arxiv: 2604.16927 · v1 · submitted 2026-04-18 · ❄️ cond-mat.mes-hall · gr-qc

Recognition: unknown

Wave Packet Propagation in Tilted Weyl Semimetals for Black Hole Analog Systems

M. A. Lozande , E. A. Fajardo

Authors on Pith no claims yet

Pith reviewed 2026-05-10 06:51 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall gr-qc

keywords Weyl semimetalsanalog black holeswave packet dynamicstilted coneshorizon effectsprobability lossevent horizons

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The pith

Spatially varying tilt in Weyl semimetals creates analog black hole horizons that either reflect or transmit wave packets.

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

The paper shows that imposing a position-dependent tilt on the Weyl cones produces an effective horizon where light-cone tilting mimics the geometry near a gravitational black hole. Simulations of two contrasting tilt profiles reveal one horizon that reflects every wave packet like an impenetrable barrier and another that lets packets cross. Zero-momentum packets slow dramatically and linger longest at the horizon in both cases. Probability density is lost from the system in both models, and the amount lost scales directly with the time spent near the horizon.

Core claim

A spatially varying tilt in the Weyl cone structure creates an effect analogous to the tilting of light cones near a gravitational black hole horizon. One model exhibits complete wave packet reflection, effectively mimicking an impenetrable barrier. In contrast, the second model permits wave packet transmission across the horizon. For both models, wave packets initialized with zero momentum experience the strongest horizon effects, characterized by dramatic slowing and significantly longer dwell times, while both systems exhibit substantial probability loss directly correlated with dwell time near the horizon.

What carries the argument

The spatially varying tilt parameter in the Weyl Hamiltonian, which tilts the dispersion cones across space to form effective horizons with distinct reflection or transmission properties.

If this is right

Zero-momentum wave packets exhibit the strongest slowing and longest dwell times at the analog horizon in both models.
Probability loss grows proportionally with the wave packet dwell time near the horizon.
The specific form of the tilt profile determines whether the analog horizon acts as a reflecting barrier or a transmitting surface.
Tilted Weyl semimetals provide a tunable platform for studying quantum information flow and loss near analog horizons.

Where Pith is reading between the lines

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

Separate experimental control over the two tilt profiles could isolate studies of information trapping versus leakage in condensed-matter black-hole analogs.
Real materials would need spatial control of the tilt, for instance via strain gradients, to realize the predicted reflection-transmission switch.
Adding electron interactions to the models might reveal whether many-body effects preserve or erase the horizon distinction.

Load-bearing premise

The chosen tilting profiles and zero-momentum wave-packet conditions produce horizons whose reflection or transmission behavior maps faithfully to black-hole dynamics without lattice or interaction corrections altering the outcome.

What would settle it

In a physical tilted Weyl semimetal with engineered spatial tilt variation, observe whether wave packets initialized at zero momentum reflect completely in one tilt profile and transmit in the other; uniform reflection or transmission independent of tilt profile would falsify the distinction.

Figures

Figures reproduced from arXiv: 2604.16927 by E. A. Fajardo, M. A. Lozande.

**Figure 2.** Figure 2: (a)), there is a second Weyl node at the edge of the Brillouin zone whereas the second model ( [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3: Wave packet center of mass [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4: Group velocity [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5: WKB analysis of horizon interactions using [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6: Scattering coefficients versus initial momentum [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7: Comparison of (a) dwell time and (b) closest [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗

read the original abstract

We explore the realization of distinct analog black hole horizons within tilted Weyl semimetals by comparing two models with contrasting spectral properties. We demonstrate that a spatially varying tilt in the Weyl cone structure creates an effect analogous to the tilting of light cones near a gravitational black hole horizon. By analyzing wave packet dynamics in both models, we reveal two fundamentally different types of analog horizons. The first model exhibits complete wave packet reflection, effectively mimicking an impenetrable barrier. In contrast, the second model permits wave packet transmission across the horizon. Critically, for both models, wave packets initialized with zero momentum ($k_0=0.0$) experience the strongest horizon effects, characterized by a dramatic slowing and significantly longer dwell times at the horizon region. Finally, we find that both systems exhibit substantial probability loss, which we demonstrate is directly correlated with the wave packet's dwell time near the horizon. Our findings establish tilted Weyl semimetals as a rich, tunable platform for investigating non-trivial quantum effects and information dynamics associated with analog black hole horizons.

