Title: Convergence of the Gradient Expansion in Hydrodynamics

Abstract

Hydrodynamic excitations corresponding to sound and shear modes in fluids are characterized by gapless dispersion relations. In the hydrodynamic gradient expansion, their frequencies are represented by power series in spatial momenta. We investigate the analytic structure and convergence properties of the hydrodynamic series by studying the associated spectral curve in the space of complexified frequency and complexified spatial momentum. For the strongly coupled N = 4 supersymmetric Yang-Mills plasma, we use the holographic duality methods to demonstrate that the derivative expansions have finite nonzero radii of convergence. Obstruction to the convergence of hydrodynamic series arises from level crossings in the quasinormal spectrum at complex momenta.

Authors:

Grozdanov, Sašo; Kovtun, Pavel K.; Starinets, Andrei O.; Tadić, Petar

Publication Date:

2019-06-28

Research Org.:

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Org.:

USDOE Office of Science (SC), Nuclear Physics (NP)

OSTI Identifier:

1530008

Alternate Identifier(s):

OSTI ID: 1637346

Grant/Contract Number:  

SC0011090

Resource Type:

Published Article

Journal Name:

Physical Review Letters

Additional Journal Information:

Journal Name: Physical Review Letters Journal Volume: 122 Journal Issue: 25; Journal ID: ISSN 0031-9007

Publisher:

American Physical Society (APS)

Country of Publication:

United States

Language:

English

Subject:

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; finite temperature field theory; gauge-gravity dualities; relativistic heavy-ion collisions; string theory techniques in condensed matter; transport phenomena; relativistic hydrodynamics