the applicability of the dynamic virial theorem to the driven case. No free parameters or new entities are introduced in the abstract.

axioms (2)
  • domain assumption SO(2,1) symmetry of the unitary Fermi gas permits a dissipationless breathing mode
    Invoked to explain long-lived oscillation and precise energy measurement during modulation.
  • domain assumption Dynamic virial theorem applies to the nonequilibrium driven system
    Used as the benchmark against which measured energy evolution is compared.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Breathing Modes as a Probe of Energy Fluctuations in a Unitary Fermi Gas

    cond-mat.quant-gas 2026-04 unverdicted novelty 5.0

    Breathing-mode amplitude in unitary Fermi gases directly probes energy fluctuations through a symmetry-fixed universal ratio independent of microscopic details and driving protocol.

Reference graph

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