Causality and dissipation in relativistic polarizable fluids

Abstract

We analyze the breakdown of causality for the perfect fluid limit in a medium with polarizeability. We show that to restore causality a relaxation term linking vorticity and polarization, analogous to the Israel-Stewart term linking viscous forces and gradients,is required. This term provides a minimum amount of dissipation a locally thermalized relativistic medium with polarizeability must have, independently of its underlying degrees of freedom. For ferromagnetic materials an infrared acausal mode remains, which we interpret as a Banks-Casher mode signaling spontaneous magnetization. With these ingredients, we propose a candidate for a fully causal Lagrangian of a relativistic polarizeable system near the perfect fluid limit.The question of weather there exists a universal limit to viscosity and/or dissipation (parameterized, in relativistic systems by the viscosity over entropy ratio η/s) is both profound and difficult to handle. On a fundamental level, it is plausible to argue that quantum uncertainty gives rise to fluctuations which dissipate information. However, the unitarity of quantum theory is difficult to reconcile rigorously with dissipation. The usual procedure, given a microscopic theory, is to assume thermal equilibrium and then use correlators obtained from finite-temperature field theory to calculate viscosity [1]. This allows us in principle to calculate transport coefficients given a thermally equilibrated microscopic theory which is also tractable. However, since relativistic systems with low viscosity are usually strongly coupled, this is a very blunt instrument for claiming "universal" limits.Thus, a fundamental limit has been claimed decades ago by combining the uncertainty principle with Boltzmann's derivation of viscosity [2], η/s ∼ O (0.1). While this is a plausible order-of-magnitude estimate, it was always clear that Boltzmann's derivation should not generally apply to strongly coupled quantum fields. More recently, Gauge-gravity correspondence allowed us to conclude [3] that theories with a classical gravity dual have η/s = (4π) −1 in their strong-coupling limit. The universality of this limit is a consequence of the black-hole no-hair theorem, and hence it critically depends on the existence of a classical gravity dual, namely a planar limit and a conformal strongly coupled fixed point. Counter examples have been argued for beyond this limit [4].These difficulties illustrate that most likely one cannot get a lower limit from top-down arguments, where hydrodynamics appears as a limit of a known microscopic theory. A bottom-up constraint, based on effective field theory constraints such as low-energy unitarity, causality, and convergence of the gradient expansion are necessary. Attempts in this direction can be formulated in terms of a basic ambiguity within hydrodynamics: The fact that in the low viscosity limit thermal fluctuations will propagate as hydrodynamic modes, and the Kubo formula will need to be "renormalized" to take this into account [5]. In [5] the renormalization happen...

Wigner function approach to polarization-vorticity coupling and hydrodynamics with spin

“…Recent measurements of the Λ-hyperon spin polarization in heavy-ion collisions by the STAR experiment [1,2] have inspired a broad interest in the theoretical studies related to spin polarization and vorticity formation. The results of various investigations that refer to: the spin-orbit coupling [3,4,5,6,7], statistical properties of matter in global equilibrium [8,9,10,11,12,13], kinetic models of spin dynamics [14,15,16,17], hydrodynamics with triangle anomalies [18,19] and the Lagrangian formulation of hydrodynamics [20,21,22] have been reported in this context.…”

Spin polarization evolution in a boost-invariant hydrodynamical background

“…In the future, it would be interesting to explore in more detail the relation of the framework given in Ref. [5] to anomalous hydrodynamics [31,32] and the Lagrangian formulation of hydrodynamics [33][34][35].…”

Fate of spin polarization in a relativistic fluid: An entropy-current analysis

“…More recently, "ideal" relativistic hydrodynamics with spin was proposed in the context of the QGP [9] (See also Refs. [10][11][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.…”

“…Linear mode analysis.-Relativistic hydrodynamic equations with spin are obtained by plugging the constitutive relations (12) and (13) into the conservation laws (1). Below, we consider linear perturbations on top of global thermal equilibrium, and solve the hydrodynamic equations to discuss the dynamic evolution of the (non-)hydrodynamic modes in a spinful relativistic fluid.…”