Focus on Brownian Motion and Diffusion in the 21st Century
Authors: Hänggi Peter , Luczka Jurek , Talkner Peter 
Published: February 2005

Without doubt, the problem of Brownian motion has played a guiding role in the development for both the foundations of thermodynamics and the dynamical aspects of statistical physics. The development of the phenomenon of Brownian motion based on the molecular-kinetic theory of heat provides a link between the microscopic dynamics and the macroscopic phenomena such as diffusion and fluctuation phenomena. It has also provided a first link between the macroscopic response and the equilibrium fluctuation characteristics via an early form of the ubiquitous fluctuation-dissipation theorem: the Einstein relation that relates the mobility to the diffusion strength.
The topic of Brownian motion has likewise inspired many scientists to deploy a consistent treatment of phenomena far from thermal equilibrium via such concepts as the Fokker–Planck or master equation descriptions of noisy nonlinear dynamics in such diverse areas as soft matter physics, surface science, solid state physics and chemical kinetics. In recent years this theme has also increasingly impacted upon the life sciences and even extends to areas such as cosmology, astrophysics and econophysics.
This celebratory Focus Issue in New Journal of Physics is not only timely but also circumstantiates that this research topic is very much alive and indeed multifaceted. As Guest Editors we share the confident belief that the contributions by leading practitioners from a diverse range of backgrounds will together provide a fair and accurate snapshot of the current state of this rich and interdisciplinary research field. Last but not least, we hope that this issue will stimulate readers into pursuing research of their own in the exciting areas represented.

Focus on Brownian Motion and Diffusion in the 21st Century Contents

Stochastic resonance in the presence of slowly varying control parameters
C Nicolis and G Nicolis

Diffusion processes and memory effects
Anatolii V Mokshin, Renat M Yulmetyev and Peter Hänggi

From Maxwell demon to Brownian motor
C Van den Broeck, P Meurs and R Kawai

On the connection between biased dichotomous diffusion and the one-dimensional Dirac equation
V Balakrishnan and S Lakshmibala

Branching of nucleation paths in a metastable lattice gas with Metropolis dynamics
Vitaly A Shneidman

Does one-dimensional (1D) adatom and cluster diffusion of Pt on the Pt(110)-(1 × 2) surface lead to 1D ripening?
T R Linderoth, S Horch, L Petersen, E Lægsgaard, I Stensgaard and F Besenbacher

Statistics of transition times, phase diffusion and synchronization in periodically driven bistable systems
Peter Talkner, Lukasz Machura, Michael Schindler, Peter Hänggi and Jerzy Luczka

Molecular dynamics under confinement to one dimension: options of measurement and accessible information
Jörg Kärger, Rustem Valiullin and Sergey Vasenkov

Bulk-mediated surface diffusion: non-Markovian desorption dynamics
Jorge A Revelli, Carlos E Budde, Domingo Prato and Horacio S Wio

Thermal activation by power-limited coloured noise
Peter Jung, Alexander Neiman, Muhammad K N Afghan, Suhita Nadkarni and Ghanim Ullah

Noise-sustained and controlled synchronization of stirred excitable media by external forcing
Changsong Zhou and Jürgen Kurths

Jump rate and jump probabilities in the two-dimensional strong-collision model
R Ferrando, M Mazroui, R Spadacini and G E Tommei

Brownian motion in a granular fluid
James W Dufty and J Javier Brey

Kinetics of subdiffusion-assisted reactions: non-Markovian stochastic Liouville equation approach
A I Shushin

Continuum limit theory of absorption in the presence of dissipation
Reuven Ianconescu, Mikhail G Brik and Eli Pollak

Tracking of single molecules as a powerful method to characterize diffusivity of organic species in mesoporous materials
Christian Hellriegel, Johanna Kirstein and Christoph Bräuchle

A model for noise effects on fibre tract trajectories in diffusion tensor imaging: theory and simulations
Marián Boguñá, Sinisa Pajevic, Peter J Basser and George H Weiss

Description of atomic friction as forced Brownian motion
Peter Reimann and Mykhaylo Evstigneev

What is special about diffusion on scale-free nets?
Erik M Bollt and Daniel ben-Avraham

Time-dependent friction and solvation time correlation function
Alok Samanta, Sk Musharaf Ali and Swapan K Ghosh

Observing Brownian motion and measuring temperatures in vibration-fluidized granular matter
Patrick Mayor, Gianfranco D'Anna, Alain Barrat and Vittorio Loreto

Transport and diffusion on crystalline surfaces under external forces
Katja Lindenberg, A M Lacasta, J M Sancho and A H Romero

Disordered iterated maps: spectral properties, escape rates and anomalous transport
Andreas Fichtner and Günter Radons

Exact substitute processes for diffusion–reaction systems with local complete exclusion rules
Michael Schulz and Peter Reineker

Lyapunov modes in soft-disk fluids
Christina Forster and Harald A Posch

Video microscopy and micromechanics studies of one- and two-dimensional colloidal crystals
Alexandros Pertsinidis and Xinsheng Sean Ling

Position-dependent diffusion coefficients and free energies from Bayesian analysis of equilibrium and replica molecular dynamics simulations
Gerhard Hummer

Mesoscopic thermodynamics of stationary non-equilibrium states
I Santamaría-Holek, J M Rubí and A Pérez-Madrid

Population explosion suppressed by noise: stationary distributions and how to simulate them
P F Góra

The colour of thermal noise in classical Brownian motion: a feasibility study of direct experimental observation
Kirstine Berg-Sørensen and Henrik Flyvbjerg

On diffusion of large matrices
Ewa Gudowska-Nowak, Romuald A Janik, Jerzy Jurkiewicz and Maciej A Nowak

Mixing and spectral-correlation properties of chaotic and stochastic systems: numerical and physical experiments
V S Anishchenko, G A Okrokvertskhov, T E Vadivasova and G I Strelkova

Brownian motion, dynamical randomness and irreversibility
Pierre Gaspard

Experimentally realizable devices for domain wall motion control
Sergey Savel'ev, Alexander Rakhmanov and Franco Nori

Stochastic pure states for quantum Brownian motion
Walter T Strunz

Transport properties of nanopores in electrolyte solutions: the diffusional model and surface currents
A Fulinski, I Kosinska and Z Siwy

Peter Hänggi, Universität Augsburg, Germany
Jurek Luczka, University of Silesia, Katowice, Poland
Peter Talkner, Universität Augsburg, Germany