Random walk is a fundamental concept with applications ranging from quantum physics to
econometrics. Remarkably, one specific model of random walks appears to be ubiquitous …

In this article we demonstrate the very inspiring role of the continuous-time random walk
(CTRW) formalism, the numerous modifications permitted by its flexibility, its various …

With focus on anharmonic chains, we develop a nonlinear version of fluctuating
hydrodynamics, in which the Euler currents are kept to second order in the deviations from …

Consider anomalous energy spread in solid phases, ie,⟨ Δ x 2 (t)⟩ E≡∫(x−⟨ x⟩ E) 2 ρ E
(x, t) dx∝ t β, as induced by a small initial excess energy perturbation distribution ρ E (x, t …

Heat conduction is an important energy transport process in nature. Phonon is the major
energy carrier for heat in semiconductors and dielectric materials. In analogy to Ohm's law of …

We study the equilibrium time correlations for the conserved fields of classical anharmonic
chains and argue that their dynamic correlator can be predicted on the basis of nonlinear …

One-dimensional chains are used as a fundamental model of condensed matter, and have
constituted the starting point for key developments in nonlinear physics and complex …

Recent work has developed a nonlinear hydrodynamic fluctuation theory for a chain of
coupled anharmonic oscillators governing the conserved fields, namely, stretch, momentum …

Strong anomalous diffusion, where⟨| x (t)| q⟩∼ tq ν (q) with a nonlinear spectrum ν (q)≠
const, is wide spread and has been found in various nonlinear dynamical systems and …

It has been observed in many numerical simulations, experiments and from various
theoretical treatments that heat transport in one-dimensional systems of interacting particles …