Rigorous Bounds on Transport from Causality
Michał P. Heller, Alexandre Serantes, Michał Spaliński, Benjamin Withers
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 in cases where stochastic fluctuations are negligible. We then give two-sided bounds on all transport coefficients in units of this radius, including an upper bound on diffusivity.
Topics & Concepts
Causality (physics)Dissipative systemGravitational singularityPhysicsRADIUSSimple (philosophy)Convergence (economics)Radius of convergenceUpper and lower boundsStatistical physicsDispersion (optics)Field (mathematics)Quantum mechanicsTheoretical physicsMathematicsMathematical analysisComputer sciencePure mathematicsEpistemologyComputer securityPower seriesEconomicsEconomic growthPhilosophyHigh-Energy Particle Collisions ResearchQuantum Chromodynamics and Particle InteractionsNoncommutative and Quantum Gravity Theories