Related papers: On the correlation functions in stable first-order…
In the first part of these short lecture notes, we will present an introduction on (auto-)correlation functions and linear-response functions in the language of a physicist. In particular, the fluctuation-dissipation theorem in classical…
The success of spectroscopy to characterise equilibrium fluids, for example the heat capacity ratio, suggests a parallel approach for active fluids. Here, we start from a hydrodynamic description of chiral active fluids composed of spinning…
We analytically examine fluctuations of vorticity excited by an external random force in two-dimensional fluid. We develop the perturbation theory enabling one to calculate nonlinear corrections to correlation functions of the flow…
The nonequilibrium hydrodynamic correlations of a Multiparticle-Collision-Dynamics (MPC) fluid in shear flow are studied by analytical calculations and simulations. The Navier-Stokes equations for a MPC fluid are linearized about the shear…
We investigate the interplay between hydrodynamic fluctuations and initial longitudinal fluctuations for their effects on the rapidity decorrelation of collective flow in high-energy nuclear collisions. We use a (3+1)-dimensional integrated…
We review the recent advances on exact results for dynamical correlation functions at large scales and related transport coefficients in interacting integrable models. We discuss Drude weights, conductivity and diffusion constants, as well…
We study the dynamics of density fluctuations in purely diffusive systems away from equilibrium. Under some conditions the static density correlation function becomes long-ranged. We then analyze this behavior in the framework of…
We construct the general theory of first-order relativistic hydrodynamics for a fluid exhibiting a chiral anomaly, including all possible viscous terms allowed by symmetry. Using standard techniques, we compute the necessary and sufficient…
The correlation theory of the thermal hydrodynamic fluctuations of liquids with internal spin within a spherical cavity is developed. For the hydrodynamic fields of such a liquid, linearized equations with random thermal sources are used.…
A computational approach is introduced for the study of the rheological properties of complex fluids and soft materials. The approach allows for a consistent treatment of microstructure elastic mechanics, hydrodynamic coupling, thermal…
We devise an iterative scheme for numerically calculating dynamical two-point correlation functions in integrable many-body systems, in the Eulerian scaling limit. Expressions for these were originally derived in Ref. [1] by combining the…
We investigate long-range correlations (LRCs) induced by shear flow using the molecular dynamics (MD) simulation. We observe the LRCs by comparing the MD results with the linearized fluctuating hydrodynamics (LFH). We find that the MD…
We solve numerically the equations of nonlinear fluctuating hydrodynamics (NFH) for the supercooled liquid. The time correlation of the density fluctuations in equilibrium obtained here shows quantitative agreement with molecular…
The present study is based on a recent success of the second-order stochastic fluctuation theory in describing time autocorrelations of equilibrium and nonequilibrium physical systems. In particular, it was shown to yield values of the…
The addition of suitable volume forces to the Navier-Stokes equation allows to simulate flows in the presence of a homogeneous shear. Because of the explicit form of the driving the flows are accessible to rigorous mathematical treatment…
We derive a relation similar to the fluctuation theorem for work done on a system obeying Langevin dynamics with thermal and colored noises. Then, we propose a method of calculating the correlation function of the colored noise by using…
We study $(m)$-type connected correlation functions of OPE blocks with respect to one spatial region in two dimensional conformal field theory. We find logarithmic divergence for these correlation functions. We justify the logarithmic…
Within the relaxation time approximation under a constant mass profile, we investigate the collective dynamics of a system of massive relativistic particles described by the Maxwell-Boltzmann equilibrium distribution. We analytically derive…
We study the fluctuations of the autocorrelation and autoresponse functions and, in particular, their variances and co-variance. In a first general part of the Article, we show the equivalence of the variance of the response function with…
The fluctuation theorem is a pivotal result of statistical physics. It quantifies the probability of observing fluctuations which are in violation of the second law of thermodynamics. More specifically, it quantifies the ratio of the…