Hydrodynamic gauge fixing and higher order hydrodynamic expansion

TY - JOUR

T1 - Hydrodynamic gauge fixing and higher order hydrodynamic expansion

AU - De Nardis, Jacopo

AU - Doyon, Benjamin

N1 - Funding Information: We acknowledge discussions with H Spohn, F Essler, B Bertini, M Fagotti, and J Durning, who contributed at the early stages of the project. We thank referee A for providing relevant references to Burnett hydrodynamics. Some of his work was performed at Aspen Center for Physics, which is supported by National Science Foundation Grant PHY-1607611 and at Galileo Galilei Institute during the scientific program ‘Randomness, Integrability, and Universality’. The work of J D N has been partially funded by the ERC Starting Grant 101042293 (HEPIQ). The work of B D was supported by the Engineering and Physical Sciences Research Council (EPSRC) under Grants EP/W000458/1 and EP/W010194/1. Publisher Copyright: © 2023 IOP Publishing Ltd.

PY - 2023/6/16

Y1 - 2023/6/16

N2 - Hydrodynamics is a powerful emergent theory for the large-scale behaviours in many-body systems, quantum or classical. It is a gradient series expansion, where different orders of spatial derivatives provide an effective description on different length scales. We report the first fully general derivation of third-order, or ‘dispersive’, terms in the hydrodynamic expansion. Our derivation is based on general principles of statistical mechanics, along with the assumption that the complete set of local and quasi-local conserved densities constitutes a good set of emergent degrees of freedom. We obtain fully general Kubo-like expressions for the associated hydrodynamic coefficients (also known as Burnett coefficients), and we determine their exact form in quantum integrable models, introducing in this way purely quantum higher-order terms into generalised hydrodynamics. We emphasise the importance of hydrodynamic gauge fixing at diffusive order, where we claim that it is parity-time-reversal, and not time-reversal, invariance that is at the source of Einstein’s relation, Onsager’s reciprocal relations, the Kubo formula and entropy production. At higher hydrodynamic orders we introduce a more general, nth order ‘symmetric’ gauge, which we show implies the validity of the higher-order hydrodynamic description.

AB - Hydrodynamics is a powerful emergent theory for the large-scale behaviours in many-body systems, quantum or classical. It is a gradient series expansion, where different orders of spatial derivatives provide an effective description on different length scales. We report the first fully general derivation of third-order, or ‘dispersive’, terms in the hydrodynamic expansion. Our derivation is based on general principles of statistical mechanics, along with the assumption that the complete set of local and quasi-local conserved densities constitutes a good set of emergent degrees of freedom. We obtain fully general Kubo-like expressions for the associated hydrodynamic coefficients (also known as Burnett coefficients), and we determine their exact form in quantum integrable models, introducing in this way purely quantum higher-order terms into generalised hydrodynamics. We emphasise the importance of hydrodynamic gauge fixing at diffusive order, where we claim that it is parity-time-reversal, and not time-reversal, invariance that is at the source of Einstein’s relation, Onsager’s reciprocal relations, the Kubo formula and entropy production. At higher hydrodynamic orders we introduce a more general, nth order ‘symmetric’ gauge, which we show implies the validity of the higher-order hydrodynamic description.

KW - dispersive hydrodynamic

KW - hydrodynamic expansion

KW - hydrodynamics

KW - integrable systems

UR - http://www.scopus.com/inward/record.url?scp=85160289707&partnerID=8YFLogxK

U2 - 10.1088/1751-8121/acd153

DO - 10.1088/1751-8121/acd153

M3 - Article

AN - SCOPUS:85160289707

SN - 1751-8113

VL - 56

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 24

M1 - 245001

ER -