100 Years of Brownian motion

In the year 1905 Albert Einstein published four papers that raised him to a giant in the history of science of all times. These works encompass the photon hypothesis (for which he obtained the Nobel prize in 1921), his first two papers on (special) relativity theory and, of course, his first paper on Brownian motion, entitled "Uber die von der molekularkinetischen Theorie der Warme geforderte Bewegung von in ruhenden Flussigkeiten suspendierten Teilchen'' (submitted on May 11, 1905). Thanks to Einstein intuition, the phenomenon observed by the Scottish botanist Rober Brown in 1827 - a little more than a naturalist's curiosity - becomes the keystone of a fully probabilistic formulation of statistical mechanics and a well-established subject of physical investigation which we celebrate in this Focus issue entitled - for this reason - : ``100 Years of Brownian Motion''.

[1]  P. Jung,et al.  Colored Noise in Dynamical Systems , 2007 .

[2]  F. Marchesoni,et al.  Basic Description of the Rules Leading to the Adiabatic Elimination of Fast Variables , 2007 .

[3]  R. Alicki.  General Theory and Applications to Unstable Particles , 2007 .

[4]  Gregoire Nicolis,et al.  Stochastic resonance , 2007, Scholarpedia.

[5]  H. Kleinert.  Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets , 2006 .

[6]  Jean-Philippe Bouchaud,et al.  The subtle nature of financial random walks. , 2005, Chaos.

[7]  P. Reimann,et al.  Moving backward noisily. , 2005, Chaos.

[8]  J. Łuczka,et al.  Non-Markovian stochastic processes: colored noise. , 2005, Chaos.

[9]  Manuel Morillo,et al.  Stochastic resonance: theory and numerics. , 2005, Chaos.

[10]  F. Marchesoni,et al.  Noise-assisted transport on symmetric periodic substrates. , 2005, Chaos.

[11]  C Bechinger,et al.  Colloids as model systems for problems in statistical physics. , 2005, Chaos.

[12]  Eli Pollak,et al.  Reaction rate theory: what it was, where is it today, and where is it going? , 2005, Chaos.

[13]  Martin J Zuckermann,et al.  Performance characteristics of Brownian motors. , 2005, Chaos.

[14]  F. Nori,et al.  Controlling the motion of interacting particles: homogeneous systems and binary mixtures. , 2005, Chaos.

[15]  T. Pöschel,et al.  Self-diffusion in granular gases: Green-Kubo versus Chapman-Enskog. , 2005, Chaos.

[16]  A. Einstein.  Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen [AdP 17, 549 (1905)] , 2005, Annalen der Physik.

[17]  Erwin Frey,et al.  Brownian motion: a paradigm of soft matter and biological physics , 2005, Annalen der Physik.

[18]  L. Sander,et al.  Random walks, diffusion limited aggregation in a wedge, and average conformal maps. , 2005, Chaos.

[19]  L. Schimansky-Geier,et al.  Noise induced complexity: from subthreshold oscillations to spiking in coupled excitable systems. , 2005, Chaos.

[20]  J. Ankerhold,et al.  Quantum Brownian motion with large friction. , 2004, Chaos.

[21]  P. Hänggi,et al.  Fundamental aspects of quantum Brownian motion. , 2004, Chaos.

[22]  J. Klafter,et al.  From diffusion to anomalous diffusion: a century after Einstein's Brownian motion. , 2004, Chaos.

[23]  F. Marchesoni,et al.  Brownian motors , 2004, cond-mat/0410033.

[24]  M Cencini,et al.  Brownian motion and diffusion: from stochastic processes to chaos and beyond. , 2004, Chaos.

[25]  M. A. Morales,et al.  Orientational Glasses , 2005 .

[26]  G. Parisi.  Brownian motion , 2005, Nature.

[27]  Fabio Marchesoni,et al.  Asymmetric confinement in a noisy bistable device , 2004 .

[28]  G. Zaslavsky.  Chaos, fractional kinetics, and anomalous transport , 2002 .

[29]  Debra J. Searles,et al.  The Fluctuation Theorem , 2002 .

[30]  M. Haw.  Colloidal suspensions, Brownian motion, molecular reality: a short history , 2002 .

[31]  R. Zwanzig.  Nonequilibrium statistical mechanics , 2001, Physics Subject Headings (PhySH).

[32]  A. Bader,et al.  Joseph Loschmidt, physicist and chemist , 2001 .

[33]  J. Klafter,et al.  The random walk's guide to anomalous diffusion: a fractional dynamics approach , 2000 .

[34]  P. Reimann.  Brownian motors: noisy transport far from equilibrium , 2000, cond-mat/0010237.

[35]  Quantum features of Brownian motors and stochastic resonance. , 1998, Chaos.

[36]  D. Lemons,et al.  Paul Langevin’s 1908 paper “On the Theory of Brownian Motion” [“Sur la théorie du mouvement brownien,” C. R. Acad. Sci. (Paris) 146, 530–533 (1908)] , 1997 .

[37]  C. Jarzynski.  Equilibrium free-energy differences from nonequilibrium measurements: A master-equation approach , 1997, cond-mat/9707325.

[38]  C. Jarzynski.  Nonequilibrium Equality for Free Energy Differences , 1996, cond-mat/9610209.

[39]  Peter Hänggi,et al.  Generalized langevin equations: A useful tool for the perplexed modeller of nonequilibrium fluctuations? , 1997 .

[40]  M. Shlesinger,et al.  Beyond Brownian motion , 1996 .

[41]  Jean-Baptiste Lully,et al.  The collected works , 1996 .

[42]  Peter Hänggi,et al.  Brownian rectifiers: How to convert brownian motion into directed transport , 1996 .

