We consider monoenergetic particles propagating in three spatial dimensions and undergoing elastic scattering off an external medium. For an arbitrary rotationally invariant scattering kernel, we derive an exact expression for the frequency- and wave-number-dependent diffusivity, thereby resumming the hydrodynamic gradient expansion to all orders. The result is an infinite continued fraction, with each successive level determined by the relaxation rate of a higher angular harmonic of the collision operator. Thus, while ordinary diffusion probes only the first angular harmonic, the resummed constitutive relation retains information about the full scattering kernel. We show how this microscopic information manifests itself in the analytic structure of the diffusivity and in the response to a localized external source. In particular, deviations from Fick's law decay exponentially with distance, at a rate determined by the nearest complex-wavenumber singularity of the inverse diffusivity. Thus, exponentially small departures from hydrodynamics retain detailed information about the underlying scattering process.
A multispecies, collisionless plasma is modeled by the relativistic Vlasov-Maxwell system. Assuming the plasma is globally neutral, we show that solutions can be constructed with arbitrarily fast, polynomial rates of decay, depending upon the cancellation properties of the limiting spatial averages, as well as the mass...
G. Mattingly, Stephen Pankavich, Jonathan Ben-Artzi· 0 citations
We study the conservative and dissipative forces on a Newtonian binary interacting with a nonrelativistic ultralight scalar medium. We derive integral expressions for the instantaneous force and the orbit-averaged energy flux generated by wake perturbations of a general background field. For a homogeneous coherent back...
We construct an exact formulation for the solution of Bjorken expanding relativistic viscous hydrodynamics with a constant relaxation time and derive its late time transseries structure. The two fundamental modes of the linear auxiliary equation separate the hydrodynamic contribution from the exponentially suppressed t...
We present a practical method for accelerating the modified Born series for high-frequency Helmholtz scattering in one, two, and three dimensions. We consider bounded, nonnegative, compactly supported media, allowing small departures from radial symmetry in two and three dimensions. The method selects a single complex...
The quantitative success of relativistic viscous hydrodynamics in describing the short-lived quark--gluon plasma raises a fundamental question: how does far-from-equilibrium QCD matter approach hydrodynamic behavior so rapidly? Microscopic kinetic-theory studies have related this onset to attractor dynamics, but typica...
When a gas of scattering particles is disturbed, each angular harmonic of its velocity distribution decays at its own rate. Hydrodynamics, and with it the shear viscosity, depends on only one of these rates, the one for the quadrupole harmonic. A system that scatters only a few times before it stops interacting remembe...
O. Soloveva· 1 citation
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