Physics Letters B 795 (2019) 100–106
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Fate of spin polarization in a relativistic fluid: An entropy-current
analysis
Koichi Hattori
a,b
, Masaru Hongo
c,d,∗
, Xu-Guang Huang
a,e
, Mamoru Matsuo
f,g,h
,
Hidetoshi Taya
a
a
Physics Department and Center for Field Theory and Particle Physics, Fudan University, Shanghai 200433, China
b
Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
c
RIKEN iTHEMS, RIKEN, Wako 351-0198, Japan
d
Research and Education Center for Natural Sciences, Keio University, Yokohama, Kanagawa 223-8521, Japan
e
Key Laboratory of Nuclear Physics and Ion-beam Application (MOE), Fudan University, Shanghai 200433, China
f
Kavli Institute of Theoretical Sciences, University of Chinese Academy of Sciences, 19 Yuquan Road, Beijing 100049, China
g
RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
h
Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, 319-1195, Japan
a r t i c l e i n f o a b s t r a c t
Article history:
Received
7 February 2019
Received
in revised form 15 May 2019
Accepted
26 May 2019
Available
online 4 June 2019
Editor:
J.-P. Blaizot
We derive relativistic hydrodynamic equations with a dynamical spin degree of freedom on the basis
of an entropy-current analysis. The first and second laws of local thermodynamics constrain possible
structures of the constitutive relations including a spin current and the antisymmetric part of the
(canonical) energy-momentum tensor. Solving the obtained hydrodynamic equations within the linear-
mode
analysis, we find spin-diffusion modes, indicating that spin density is damped out after a
characteristic time scale controlled by transport coefficients introduced in the antisymmetric part of the
energy-momentum tensor in the entropy-current analysis. This is a consequence of mutual convertibility
between spin and orbital angular momentum.
© 2019 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
Recent experimental developments opened a new avenue to study spin-dependent observables. For example, in relativistic heavy-ion
collisions, the spin polarization of hyperons has been measured [1]. The result suggests that a fraction of quark spin (and perhaps
gluon spin) in the hyperons is aligned along a particular direction, and in turn implies that a quark-gluon plasma (QGP) carries significant
magnitudes of angular momentum and/or vorticity which cause the spin alignments. On the other hand, dynamics of spin is also a hot
subject in condensed matter physics, especially in the field of spintronics, where generation of a spin current—a flow of spin angular
momentum—is one of the key issues (see Ref. [2]for a review).
To
describe macroscopic dynamics of spin, it is desirable to generalize hydrodynamics to a spinful fluid. In the field of spintronics, a
nonrelativistic framework of spin hydrodynamics has been utilized for describing the spin-current generation in the presence of a coupling
between spin and vorticity in elastic materials [3,4]as well as in liquid metals [5,6]. A similar framework was also used to describe the
so-called micropolar fluids [7,8]. More recently, “ideal” relativistic hydrodynamics with spin was proposed in the context of the QGP [9]
(See
also Refs. [10–12]for recent attempts to apply a Lagrangian description of the spinful relativistic fluid), in which spin is regarded as a
conserved quantity in the leading-order of a gradient expansion. However, the aforementioned nonrelativistic formulation has shown that
spin is not conserved even at the leading order.
In
this Letter, we elaborate a relativistic framework to resolve the disharmony between the nonrelativistic and relativistic formulations
and to describe the spin-dependent spacetime evolution of relativistic fluids like the QGP. We employ a phenomenological entropy-current
*
Corresponding author.
E-mail
addresses: koichi.hattori@outlook.com (K. Hattori), masaru.hongo@riken.jp (M. Hongo), huangxuguang@fudan.edu.cn (X.-G. Huang), mamoru@ucas.ac.cn
(M. Matsuo),
h_taya@fudan.edu.cn (H. Taya).
https://doi.org/10.1016/j.physletb.2019.05.040
0370-2693/
© 2019 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.