[43]  J. Bouchaud,et al.  Mode-coupling approximations, glass theory and disordered systems , 1995, cond-mat/9511042.

[44]  E. Cohen,et al.  Dynamical ensembles in stationary states , 1995, chao-dyn/9501015.

[45]  Kurt Wiesenfeld,et al.  Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs , 1995, Nature.

[46]  Cohen,et al.  Dynamical Ensembles in Nonequilibrium Statistical Mechanics. , 1994, Physical review letters.

[47]  Mathematical work of Norbert Wiener , 1995 .

[48]  George M. Zaslavsky,et al.  Fractional kinetic equation for Hamiltonian chaos , 1994 .

[49]  W. Gotze,et al.  Relaxation processes in supercooled liquids , 1992 .

[50]  J. Bouchaud,et al.  Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications , 1990 .

[51]  C. Angell.  Dynamic processes in ionic glasses , 1990 .

[52]  P. Hänggi,et al.  Reaction-rate theory: fifty years after Kramers , 1990 .

[53]  Wio,et al.  Path-integral formulation for stochastic processes driven by colored noise. , 1989, Physical review. A, General physics.

[54]  P. Hänggi.  Path integral solutions for non-Markovian processes , 1989 .

[55]  Sodano,et al.  Nucleation of thermal sine-Gordon solitons: Effect of many-body interactions. , 1988, Physical review letters.

[56]  Ford,et al.  On the quantum langevin equation , 1981, Physical review. A, General physics.

[57]  K. Binder,et al.  Spin glasses: Experimental facts, theoretical concepts, and open questions , 1986 .

[58]  R. Kubo.  Brownian Motion and Nonequilibrium Statistical Mechanics , 1986, Science.

[59]  F. Marchesoni.  Solitons in a random field of force: A Langevin equation approach , 1986 .

[60]  H. Risken.  The Fokker-Planck equation : methods of solution and applications , 1985 .

[61]  E. Leutheusser.  Dynamical model of the liquid-glass transition , 1984 .

[62]  F. Marchesoni,et al.  On the extension of the Kramers theory of chemical relaxation to the case of nonwhite noise , 1983 .

[63]  E. Santos,et al.  Path integrals for non-markovian processes , 1983 .

[64]  Abraham Pais,et al.  ‘Subtle Is the Lord …’: The Science and the Life of Albert Einstein by Abraham Pais (review) , 1984 .

[65]  Peter Hänggi,et al.  Stochastic processes: Time evolution, symmetries and linear response , 1982 .

[66]  H. Spohn.  Kinetic equations from Hamiltonian dynamics: Markovian limits , 1980 .

[67]  Peter Hänggi,et al.  Microdynamics and nonlinear stochastic processes of gross variables , 1980 .

[68]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[69]  Robert Graham,et al.  Path integral formulation of general diffusion processes , 1977 .

[70]  Hermann Haken,et al.  Generalized Onsager-Machlup function and classes of path integral solutions of the Fokker-Planck equation and the master equation , 1976 .

[71]  Sture Nordholm,et al.  A systematic derivation of exact generalized Brownian motion theory , 1975 .

[72]  Kyozi Kawasaki,et al.  Simple derivations of generalized linear and nonlinear Langevin equations , 1973 .

[73]  F. Haake.  Statistical treatment of open systems by generalized master equations , 1973 .

[74]  Kyozi Kawasaki,et al.  Kinetic equations and time correlation functions of critical fluctuations , 1970 .

[75]  Edward Nelson.  Dynamical Theories of Brownian Motion , 1967 .

[76]  R. Kubo.  The fluctuation-dissipation theorem , 1966 .

[77]  H. Mori.  Transport, Collective Motion, and Brownian Motion , 1965 .

[78]  Robert Zwanzig,et al.  Memory Effects in Irreversible Thermodynamics , 1961 .

[79]  R. Kubo.  Statistical-Mechanical Theory of Irreversible Processes : I. General Theory and Simple Applications to Magnetic and Conduction Problems , 1957 .

[80]  Melville S. Green,et al.  Markoff Random Processes and the Statistical Mechanics of Time‐Dependent Phenomena. II. Irreversible Processes in Fluids , 1954 .

[81]  Lars Onsager,et al.  Fluctuations and Irreversible Processes , 1953 .

[82]  Lars Onsager,et al.  Fluctuations and Irreversible Process. II. Systems with Kinetic Energy , 1953 .

[83]  Melville S. Green,et al.  Markoff Random Processes and the Statistical Mechanics of Time-Dependent Phenomena , 1952 .

[84]  H. Callen,et al.  Irreversibility and Generalized Noise , 1951 .

[85]  R. Feynman,et al.  Space-Time Approach to Non-Relativistic Quantum Mechanics , 1948 .

[86]  L. Onsager.  Reciprocal Relations in Irreversible Processes. II. , 1931 .

[87]  N Wiener,et al.  The Average of an Analytic Functional and the Brownian Movement. , 1921, Proceedings of the National Academy of Sciences of the United States of America.

[88]  N. Wiener.  The Mean of a Functional of Arbitrary Elements , 1920 .

[89]  Albert Einstein,et al.  Elementare Theorie der Brownschen) Bewegung , 1908 .

[90]  M. Smoluchowski.  Zur kinetischen Theorie der Brownschen Molekularbewegung und der Suspensionen , 1906 .

[91]  W. Sutherland,et al.  LXXV. A dynamical theory of diffusion for non-electrolytes and the molecular mass of albumin , 1905 .

[92]  A. Einstein.  Eine neue Bestimmung der Moleküldimensionen , 1905 .

[93]  R. Brown.  XXVII. A brief account of microscopical observations made in the months of June, July and August 1827, on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies , 1828 .

[94]  Stochastic processes II : Response theory and fluctuation theorems 1 ) , 2022 .