Rigorous Bounds on Transport from Causality

Open Access

Rigorous Bounds on Transport from Causality

Michal P. Heller, Alexandre Serantes, Michał Spaliński, and Benjamin Withers

Phys. Rev. Lett. 130, 261601 – Published 26 June 2023

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.

Received 25 January 2023
Revised 31 March 2023
Accepted 6 June 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.261601

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Diffusion Gauge-gravity dualities Quantum field theory Quantum transport

Methods in transport Relativistic hydrodynamics String theory techniques in condensed matter

Particles & FieldsFluid DynamicsCondensed Matter, Materials & Applied PhysicsNuclear PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Michal P. Heller ^1,*, Alexandre Serantes ^2,†, Michał Spaliński^3,4,‡, and Benjamin Withers ^5,§

¹Department of Physics and Astronomy, Ghent University, 9000 Ghent, Belgium
²Departament de Física Quàntica i Astrofísica, Institut de Ciències del Cosmos (ICCUB), Facultat de Física, Universitat de Barcelona, Martí i Franquès 1, E-08028 Barcelona, Spain
³National Centre for Nuclear Research, 02-093 Warsaw, Poland
⁴Physics Department, University of Białystok, 15-245 Białystok, Poland
⁵Mathematical Sciences and STAG Research Centre, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom