相关论文: Equilibrium Spacetime Correlations of the Toda Lat…

We investigate the form of equilibrium spatio-temporal correlation functions of conserved quantities, and of energy transport in the Toda lattice and in other integrable models. From numerical simulations we find that the correlations…

Passing from a microscopic discrete lattice system with many degrees of freedom to a mesoscopic continuum system described by a few coarse-grained equations is challenging. The common folklore is to take the thermodynamic limit so that the…

In this paper we consider the Toda lattice $(\mathbf{p}(t);\mathbf{q}(t))$ at thermal equilibrium, meaning that its variables $(p_j)$ and $(e^{q_j-q_{j+1}})$ are independent Gaussian and Gamma random variables, respectively. We show under…

We study the classical Toda lattice with domain wall initial conditions, for which left and right half lattice are in thermal equilibrium but with distinct parameters of pressure, mean velocity, and temperature. In the hydrodynamic regime…

The Toda lattice is an integrable system and its natural space-time stationary states are the generalized Gibbs ensembles (GGE). Of particular physical interest are then the space-time correlations of the conserved fields. To leading order…

As recently proposed, the long-time behavior of equilibrium time-correlation functions for one-dimensional systems are expected to be captured by a nonlinear extension of fluctuating hydrodynamics. We outline the predictions from the theory…

1. Introduction, 2. Dynamics of the classical Toda lattice, 3. Static properties, 4. Mean-field Dyson Brownian motion, 5. Hydrodynamics for hard rods, 6. Generalized hydrodynamic equations, 7. Linearized hydrodynamics and GGE dynamical…

Spatial correlations for sheared isothermal elastic liquids and granular liquids are theoretically investigated. Using the generalized fluctuating hydrodynamics, correlation functions for both the microscopic scale and the macroscopic scale…

We examine the scaling with activity of the emergent length scales that control the nonequilibrium dynamics of an active nematic liquid crystal, using two popular hydrodynamic models that have been employed in previous studies. In both…

We present the results of a detailed study of energy correlations at steady state for a 1-D model of coupled energy and matter transport. Our aim is to discover -- via theoretical arguments, conjectures, and numerical simulations -- how…

We have simulated energy relaxation and equilibrium dynamics in Coulomb Glasses using the random energy lattice model. We show that in a temperature range where the Coulomb Gap is already well developed, (T=0.03-0.1) the system still…

At large scales of space and time, the nonequilibrium dynamics of local observables in extensive many-body systems is well described by hydrodynamics. At the Euler scale, one assumes that each mesoscopic region independently reaches a state…

A multi-time probing of density fluctuations is introduced to investigate hidden time scales of heterogeneous dynamics in glass-forming liquids. Molecular dynamics simulations for simple glass-forming liquids are performed, and a three-time…

We show that in the equilibrium phase of glass-forming hard-sphere fluids in three dimensions, the static length scales tentatively associated with the dynamical slowdown and the dynamical length characterizing spatial heterogeneities in…

Hydrodynamic fluctuations in simple fluids under shear flow are demonstrated to be spatially correlated, in contrast to the fluctuations at equilibrium, using mesoscopic hydrodynamic simulations. The simulation results for the equal-time…

Understanding the realization of thermal equilibrium through the thermalization process in a many-body system is a fundamental and complex scientific question, bridging thermodynamics and classical dynamics and connecting to a host of…

Local thermal equilibrium generally implies the absence of heat flux within a fluid. We find the relations between a set of thermodynamic variables of a fluid on a general spacetime and those defined on a conformally connected spacetime,…

Spatial coherence of thermal fields in far- and near-field zones generated by heated half-space into vacuum is studied at essentially different thermodynamical conditions. It is shown that correlation lengths of fields in any field zone are…

We investigate experimentally three-dimensional (3D) hydrodynamic turbulence at scales larger than the forcing scale. We manage to perform a scale separation between the forcing scale and the container size by injecting energy into the…

We derive exact scaling relations for two-dimensional relativistic hydrodynamic turbulence in the inertial range of scales. We consider both the energy cascade towards large scales and the enstrophy cascade towards small scales. We…