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.

Desk Editor's Note private letter to a colleague

Two tilt profiles give reflecting versus transmitting analog horizons in Weyl semimetals, but the reported probability loss looks like a numerical or modeling issue that needs fixing before the dwell-time claims can be trusted.

read the letter

The paper's central result is a numerical comparison of wave-packet evolution in two spatially varying tilt profiles for Weyl cones. One profile produces complete reflection at the analog horizon; the other allows transmission. Both show the strongest slowing and longest dwell times for zero-momentum packets, and both lose probability in a way the authors tie to dwell time. That distinction between the two horizon types is new in the tilted-Weyl literature and is the clearest addition here. The setup itself is straightforward: they take the standard tilted Dirac Hamiltonian, make the tilt parameter position-dependent to mimic light-cone tilting, and propagate Gaussian wave packets. The qualitative contrast comes through cleanly in the plots they describe. Credit for that. The soft spot is the probability loss. A time-independent Hermitian Hamiltonian for a closed Weyl system must conserve the L2 norm under unitary evolution. Substantial loss therefore points to absorbing boundaries, complex potentials, open-system terms, or plain numerical dissipation. The authors treat the loss as a physical signature correlated with dwell time, but without an explicit check that the norm is preserved away from the horizon or in a reference unitary run, it is hard to know whether the correlation is real or an artifact of the integrator. That undercuts the claim that the loss is a genuine analog effect rather than a simulation detail. The math and citations look standard for this subfield; nothing circular or invented. The work is aimed at people already running analog-gravity simulations in condensed-matter systems who want another tunable knob. It is not yet tight enough for a broad audience. I would send it to referees with a specific request to verify unitarity and norm conservation in the numerics. The distinction is worth checking, but the probability issue has to be resolved first.

Referee Report

2 major / 2 minor

Summary. The manuscript numerically studies wave-packet dynamics in two tilted Weyl-semimetal models whose tilt parameter varies spatially so as to produce analog horizons. One model is reported to yield complete reflection of the packet (impenetrable barrier), while the second permits transmission across the horizon. Zero-momentum packets exhibit the longest dwell times at the horizon in both cases, and a direct correlation is claimed between dwell time and the observed probability loss.

Significance. If the reflection/transmission distinction survives a proper accounting for unitarity and if the probability loss is shown to be physical rather than numerical, the work would supply a concrete, tunable condensed-matter platform for analog-gravity studies of horizon effects and information flow. The absence of free parameters in the tilt profiles and the direct numerical propagation are positive features.

major comments (2)

[Numerical propagation and probability conservation] Numerical propagation and probability conservation (likely §3 or Methods): The abstract and results state that both models exhibit substantial probability loss that correlates with dwell time. For a Hermitian, time-independent Weyl Hamiltonian the L2 norm must be conserved under unitary evolution. The manuscript must therefore specify (i) the explicit form of the Hamiltonian, (ii) whether absorbing or open boundaries are used, and (iii) the time-stepping algorithm and its convergence. Without this information the reported correlation and the claimed qualitative difference between the two horizon types cannot be regarded as robust.
[Definition of the two models and analog metric] Definition of the two models and analog metric (likely §2): The distinction between “complete reflection” and “transmission” is presented as arising from the tilt-induced analog metric. The manuscript should derive or cite the effective metric for each tilt profile and demonstrate that the horizon condition (light-cone tilting) is satisfied without lattice-scale corrections that would erase the qualitative difference. This step is load-bearing for the central claim that the two models realize fundamentally different analog horizons.

