Rigorous bounds on transport from causality

Abstract

We use causality to derive a number of simple and universal constraints on dispersion relations, which describe the location of singularities of retarded two-point functions in relativistic quantum field theories. We prove that all causal dissipative dispersion relations have a finite radius of convergence. We then give two-sided bounds on all transport coefficients in units of this radius, including an upper bound on diffusivity.

4 pages. New relational bound on sound attenuation, improved test function, references added

References in corpus (12)

• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Dissipative Dynamics of Highly Anisotropic Systems
• Highly-anisotropic and strongly-dissipative hydrodynamics for early stages of relativistic heavy-ion collisions
• On the convergence of the gradient expansion in hydrodynamics
• Causality constraints on corrections to Einstein gravity
• An upper bound on transport
• Causal Effective Field Theories
• Constraints on quasinormal modes and bounds for critical points from pole-skipping
• Dissipation in Holographic Superfluids
• Upper bound of the charge diffusion constant in holography
• Relativistic Hydrodynamics: A Singulant Perspective

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• Causality and classical dispersion relations
• Recent developments in mathematical aspects of relativistic fluids
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• A Bound on Thermalization from Diffusive Fluctuations
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• Non-modal effects in black hole perturbation theory: Transient Superradiance
• Convergence of the hydrodynamic gradient expansion in relativistic kinetic theory
• Infinite Order Hydrodynamics: An Analytical Example
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• Analytic solutions for the linearized first-order magnetohydrodynamics and implications for causality and stability
• Dispersion relations of relativistic radiation hydrodynamics
• Noncovariant parabolic theories of relativistic diffusion
• Causality constraints on radiative transfer
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• Causal and Stable Superfluid Hydrodynamics
• Universal thermalization dynamics in (1+1)d QFTs
• Propagator positivity bounds for cosmological correlators
• The quasi-normal modes of relativistic Fokker-Planck kinetic theory
• How Lorentz boosts reshape relaxation spectra
• Relativistic Dispersion Spectra across Lorentz boosted frames: Spurious modes and the enigma of causality
• Solitons and singularities in relativistic ultrastiff fluids
• Lorentz-boosted diffusion: initial value formulation and exact solutions
• The diffusion equation is compatible with special relativity