Brownian motors

In systems possessing a spatial or dynamical symmetry breaking, thermal Brownian motion combined with unbiased, non‐equilibrium noise gives rise to a channelling of chance that can be used to exercise control over systems at the micro‐ and even on the nano‐scale. This theme is known as the “Brownian motor” concept. The constructive role of (the generally overdamped) Brownian motion is exemplified for a noise‐induced transport of particles within various set‐ups. We first present the working principles and characteristics with a proof‐of‐principle device, a diffusive temperature Brownian motor. Next, we consider very recent applications based on the phenomenon of signal mixing. The latter is particularly simple to implement experimentally in order to optimize and selectively control a rich variety of directed transport behaviors. The subtleties and also the potential for Brownian motors operating in the quantum regime are outlined and some state‐of‐the‐art applications, together with future roadways, are presented.

[1]  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.

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

[3]  P. Hänggi,et al.  Nonlinear signal mixing in a ratchet device , 2004 .

[4]  Franco Nori,et al.  A Superconducting Reversible Rectifier That Controls the Motion of Magnetic Flux Quanta , 2003, Science.

[5]  Sven Matthias,et al.  Asymmetric pores in a silicon membrane acting as massively parallel brownian ratchets , 2003, Nature.

[6]  S. Savel'ev,et al.  Experimentally realizable devices for controlling the motion of magnetic flux quanta in anisotropic superconductors , 2002, Nature materials.

[7]  Heiner Linke,et al.  Ratches and Brownian motors: Basics, experiments and applications , 2002 .

[8]  Hongqi Xu,et al.  Quantum ratchets and quantum heat pumps , 2002 .

[9]  Peter Hänggi,et al.  Introduction to the physics of Brownian motors , 2001 .

[10]  Luis Moroder,et al.  Single-Molecule Optomechanical Cycle , 2002, Science.

[11]  Linke,et al.  Experimental tunneling ratchets , 1999, Science.

[12]  Stokes' drift: An exact result , 1999 .

[13]  C. Broeck,et al.  Coupled Brownian motors: Anomalous hysteresis and zero-bias negative conductance , 1999 .

[14]  P. Hänggi,et al.  Quantum rectifiers from harmonic mixing , 1998 .

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

[16]  H. Grabert,et al.  Phase diffusion and charging effects in Josephson junctions , 1998, cond-mat/9801172.

[17]  R. Astumian Thermodynamics and kinetics of a Brownian motor. , 1997, Science.

[18]  I. Sokolov,et al.  Non-equilibrium directed diffusion and inherently irreversible heat engines , 1997 .

[19]  P. Hänggi,et al.  Noise-induced transport in symmetric periodic potentials: White shot noise versus deterministic noise , 1996 .

[20]  P. Hänggi,et al.  Brownian motors driven by temperature oscillations , 1996 .

[21]  Andrew F. Rex Maxwell’s Demon , 1996 .

[22]  Peter Hänggi,et al.  White-Noise-Induced Transport in Periodic Structures , 1995 .

[23]  Roland Bartussek,et al.  Brownsche Motoren: Wie aus Brownscher Bewegung makroskopischer Transport wird , 1995 .

[24]  Peter Hänggi,et al.  Periodically Rocked Thermal Ratchets , 1994 .

[25]  L. Duenkel,et al.  Topics in Current Physics , 1991 .

[26]  Andrew F. Rex,et al.  Maxwell's Demon, Entropy, Information, Computing , 1990 .

[27]  Gert-Ludwig Ingold,et al.  Quantum Brownian motion: The functional integral approach , 1988 .

[28]  F. Marchesoni Harmonic mixing signal: doubly dithered ring laser gyroscope , 1986 .

[29]  Peter Talkner,et al.  The failure of the quantum regression hypothesis , 1986 .

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

[31]  A. Hald,et al.  T. N. Thiele's Contributions to Statistics' , 1981 .

[32]  Peter Fulde,et al.  Theoretical models for superionic conductors , 1980 .

[33]  T. Geisel Modulation and incommensurability in a superionic conductor , 1979 .

[34]  K. Seeger,et al.  HARMONIC MIXING OF MICROWAVES BY WARM ELECTRONS IN GERMANIUM , 1966 .

[35]  A. Einstein Theoretische Bemerkungen Über die Brownsche Bewegung , 1907 .

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

[37]  A. Einstein Zur Theorie der Brownschen Bewegung , 1906 .

[38]  Felix M. Exner Notiz zu Brown's Molecularbewegung , 1900 .

[39]  L. Bachelier,et al.  Théorie de la spéculation , 1900 .

[40]  L. Rayleigh,et al.  LIII. Dynamical problems in illustration of the theory of gases , 1891 .

[41]  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 .