REVIEW 5 cited by
Branch-cut in the shear-stress response function of massless λ φ⁴ with Boltzmann statistics
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Branch-cut in the shear-stress response function of massless λ φ⁴ with Boltzmann statistics
read the original abstract
Using an analytical result for the eigensystem of the linearized collision term for a classical system of massless scalar particles with quartic self-interactions, we show that the shear-stress linear response function possesses a branch-cut singularity that covers the whole positive imaginary semi-axis. This is demonstrated in two ways: (1) by truncating the exact, infinite linear system of linear equations for the rank-two tensor modes, which reveals the cut touching the origin; and (2) by employing the Trotterization techniques to invert the linear response problem. The former shows that the first pole tends towards the origin and the average separation between consecutive poles tends towards zero as power laws in the dimension of the basis. The latter allows one to obtain the response function in closed form in terms of Tricomi hypergeometrical functions, which possess a branch-cut on the above-mentioned semi-axis. This suggests that the presence of a cut along the imaginary frequency axis of the shear stress correlator, inferred from previous numerical analyses of weakly coupled scalar $\lambda \varphi^4$ theories, does not arise due to quantum statistics but instead emerges from the fundamental properties of this system's interactions.
Forward citations
Cited by 5 Pith papers
-
The Lorentzian geometry of relaxation
Causality forces purely relaxational dispersion relations to follow spacelike trajectories on the Lorentzian {iω,ik} plane, producing universal bounds on diffusivity, viscosity, time-dilation deviations, and hydrodyna...
-
How Lorentz boosts reshape relaxation spectra
Under an Onsager-type symmetry, boosted k=0 non-hydrodynamic relaxation rates of a relativistic fluid are bounded by a(1-v)/γ ≤ iω' ≤ b/[γ(1-v)] in terms of rest-frame bounds a,b and boost speed v.
-
Normal mode analysis within relativistic massive transport
Normal mode analysis of the relativistic Boltzmann equation for massive particles reveals coupling between sound and heat channels, mass-dependent critical wavenumbers, and an infinite branch cut for Landau damping.
-
The quasi-normal modes of relativistic Fokker-Planck kinetic theory
The quasi-normal spectrum of ultrarelativistic Fokker-Planck kinetic theory consists of an exact diffusive hydrodynamic mode, continuous ballistic bands, and a hydrogenic discrete tower in three dimensions.
-
Analytic structure of stress-energy response functions and new Kubo formulae
Authors derive new Kubo formulae for transport coefficients by analyzing analytic structures of stress-energy response functions in second- and third-order hydrodynamics.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.