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arxiv: 2512.21690 · v2 · pith:TJ2O3LCFnew · submitted 2025-12-25 · ✦ hep-th · cond-mat.stat-mech· quant-ph

On prethermal time crystals from semi-holography

Toshali Mitra , Sukrut Mondkar , Ayan Mukhopadhyay , Alexander Soloviev This is my paper

Pith reviewed 2026-05-21 16:31 UTC · model grok-4.3

classification ✦ hep-th cond-mat.stat-mechquant-ph
keywords prethermal time crystalssemi-holographyholographic black holeshydrodynamic modesshear and sound channelsmetastable phasesnon-Abelian plasmasinhomogeneities
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0 comments X

The pith

A hybrid quantum system of perturbative and holographic sectors exhibits prethermal time-crystal behavior through almost dissipationless oscillating modes in shear and sound channels without fine-tuning.

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

The paper examines a hybrid quantum system where a weakly self-interacting perturbative sector is coupled to strongly self-interacting holographic degrees of freedom modeled by a black hole geometry. It finds pairs of nearly dissipationless oscillating modes in the shear and sound channels at low temperatures. These modes are argued to exhibit prethermal time-crystal behavior that can be observed by probing either sector. The work also identifies short-wavelength instabilities that cause inhomogeneities at higher temperatures. This suggests that such phases can occur in non-Abelian plasmas without external driving over a range of temperatures set by the coupling scale.

Core claim

We demonstrate the existence of a pair of almost dissipationless oscillating modes at low temperatures in both the shear and sound channels of a hybrid quantum system, comprised of a weakly self-interacting perturbative sector coupled to strongly self-interacting holographic degrees of freedom described by a black hole geometry. These modes realize prethermal time-crystal behavior in semi-holographic systems without fine-tuning and can be observed by measuring operators that probe either the hard or the soft sector. Novel short wavelength instabilities lead to the formation of inhomogeneities even at higher temperatures. Black holes with planar horizons and dynamical boundary conditions can,

What carries the argument

The hybrid semi-holographic system consisting of a perturbative sector weakly coupled to holographic degrees of freedom represented by black hole geometries with planar horizons and dynamical boundary conditions, which generate the hydrodynamic modes.

If this is right

  • These oscillating modes can be observed by measuring operators that probe either the perturbative or holographic sector.
  • Novel short wavelength instabilities lead to the formation of inhomogeneities even at higher temperatures.
  • Black holes with planar horizons and dynamical boundary conditions develop inhomogeneous and metastable time-crystal phases.
  • Such phases can be realized without external driving in non-Abelian plasmas of asymptotically free gauge theories in the large-N limit.

Where Pith is reading between the lines

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

  • The intermediate coupling scale between sectors determines the temperature window for these phases.
  • This approach might extend to other strongly coupled systems where holographic methods apply, potentially revealing similar metastable phases.
  • Experimental realization could involve analogs in condensed matter or high-energy physics simulations of large-N gauge theories.

Load-bearing premise

The hybrid system can be accurately modeled by weakly coupling a perturbative sector to strongly interacting holographic degrees of freedom described by a black hole geometry with planar horizons and dynamical boundary conditions such that the resulting hydrodynamic modes correspond to prethermal time crystals.

What would settle it

A calculation or simulation showing the absence of almost dissipationless oscillating modes in the shear and sound channels at low temperatures in the described semi-holographic setup, or the presence of significant dissipation in those modes.

Figures

Figures reproduced from arXiv: 2512.21690 by Alexander Soloviev, Ayan Mukhopadhyay, Sukrut Mondkar, Toshali Mitra.

Figure 1
Figure 1. Figure 1: FIG. 1. The QNM of AdS [PITH_FULL_IMAGE:figures/full_fig_p022_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: , while their dispersion relations are displayed in [PITH_FULL_IMAGE:figures/full_fig_p024_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p025_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The absolute value of the imaginary part of frequency, [PITH_FULL_IMAGE:figures/full_fig_p026_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) The absolute value of the real part of frequency, [PITH_FULL_IMAGE:figures/full_fig_p027_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p028_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p031_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. (a) The behavior of the imaginary part of the frequency of the inhomogeneous zero mode [PITH_FULL_IMAGE:figures/full_fig_p034_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. (a) Shear modes in the case of weakly broken momentum conservation on a timescale [PITH_FULL_IMAGE:figures/full_fig_p039_9.png] view at source ↗
read the original abstract

We demonstrate the existence of a pair of almost dissipationless oscillating modes at low temperatures in both the shear and sound channels of a hybrid quantum system, comprised of a weakly self-interacting perturbative sector coupled to strongly self-interacting holographic degrees of freedom described by a black hole geometry. We argue that these modes realize prethermal time-crystal behavior in semi-holographic systems without fine-tuning and can be observed by measuring operators that probe either the hard (perturbative) or the soft (holographic) sector. We also find novel {short wavelength} instabilities that lead to the formation of inhomogeneities even at higher temperatures. These results provide evidence that black holes with planar horizons and dynamical boundary conditions can develop both inhomogeneous and metastable time-crystal phases over a wide range of temperatures set by an intermediate scale given by the intersector coupling. Furthermore, they suggest that such phases can be realized without external driving in non-Abelian plasmas of asymptotically free gauge theories in the large-$N$ limit.

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 / 2 minor

Summary. The manuscript constructs a semi-holographic hybrid system in which a weakly self-interacting perturbative sector is coupled to strongly interacting holographic degrees of freedom modeled by a black hole with planar horizons and dynamical boundary conditions. It reports the existence of a pair of nearly dissipationless oscillating modes in both the shear and sound channels at low temperatures, argues that these modes realize prethermal time-crystal behavior without fine-tuning, and identifies novel short-wavelength instabilities that produce inhomogeneities even at higher temperatures. The results are claimed to be observable via operators probing either sector and to suggest the possibility of inhomogeneous and metastable time-crystal phases in black-hole geometries over a temperature range set by the intersector coupling, with implications for large-N non-Abelian plasmas.

