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Abstract Collisionless systems often exhibit nonthermal power-law tails in their distribution functions. Interestingly, collisionless plasmas in various physical scenarios (e.g., the ion population of the solar wind) feature av−5tail in their velocity (v) distribution, whose origin has been a long-standing puzzle. We show this power-law tail to be a natural outcome of the collisionless relaxation of driven electrostatic plasmas. Using a quasi-linear analysis of the perturbed Vlasov–Poisson equations, we show that the coarse-grained mean distribution function (DF),f0, follows a quasi-linear diffusion equation with a diffusion coefficientD(v) that depends onvthrough the plasma dielectric constant. If the plasma is isotropically forced on scales larger than the Debye length with a white-noise-like electric field,D(v) ∼v4forσ<v<ωP/k, withσthe thermal velocity,ωPthe plasma frequency, andkthe characteristic wavenumber of the perturbation; the corresponding quasi-steady-statef0develops av−(d+ 2)tail inddimensions (v−5tail in 3D), while the energy (E) distribution develops anE−2tail independent of dimensionality. Any redness of the noise only alters the scaling in the highvend. Nonresonant particles moving slower than the phase velocity of the plasma waves (ωP/k) experience a Debye-screened electric field, and significantly less (power-law suppressed) acceleration than the near-resonant particles. Thus, a Maxwellian DF develops a power-law tail, while its core (v<σ) eventually also heats up but over a much longer timescale. We definitively show that self-consistency (ignored in test-particle treatments) is crucial for the emergence of the universalv−5tail.
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Can you hear the Planck mass?
A<sc>bstract</sc> For the Laplacian of ann-Riemannian manifoldX, the Weyl law states that thek-th eigenvalue is asymptotically proportional to (k/V)2/n, whereVis the volume ofX. We show that this result can be derived via physical considerations by demanding that the gravitational potential for a compactification onXbehaves in the expected (4+n)-dimensional way at short distances. In simple product compactifications, when particle motion onXis ergodic, for largekthe eigenfunctions oscillate around a constant, and the argument is relatively straightforward. The Weyl law thus allows to reconstruct the four-dimensional Planck mass from the asymptotics of the masses of the spin 2 Kaluza-Klein modes. For warped compactifications, a puzzle appears: the Weyl law still depends on the ordinary volumeV, while the Planck mass famously depends on a weighted volume obtained as an integral of the warping function. We resolve this tension by arguing that in the ergodic case the eigenfunctions oscillate now around a power of the warping function rather than around a constant, a property that we callweighted quantum ergodicity. This has implications for the problem of gravity localization, which we discuss. We show that for spaces with Dp-brane singularities the spectrum is discrete only forp= 6,7,8, and for these cases we rigorously prove the Weyl law by applying modern techniques from RCD theory.
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- Award ID(s):
- 2310429
- PAR ID:
- 10614681
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2024
- Issue:
- 8
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/JHEP08(2024)123
