Hydrodynamic magneto-transport in holographic charge density wave states

We employ hydrodynamics and gauge/gravity to study magneto-transport in phases of matter where translations are broken (pseudo-)spontaneously. First we provide a hydrodynamic description of systems where translations are broken homogeneously at nonzero lattice pressure and magnetic field. This allows us to determine analytic expressions for all the relevant transport coefficients. Next we construct holographic models of those phases and determine all the DC conductivities in terms of the dual black hole geometry. Combining the hydrodynamic and holographic descriptions we obtain analytic expression for the AC thermo-electric correlators. These are fixed in terms of the black hole geometry and a pinning frequency we determine numerically. We find an excellent agreement between our hydrodynamic and holographic descriptions and show that the holographic models are good avatars for the study of magneto-phonons.

Relativistic spin hydrodynamics with torsion and linear response theory for spin relaxation

Using the second law of local thermodynamics and the first-order Palatini formalism, we formulate relativistic spin hydrodynamics for quantum field theories with Dirac fermions, such as QED and QCD, in a torsionful curved background. We work in a regime where spin density, which is assumed to relax much slower than other non-hydrodynamic modes, is treated as an independent degree of freedom in an extended hydrodynamic description. Spin hydrodynamics in our approach contains only three non-hydrodynamic modes corresponding to a spin vector, whose relaxation time is controlled by a new transport coefficient: the rotational viscosity. We study linear response theory and observe an interesting mode mixing phenomenon between the transverse shear and the spin density modes. We propose several field-theoretical ways to compute the spin relaxation time and the rotational viscosity, via the Green-Kubo formula based on retarded correlation functions.

Hydrodynamics

This chapter begins the argument that the best way to understand the relations of relative autonomy between theories at different scales is through a mesoscale hydrodynamic description of many-body systems. It focuses on the evolution of conserved quantities of those systems in near, but out of equilibrium states. A relatively simple example is presented of a system of spins where the magnetization is the conserved quantity of interest. The chapter introduces the concepts of order parameters, of local quantities, and explains why we should be focused on the gradients of densities that inhabit the mesoscale between the scale of the continuum and that of the atomic. It introduces the importance of correlation functions and linear response.

Brownian Motion

This chapter discusses the phenomenon of Brownian motion and Einstein’s pioneering arguments that explained various aspects of it. It shows how Einstein presented two arguments that relate directly to the themes of this book. The first is the upscaling or homogenization to effective continuum parameters from correlational structures in representative volume elements at mesoscales. Einstein’s argument is shown to answer the question about autonomy raised in Chapter 2. The second relates to the Fluctuation-Dissipation theorem. This theorem justifies the mesoscale hydrodynamic description of many-body systems and Einstein provided the first statement of the theorem.

Coarse Graining Nonisothermal Microswimmer Suspensions

We investigate coarse-grained models of suspended self-thermophoretic microswimmers. Upon heating, the Janus spheres, with hemispheres made of different materials, induce a heterogeneous local solvent temperature that causes the self-phoretic particle propulsion. Starting from molecular dynamics simulations that schematically resolve the molecular composition of the solvent and the microswimmer, we verify the coarse-grained description of the fluid in terms of a local molecular temperature field, and its role for the particle’s thermophoretic self-propulsion and hot Brownian motion. The latter is governed by effective nonequilibrium temperatures, which are measured from simulations by confining the particle position and orientation. They are theoretically shown to remain relevant for any further spatial coarse-graining towards a hydrodynamic description of the entire suspension as a homogeneous complex fluid.

Chiral hydrodynamics in strong external magnetic fields

We construct the general hydrodynamic description of (3+1)-dimensional chiral charged (quantum) fluids subject to a strong external magnetic field with effective field theory methods. We determine the constitutive equations for the energy-momentum tensor and the axial charge current, in part from a generating functional. Furthermore, we derive the Kubo formulas which relate two-point functions of the energy-momentum tensor and charge current to 27 transport coefficients: 8 independent thermodynamic, 4 independent non-dissipative hydrodynamic, and 10 independent dissipative hydrodynamic transport coefficients. Five Onsager relations render 5 more transport coefficients dependent. We uncover four novel transport effects, which are encoded in what we call the shear-induced conductivity, the two expansion-induced longitudinal conductivities and the shear-induced Hall conductivity. Remarkably, the shear-induced Hall conductivity constitutes a novel non-dissipative transport effect. As a demonstration, we compute all transport coefficients explicitly in a strongly coupled quantum fluid via holography.