Significance. If the central claims are substantiated, the work would provide a concrete, tunable example of prethermal time crystals arising from weak coupling to a holographic sector without external driving or fine-tuning. This would strengthen the case that holographic black holes with dynamical boundaries can host metastable non-equilibrium phases and would offer a potential bridge to asymptotically free gauge theories in the large-N limit. The semi-holographic framework itself is a methodological strength that allows controlled access to both perturbative and strongly coupled regimes.

major comments (2)
  1. [§4] §4 (hydrodynamic modes and quasinormal-mode analysis): The central claim that the identified modes are prethermal requires a parametric separation between the oscillation period and the lifetime, controlled solely by the weak intersector coupling. The linear dispersion relations obtained from the holographic black-hole geometry with dynamical boundary conditions do not automatically guarantee that Im(ω) remains parametrically smaller than Re(ω) once nonlinear interactions or backreaction from the perturbative sector are restored; an explicit scaling argument or numerical check demonstrating this suppression is needed to support the prethermal time-crystal interpretation.
  2. [§5] §5 (short-wavelength instabilities): The reported novel instabilities at higher temperatures are load-bearing for the claim that black holes with planar horizons can develop inhomogeneous phases over a wide temperature range. The manuscript should clarify whether these instabilities persist when the weak coupling is taken to zero and whether they are artifacts of the linearised analysis or survive in the full nonlinear evolution.
minor comments (2)
  1. [Model section] The definition of the intermediate scale set by the intersector coupling should be stated explicitly with its relation to the temperature and the holographic radius, preferably in an equation in the model section.
  2. [Figures] Figure captions for the dispersion plots should include the precise values of the coupling strength and temperature used, to allow direct comparison with the analytic claims.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their detailed and insightful report. We have carefully considered the major comments and provide point-by-point responses below. Where appropriate, we have revised the manuscript to address the concerns raised.

read point-by-point responses

  1. Referee: §4 (hydrodynamic modes and quasinormal-mode analysis): The central claim that the identified modes are prethermal requires a parametric separation between the oscillation period and the lifetime, controlled solely by the weak intersector coupling. The linear dispersion relations obtained from the holographic black-hole geometry with dynamical boundary conditions do not automatically guarantee that Im(ω) remains parametrically smaller than Re(ω) once nonlinear interactions or backreaction from the perturbative sector are restored; an explicit scaling argument or numerical check demonstrating this suppression is needed to support the prethermal time-crystal interpretation.

    Authors: We appreciate this comment, which highlights an important aspect of the prethermal interpretation. In our setup, the intersector coupling is weak and perturbative, allowing us to treat the holographic sector as dominant. We have added an explicit scaling argument in the revised §4 demonstrating that the damping rate Im(ω) scales quadratically with the coupling strength g, while the oscillation frequency Re(ω) is set by the hydrodynamic scales and remains O(1) in the weak-coupling limit. This ensures the required parametric separation. Regarding nonlinear interactions and backreaction, the perturbative nature of the sector suppresses higher-order effects by powers of g. A complete numerical verification of the nonlinear regime would require extensive time-dependent simulations, which we consider beyond the current scope but plan to address in future work. We have updated the manuscript to include this scaling discussion and a note on the limitations. revision: partial

  2. Referee: §5 (short-wavelength instabilities): The reported novel instabilities at higher temperatures are load-bearing for the claim that black holes with planar horizons can develop inhomogeneous phases over a wide temperature range. The manuscript should clarify whether these instabilities persist when the weak coupling is taken to zero and whether they are artifacts of the linearised analysis or survive in the full nonlinear evolution.

    Authors: We agree that these points require clarification. The short-wavelength instabilities emerge from the mode mixing induced by the finite intersector coupling. In the limit where this coupling vanishes, the sectors decouple, and the instabilities are absent, as confirmed by our analysis of the decoupled dispersion relations. Thus, they are a feature of the semi-holographic hybrid system. Our results are based on a linearised analysis around the homogeneous background. While such instabilities typically signal the development of inhomogeneous structures in the nonlinear regime, we acknowledge that confirming their survival and the resulting phase structure would necessitate full nonlinear simulations. We have revised §5 to explicitly state the coupling dependence and to discuss the linear nature of the analysis, including a brief outlook on nonlinear extensions. revision: partial

standing simulated objections not resolved
  • Full nonlinear time evolution to confirm the long-term behavior of the prethermal modes and the development of inhomogeneous phases from the short-wavelength instabilities

Circularity Check

0 steps flagged

No significant circularity; derivation relies on independent hydrodynamic analysis

full rationale

The paper constructs a semi-holographic hybrid system by weakly coupling a perturbative sector to a holographic black-hole geometry with planar horizons and dynamical boundary conditions. It then computes quasinormal modes in shear and sound channels to identify nearly dissipationless oscillating modes at low temperatures. These modes are argued to realize prethermal time-crystal behavior via an intermediate scale set by the intersector coupling. No equations reduce the target result to a fitted parameter or self-citation by construction; the dispersion relations and instability analysis are derived from the bulk geometry and boundary conditions rather than presupposing the prethermal timescale separation. The central claim therefore remains self-contained against external benchmarks such as standard holographic hydrodynamics.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities are identifiable. The modeling implicitly relies on standard holographic duality and assumptions about sector coupling, but details are absent.

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