An official website of the United States government
A bstract We explore possible extensions of the t -channel and s -channel unitary model of high energy evolution in zero transverse dimensions appropriate to very high energy/atomic number where the dipole density in a toy hadron is parametrically high. We suggest that the appropriate generalization is to allow emission of more than one dipole in a single step of energy evolution. We construct explicitly such a model that preserves the t -channel and s-channel unitarity and have the correct low density limit, and study the particle multiplicity distribution resulting from this evolution. We consider initial conditions of a single dipole and many dipoles at initial rapidity. We observe that the saturation regime in this model is preceded by a parametric range of rapidities $$ \frac{1}{\alpha_s}\ln \frac{1}{\alpha_s}<\frac{1}{\alpha_s}\ln \frac{1}{\alpha_s^2} $$ 1 α s ln 1 α s < Y < 1 α s ln 1 α s 2 , where the saturation effects are still unimportant, but multiple emissions determine the properties of the evolution. We also discuss the influence of the saturation on the parton cascade and, in particular, find that in the saturation regime the entropy of partons becomes S ≈ $$ \frac{1}{2} $$ 1 2 ln N where N is the mean multiplicity.
more »
« less
This content will become publicly available on March 1, 2026
Resonance cascades and number theory
In this article, we are interested in situations where the existence of a contiguous cascade of quantum resonant transitions is predicated on the validity of a particular statement in number theory. The setting is a tailored one-atom one-dimensional potential with a prescribed spectrum under a weak periodic perturbation. The former is, by now, an experimental reality [Cassettari et al., PNAS Nexus 2, pgac279 (2022)]. As a case study, we look at the following trivial statement: “Any power of 3 is an integer.” Consequently, we “test” this statement in a numerical experiment where we demonstrate an unimpeded upward mobility along an equidistant ln (3)-spaced subsequence of the energy levels of a potential with a log-natural spectrum under a frequency ln (3) time-periodic perturbation. We further show that when we “remove” 9 from the set of integers—by excluding the corresponding energy level from the spectrum—the cascade halts abruptly.
more »
« less
- Award ID(s):
- 2309271
- PAR ID:
- 10615717
- Publisher / Repository:
- AIP
- Date Published:
- Journal Name:
- AVS Quantum Science
- Volume:
- 7
- Issue:
- 1
- ISSN:
- 2639-0213
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract The influence of gravity waves generated by surface stress and by topography on the atmospheric kinetic energy (KE) spectrum is examined using idealized simulations of a cyclone growing in baroclinically unstable shear flow. Even in the absence of topography, surface stress greatly enhances the generation of gravity waves in the vicinity of the cold front, and vertical energy fluxes associated with these waves produce a pronounced shallowing of the KE spectrum at mesoscale wavelengths relative to the corresponding free-slip case. The impact of a single isolated ridge is, however, much more pronounced than that of surface stress. When the mountain waves are well developed, they produce a wavenumber to the −5/3 spectrum in the lower stratosphere over a broad range of mesoscale wavelengths. In the midtroposphere, a smaller range of wavelengths also exhibits a −5/3 spectrum. When the mountain is 500 m high, the waves do not break, and their KE is entirely associated with the divergent component of the velocity field, which is almost constant with height. When the mountain is 2 km high, wave breaking creates potential vorticity, and the rotational component of the KE spectrum is also strongly energized by the waves. Analysis of the spectral KE budgets shows that the actual spectrum is the result of continually shifting balances of direct forcing from vertical energy flux divergence, conservative advective transport, and buoyancy flux. Nevertheless, there is one interesting example where the −5/3-sloped lower-stratospheric energy spectrum appears to be associated with a gravity-wave-induced upscale inertial cascade.more » « less
-
Abstract In a strongly magnetized, magnetically dominated relativistic plasma, Alfvénic turbulence can extend to scales much smaller than the particle inertial scales. It leads to an energy cascade somewhat analogous to inertial- or kinetic-Alfvén turbulent cascades existing in nonrelativistic space and astrophysical plasmas. Based on phenomenological modeling and particle-in-cell numerical simulations, we propose that the energy spectrum of such relativistic kinetic-scale Alfvénic turbulence is close tok−3or slightly steeper than that due to intermittency corrections or Landau damping. We note the analogy of this spectrum with the Kraichnan spectrum corresponding to the enstrophy cascade in 2D incompressible fluid turbulence. Such turbulence strongly energizes particles in the direction parallel to the background magnetic field, leading to nearly one-dimensional particle momentum distributions. We find that these distributions have universal log-normal statistics.more » « less
