We have considered heat conduction in a one-dimensional mass disordered harmonic chain of $N$ particles connected to two Langevin type reservoirs at different temperatures. An exact expression for the boundary heat current-current auto-correlation function in the non-equilibrium steady state (NESS) is obtained in terms of non-equilibrium phonon Green's functions. The time integral of the correlation function gives expected result, both in non-equilibrium as well as equilibrium cases. Using the form of this correlation function we show that asymptotic system size dependence of current fluctuation in NESS for a mass disordered harmonic chain is $N^{-α}$ for different boundary conditions. For free and fixed boundary conditions we get $α=1/2$ and 3/2 respectively, while for pinned case the fluctuation decays exponentially with system size.
Application of CTRW to dipole hopping transport is considered. Correct versions of derivation of the CTRW-equations are presented. Existence of different forms of memory kernels is demonstrated. Correction of Scher-Lax memory kernel within geometrical memory approach is fulfilled in accordance with leading terms of concentration expansion. Approximate solution for autocorrelation function is constructed. Modern state of numerical simulation and experimental measurements of autocorrelation function in nuclear polarization delocalization is described.
Probabilistic cellular automata (PCA) are used to model a variety of discrete spatially extended systems undergoing parallel-updating. We propose an embedding of a number of classical nonequilibrium concepts in the PCA-world. We start from time-symmetric PCA, satisfying detailed balance, and we give their Kubo formula for linear response. Close-to-detailed balance we investigate the form of the McLennan distribution and the minimum entropy production principle. More generally, when time-symmetry is broken in the stationary process, there is a fluctuation symmetry for a corresponding entropy fl…
By using recent developments for the Langevin dynamics of spatially asymmetric systems, we routinely generalize the Onsager-Machlup fluctuation theory of the second order in time. In this form, it becomes applicable to fluctuating variables, including hydrodynamic currents, in equilibrium as well as nonequilibrium steady states. From the solution of the obtained stochastic equations we derive an analytical expression for the time autocorrelation function of a general fluctuating quantity. This theoretical result is then tested in a study of a shear flow by molecular dynamics simulations. The p…
Molecular dynamics in binary mixtures of water and glycerol was studied by measuring the spectrum of water velocity auto-correlation in the frequency range from 0.05 to 10 kHz by using the NMR method of modulated gradient spin echo. The method shows that the diversity of diffusion signature in the short spin trajectories provides information about heterogeneity of molecular motion due to the motion in the micro-vortexes of hydrodynamic fluctuation, which is especially pronounced for the mixtures with the low glycerol content. As concentration of glycerol increases above 10vol%, a new feature o…
We propose a Fokker-Planck equation (FPE) theory to describe stochastic fluctuation and relaxation processes of lattice vibration at a wide range of conditions, including those beyond the phonon gas (PG) limit. Using the time-dependent, multiple state-variable probability function of a FPE, we first derive time-correlation functions of lattice heat currents in terms of correlation functions among multiple vibrational modes, and subsequently predict the thermal conductivity based on the Green-Kubo formalism. When the kinetic transport theories are valid, this FPE not only predicts a thermal con…
We explore thermalization and quantum dynamics in a one-dimensional disordered SU(2)-symmetric Floquet model, where a many-body localized phase is prohibited by the non-abelian symmetry. Despite the absence of localization, we find an extended nonergodic regime at strong disorder where the system exhibits nonthermal behaviors. In the strong disorder regime, the level spacing statistics exhibit neither a Wigner-Dyson nor a Poisson distribution, and the spectral form factor does not show a linear-in-time growth at early times characteristic of random matrix theory. The average entanglement entro…
