Refine
Document Type
- Article (10)
- Preprint (5)
- Doctoral Thesis (1)
Language
- English (16)
Keywords
Institute
The transport properties of Brownian motors have attracted many attention in the last years. The vast majority of works focused on this topic is concentrated on the behavior of the overdamped regime and the control of the emerging directed transport as a function of control parameters such as temperature, external load, or some other control variable. In this thesis we will study transport of an inertial Brownian particle in a periodic ratchet-type potential additionally subjected to an external, time periodic force, i.e. rocked ratchet. We focus here in more detail on the fluctuating behavior of the Brownian motor position and current. The average drift motion together with its fluctuation statistics are salient features when characterizing the performance of a Brownian motor. The goal of this work is to constitute the most significant characteristics relevant for optimization of the Brownian motors modus operandi. We identify the operating conditions that both maximize the motor current and minimize its dispersion. Extensive numerical simulation of an inertial rocked ratchet displays that two quantifiers, namely the energetic efficiency and the Peclet number (or equivalently the Fano factor), suffice to determine the regimes of optimal transport. We demonstrate also that the velocity-load characteristics is distinctly non-monotonic, possessing regimes with a negative differential mobility or even absolute negative mobility.
In order to optimize the directed motion of an inertial Brownian motor, we identify the operating conditions that both maximize the motor current and minimize its dispersion. Extensive numerical simulation of an inertial rocked ratchet displays that two quantifiers, namely the energetic efficiency and the Péclet number (or equivalently the Fano factor), suffice to determine the regimes of optimal transport. The effective diffusion of this rocked inertial Brownian motor can be expressed as a generalized fluctuation theorem of the Green -- Kubo type. -- Addendum and Erratum: The expression for the effective diffusion of an inertial, periodically driven Brownian particle in an asymmetric, periodic potential is compared with the step number diffusion which is extracted from the corresponding coarse grained hopping process specifying the number of covered spatial periods within each temporal period. The two expressions are typically different and involve the correlations between the number of hops.
The noise-assisted, directed transport in a one-dimensional dissipative, inertial Brownian motor of the rocking type that is exposed to an external bias is investigated. We demonstrate that the velocity-load characteristics is distinctly non-monotonic, possessing regimes with a negative differential mobility. In addition, we evaluate several possible efficiency quantifiers which are compared among each other. These quantifiers characterize the mutual interplay between the viscous drag and the external load differently, weighing the inherent rectification features from different physical perspectives.
Diffusive transport properties of a quantum Brownian particle moving in a tilted spatially periodic potential and strongly interacting with a thermostat are explored. Apart from the average stationary velocity, we foremost investigate the diffusive behavior by evaluating the effective diffusion coefficient together with the corresponding Peclet number. Corrections due to quantum effects, such as quantum tunneling and quantum fluctuations, are shown to substantially enhance the effectiveness of diffusive transport if only the thermostat temperature resides within an appropriate interval of intermediate values.
The statistics of transitions between the metastable states of a periodically driven bistable Brownian oscillator are investigated on the basis of a two-state description by means of a master equation with time-dependent rates. The results are compared with extensive numerical simulations of the Langevin equation for a sinusoidal driving force. Very good agreement is achieved both for the counting statistics of the number of transitions and the residence time distribution of the process in either state. The counting statistics corroborate in a consistent way the interpretation of stochastic resonance as a synchronisation phenomenon for a properly defined generalized Rice phase.
With this work we investigate an often neglected aspect of Brownian motor transport: The role of fluctuations of the noise-induced current and its consequences for the efficiency of rectifying noise. In doing so, we consider a Brownian inertial motor that is driven by an unbiased monochromatic, time-periodic force and thermal noise. Typically, we find that the asymptotic, time- and noise-averaged transport velocities are small, possessing rather broad velocity fluctuations. This implies a corresponding poor performance for the rectification power. However, for tailored profiles of the ratchet potential and appropriate drive parameters, we can identify a drastic enhancement of the rectification efficiency. This regime is marked by persistent, uni-directional motion of the Brownian motor with few back-turns, only. The corresponding asymmetric velocity distribution is then rather narrow, with a support that predominantly favors only one sign for the velocity.