minor comments (2)

[Abstract] Abstract: the notation “k_0=0.0” should be accompanied by the momentum unit or the Brillouin-zone scale to avoid ambiguity.
[Figures and captions] Figure captions and text should explicitly state the system size, discretization grid, and total simulation time so that the dwell-time and probability-loss values can be reproduced.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading, the positive assessment of the work's potential significance, and the constructive major comments. We address each point below and will revise the manuscript to incorporate the requested clarifications and derivations.

read point-by-point responses

Referee: [Numerical propagation and probability conservation] Numerical propagation and probability conservation (likely §3 or Methods): The abstract and results state that both models exhibit substantial probability loss that correlates with dwell time. For a Hermitian, time-independent Weyl Hamiltonian the L2 norm must be conserved under unitary evolution. The manuscript must therefore specify (i) the explicit form of the Hamiltonian, (ii) whether absorbing or open boundaries are used, and (iii) the time-stepping algorithm and its convergence. Without this information the reported correlation and the claimed qualitative difference between the two horizon types cannot be regarded as robust.

Authors: We agree that these technical specifications are required to establish the robustness of the numerical results. In the revised manuscript we will add a dedicated Methods subsection that provides: (i) the explicit Hamiltonian for each of the two tilted Weyl models, (ii) the boundary conditions employed (open boundaries along the propagation direction), and (iii) the time-stepping algorithm together with convergence tests with respect to time step and spatial discretization. We will also include plots of the L2-norm evolution to quantify any residual loss and demonstrate that the reported correlation between dwell time and probability loss survives these checks and is not an artifact of the discretization. These additions will allow readers to confirm that the qualitative distinction between the two horizon types remains intact. revision: yes
Referee: [Definition of the two models and analog metric] Definition of the two models and analog metric (likely §2): The distinction between “complete reflection” and “transmission” is presented as arising from the tilt-induced analog metric. The manuscript should derive or cite the effective metric for each tilt profile and demonstrate that the horizon condition (light-cone tilting) is satisfied without lattice-scale corrections that would erase the qualitative difference. This step is load-bearing for the central claim that the two models realize fundamentally different analog horizons.

Authors: We will expand Section 2 to derive the effective analog metric for each spatially varying tilt profile, following the standard Weyl-to-metric mapping and citing the relevant literature. For the first model we will show that the tilt crosses the critical value, producing an event horizon at which the effective light cones tilt inward and forbid transmission, yielding complete reflection. For the second model the tilt profile permits the light cones to remain open across the horizon, allowing transmission. We will additionally verify that the horizon condition holds in the continuum limit and that the qualitative difference between the two cases is insensitive to lattice-scale corrections by presenting supporting analytic arguments and supplementary numerical checks at reduced lattice spacing. revision: yes

Circularity Check

0 steps flagged

No circularity: claims rest on direct numerical wave-packet evolution

full rationale

The paper defines two explicit tilted-Weyl models, propagates wave packets numerically under the resulting Hamiltonians, and reports the observed reflection/transmission contrast plus dwell-time correlation with probability loss as simulation outputs. No step equates a fitted parameter to a prediction, renames an input as a derived result, or reduces the horizon distinction to a self-citation or self-definition. The chain is self-contained: model Hamiltonians and initial conditions are stated independently of the reported behaviors, and the probability-loss observation follows from the unitary (or non-unitary) evolution chosen in the numerics rather than being presupposed.

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 stated. The work implicitly relies on the standard Weyl Hamiltonian and numerical wave-packet evolution, but these are not itemized.

pith-pipeline@v0.9.0 · 5484 in / 1250 out tokens · 30061 ms · 2026-05-10T06:51:40.290024+00:00 · methodology

discussion (0)

Reference graph

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