-
Abstract Oceanic mesoscale motions including eddies, meanders, fronts, and filaments comprise a dominant fraction of oceanic kinetic energy and contribute to the redistribution of tracers in the ocean such as heat, salt, and nutrients. This reservoir of mesoscale energy is regulated by the conversion of potential energy and transfers of kinetic energy across spatial scales. Whether and under what circumstances mesoscale turbulence precipitates forward or inverse cascades, and the rates of these cascades, remain difficult to directly observe and quantify despite their impacts on physical and biological processes. Here we use global observations to investigate the seasonality of surface kinetic energy and upper-ocean potential energy. We apply spatial filters to along-track satellite measurements of sea surface height to diagnose surface eddy kinetic energy across 60–300-km scales. A geographic and scale-dependent seasonal cycle appears throughout much of the midlatitudes, with eddy kinetic energy at scales less than 60 km peaking 1–4 months before that at 60–300-km scales. Spatial patterns in this lag align with geographic regions where an Argo-derived estimate of the conversion of potential to kinetic energy is seasonally varying. In midlatitudes, the conversion rate peaks 0–2 months prior to kinetic energy at scales less than 60 km. The consistent geographic patterns between the seasonality of potential energy conversion and kinetic energy across spatial scale provide observational evidence for the inverse cascade and demonstrate that some component of it is seasonally modulated. Implications for mesoscale parameterizations and numerical modeling are discussed. Significance Statement This study investigates the seasonality of upper-ocean potential and kinetic energy in the context of an inverse cascade, consisting of energy transfers to and through the mesoscale. Observations show a scale-dependent cycle in kinetic energy that coincides with temporal variability in mixed layer potential energy and progresses seasonally from smaller to larger scales. This pattern appears dominant over large regions of the ocean. Results are relevant to ocean and climate models, where a large fraction of ocean energy is often parameterized. A customizable code repository and dataset are provided to enable comparisons of model-based resolved and unresolved kinetic energy to observational equivalents. Implications result for a range of processes including mixed layer stratification and vertical structure of ocean currents.more » « less
-
ABSTRACT Simulations of isolated giant molecular clouds (GMCs) are an important tool for studying the dynamics of star formation, but their turbulent initial conditions (ICs) are uncertain. Most simulations have either initialized a velocity field with a prescribed power spectrum on a smooth density field (failing to model the full structure of turbulence) or ‘stirred’ turbulence with periodic boundary conditions (which may not model real GMC boundary conditions). We develop and test a new GMC simulation setup (called turbsphere) that combines advantages of both approaches: we continuously stir an isolated cloud to model the energy cascade from larger scales, and use a static potential to confine the gas. The resulting cloud and surrounding envelope achieve a quasi-equilibrium state with the desired hallmarks of supersonic ISM turbulence (e.g. density PDF and a ∼k−2 velocity power spectrum), whose bulk properties can be tuned as desired. We use the final stirred state as initial conditions for star formation simulations with self-gravity, both with and without continued driving and protostellar jet feedback, respectively. We then disentangle the respective effects of the turbulent cascade, simulation geometry, external driving, and gravity/MHD boundary conditions on the resulting star formation. Without external driving, the new setup obtains results similar to previous simple spherical cloud setups, but external driving can suppress star formation considerably in the new setup. Periodic box simulations with the same dimensions and turbulence parameters form stars significantly slower, highlighting the importance of boundary conditions and the presence or absence of a global collapse mode in the results of star formation calculations.more » « less
