Escape rate of an active Brownian particle over a potential barrier

We study the dynamics of an active Brownian particle with a nonlinear friction function located in a spatial cubic potential. For strong but finite damping, the escape rate of the particle over the spatial potential barrier shows a nonmonotonic dependence on the noise intensity. We relate this behavior to the fact that the active particle escapes from a limit cycle rather than from a fixed point and that a certain amount of noise can stabilize the sojourn of the particle on this limit cycle

Steering the potential barriers: entropic to energetic

We propose a new mechanism to alter the nature of the potential barriers when a biased Brownian particle under goes a constrained motion in narrow, periodic channel. By changing the angle of the external bias, the nature of the potential barriers changes from purely entropic to energetic which in turn effects the diffusion process in the system. At an optimum angle of the bias, the nonlinear mobility exhibits a striking bell-shaped behavior. Moreover, the enhancement of the scaled effective diffusion coefficient can be efficiently controlled by the angle of the bias. This mechanism enables the proper design of channel structures for transport of molecules and small particles. The approximative analytical predictions have been verified by precise Brownian dynamic simulations.Comment: (6 pages, 7 figures) Submitted to PR

Controlling diffusive transport in confined geometries

We analyze the diffusive transport of Brownian particles in narrow channels with periodically varying cross-section. The geometrical confinements lead to entropic barriers, the particle has to overcome in order to proceed in transport direction. The transport characteristics exhibit peculiar behaviors which are in contrast to what is observed for the transport in potentials with purely energetic barriers. By adjusting the geometric parameters of the channel one can effectively tune the transport and diffusion properties. A prominent example is the maximized enhancement of diffusion for particular channel parameters. The understanding of the role of channel-shape provides the possibility for a design of stylized channels wherein the quality of the transport can be efficiently optimized.Comment: accepted for publication in Acta Physica Polonica

Entropic stochastic resonance: the constructive role of the unevenness

We demonstrate the existence of stochastic resonance (SR) in confined systems arising from entropy variations associated to the presence of irregular boundaries. When the motion of a Brownian particle is constrained to a region with uneven boundaries, the presence of a periodic input may give rise to a peak in the spectral amplification factor and therefore to the appearance of the SR phenomenon. We have proved that the amplification factor depends on the shape of the region through which the particle moves and that by adjusting its characteristic geometric parameters one may optimize the response of the system. The situation in which the appearance of such entropic stochastic resonance (ESR) occurs is common for small-scale systems in which confinement and noise play an prominent role. The novel mechanism found could thus constitute an important tool for the characterization of these systems and can put to use for controlling their basic properties.Comment: 8 pages, 8 figure

Biased diffusion in confined media: Test of the Fick-Jacobs approximation and validity criteria

We study biased, diffusive transport of Brownian particles through narrow, spatially periodic structures in which the motion is constrained in lateral directions. The problem is analyzed under the perspective of the Fick-Jacobs equation which accounts for the effect of the lateral confinement by introducing an entropic barrier in a one dimensional diffusion. The validity of this approximation, being based on the assumption of an instantaneous equilibration of the particle distribution in the cross-section of the structure, is analyzed by comparing the different time scales that characterize the problem. A validity criterion is established in terms of the shape of the structure and of the applied force. It is analytically corroborated and verified by numerical simulations that the critical value of the force up to which this description holds true scales as the square of the periodicity of the structure. The criterion can be visualized by means of a diagram representing the regions where the Fick-Jacobs description becomes inaccurate in terms of the scaled force versus the periodicity of the structure.Comment: 20 pages, 7 figure

Double Entropic Stochastic Resonance

We demonstrate the appearance of a purely entropic stochastic resonance (ESR) occurring in a geometrically confined system, where the irregular boundaries cause entropic barriers. The interplay between a periodic input signal, a constant bias and intrinsic thermal noise leads to a resonant ESR-phenomenon in which feeble signals become amplified. This new phenomenon is characterized by the presence of two peaks in the spectral amplification at corresponding optimal values of the noise strength. The main peak is associated with the manifest stochastic resonance synchronization mechanism involving the inter-well noise-activated dynamics while a second peak relates to a regime of optimal sensitivity for intra-well dynamics. The nature of ESR, occurring when the origin of the barrier is entropic rather than energetic, offers new perspectives for novel investigations and potential applications. ESR by itself presents yet another case where one constructively can harvest noise in driven nonequilibrium systems.Comment: 6 pages, 7 figures ; Europhys. Lett., in press (2009

Entropic Stochastic Resonance

We present a novel scheme for the appearance of Stochastic Resonance when the dynamics of a Brownian particle takes place in a confined medium. The presence of uneven boundaries, giving rise to an entropic contribution to the potential, may upon application of a periodic driving force result in an increase of the spectral amplification at an optimum value of the ambient noise level. This Entropic Stochastic Resonance (ESR), characteristic of small-scale systems, may constitute a useful mechanism for the manipulation and control of single-molecules and nano-devices.Comment: 4 pages, 3 figure

Statistics of work performed on a forced quantum oscillator

Various aspects of the statistics of work performed by an external classical force on a quantum mechanical system are elucidated for a driven harmonic oscillator. In this special case two parameters are introduced that are sufficient to completely characterize the force protocol. Explicit results for the characteristic function of work and the respective probability distribution are provided and discussed for three different types of initial states of the oscillator: microcanonical, canonical and coherent states. Depending on the choice of the initial state the probability distributions of the performed work may grossly differ. This result in particular holds also true for identical force protocols. General fluctuation and work theorems holding for microcanonical and canonical initial states are confirmed