The Unequal Twins - Probability Distributions Aren't Everything

It is the common lore to assume that knowing the equation for the probability distribution function (PDF) of a stochastic model as a function of time tells the whole picture defining all other characteristics of the model. We show that this is not the case by comparing two exactly solvable models of anomalous diffusion due to geometric constraints: The comb model and the random walk on a random walk (RWRW). We show that though the two models have exactly the same PDFs, they differ in other respects, like their first passage time (FPT) distributions, their autocorrelation functions and their aging properties

Stochastic versus dynamic approach to Levy statistics in the presence of an external perturbation

We study the influence of a dissipation process on diffusion dynamics triggered by slow fluctuations. We study both strong- and weak-friction regime. When the latter regime applies, the system is attracted by the basin of either Gauss or Levy statistics according to whether the fluctuation correlation function is integrable or not. We analyze with a numerical calculation the border between the two basins of attraction.Comment: RevTex, 7 pages, 4 figures, submitted to Physics Letters

From deterministic dynamics to kinetic phenomena

We investigate a one-dimenisonal Hamiltonian system that describes a system of particles interacting through short-range repulsive potentials. Depending on the particle mean energy, $\epsilon$, the system demonstrates a spectrum of kinetic regimes, characterized by their transport properties ranging from ballistic motion to localized oscillations through anomalous diffusion regimes. We etsablish relationships between the observed kinetic regimes and the "thermodynamic" states of the system. The nature of heat conduction in the proposed model is discussed.Comment: 4 pages, 4 figure

Dynamical heat channels

We consider heat conduction in a 1D dynamical channel. The channel consists of a group of noninteracting particles, which move between two heat baths according to some dynamical process. We show that the essential thermodynamic properties of the heat channel can be evaluated from the diffusion properties of the underlying particles. Emphasis is put on the conduction under anomalous diffusion conditions. \\{\bf PACS number}: 05.40.+j, 05.45.ac, 05.60.cdComment: 4 figure

Generalized Elastic Model: thermal vs non-thermal initial conditions. Universal scaling, roughening, ageing and ergodicity

We study correlation properties of the generalized elastic model which accounts for the dynamics of polymers, membranes, surfaces and fluctuating interfaces, among others. We develop a theoretical framework which leads to the emergence of universal scaling laws for systems starting from thermal (equilibrium) or non-thermal (non-equilibrium) initial conditions. Our analysis incorporates and broadens previous results such as observables' double scaling regimes, (super)roughening and anomalous diffusion, and furnishes a new scaling behavior for correlation functions at small times (long distances). We discuss ageing and ergodic properties of the generalized elastic model in non-equilibrium conditions, providing a comparison with the situation occurring in continuous time random walk. Our analysis also allows to assess which observable is able to distinguish whether the system is in or far from equilibrium conditions in an experimental set-up

Molecular motor with a build-in escapement device

We study dynamics of a classical particle in a one-dimensional potential, which is composed of two periodic components, that are time-independent, have equal amplitudes and periodicities. One of them is externally driven by a random force and thus performs a diffusive-type motion with respect to the other. We demonstrate that here, under certain conditions, the particle may move unidirectionally with a constant velocity, despite the fact that the random force averages out to zero. We show that the physical mechanism underlying such a phenomenon resembles the work of an escapement-type device in watches; upon reaching certain level, random fluctuations exercise a locking function creating the points of irreversibility in particle's trajectories such that the particle gets uncompensated displacements. Repeated (randomly) in each cycle, this process ultimately results in a random ballistic-type motion. In the overdamped limit, we work out simple analytical estimates for the particle's terminal velocity. Our analytical results are in a very good agreement with the Monte Carlo data.Comment: 7 pages, 4 figure