Lukasz Machura

Absolute negative mobility induced by thermal equilibrium fluctuations

A novel transport phenomenon is identified that is induced by inertial Brownian particles which move in simple one-dimensional, symmetric periodic potentials under the influence of both a time periodic and a constant, biasing driving force. Within tailored parameter regimes, thermal equilibrium fluctuations induce the phenomenon of absolute negative mobility (ANM), which means that the particle noisily moves backwards against a small constant bias. When no thermal fluctuations act, the transport vanishes identically in these tailored regimes. ANM can also occur in the absence of fluctuations on grounds which are rooted solely in the complex, inertial deterministic dynamics. The experimental verification of this new transport scheme is elucidated for the archetype symmetric physical system: a convenient setup consisting of a resistively and capacitively shunted Josephson junction device.

Brownian motors: Current fluctuations and rectification efficiency

With this work, we investigate an often neglected aspect of Brownian motor transport, namely, 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, unidirectional 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.

Consistent description of quantum Brownian motors operating at strong friction.

A quantum Smoluchowski equation is put forward that consistently describes thermal quantum states. In particular, it notably does not induce a violation of the second law of thermodynamics. This so modified kinetic equation is applied to study {\it analytically} directed quantum transport at strong friction in arbitrarily shaped ratchet potentials that are driven by nonthermal two-state noise. Depending on the mutual interplay of quantum tunneling and quantum reflection these quantum corrections can induce both, either a sizable enhancement or a suppression of transport. Moreover, the threshold for current reversals becomes markedly shifted due to such quantum fluctuations.

Anomalous transport in biased ac-driven Josephson junctions: Negative conductances

We investigate classical anomalous electrical transport in a driven, resistively, and capacitively shunted Josephson junction device. Intriguing transport phenomena are identified in chaotic regimes when the junction is subjected to both a time-periodic (ac) and a constant biasing (dc) current. The dependence of the voltage across the junction on the dc exhibits a rich diversity of anomalous transport characteristics. In particular, depending on the chosen parameter regime, we can identify the so termed absolute negative conductance around zero dc bias, the occurrence of negative differential conductance, and, after crossing a zero conductance, the emergence of a negative nonlinear conductance in the nonequilibrium response regime remote from zero dc bias.

Forcing inertial Brownian motors: Efficiency and negative differential mobility

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.

GPU accelerated Monte Carlo simulation of Brownian motors dynamics with CUDA

Abstract This work presents an updated and extended guide on methods of a proper acceleration of the Monte Carlo integration of stochastic differential equations with the commonly available NVIDIA Graphics Processing Units using the CUDA programming environment. We outline the general aspects of the scientific computing on graphics cards and demonstrate them with two models of a well known phenomenon of the noise induced transport of Brownian motors in periodic structures. As a source of fluctuations in the considered systems we selected the three most commonly occurring noises: the Gaussian white noise, the white Poissonian noise and the dichotomous process also known as a random telegraph signal. The detailed discussion on various aspects of the applied numerical schemes is also presented. The measured speedup can be of the astonishing order of about 3000 when compared to a typical CPU. This number significantly expands the range of problems solvable by use of stochastic simulations, allowing even an interactive research in some cases. Program Summary Program title: Poisson, dich Catalogue identifier: AEVP_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEVP_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU Lesser General Public License. version 3 No. of lines in distributed program, including test data, etc.: 3338 No. of bytes in distributed program, including test data, etc.: 45009 Distribution format: tar.gz Programming language: CUDA C. Computer: Any with CUDA-compliant GPU. Operating system: No limits (tested on Linux). RAM: Hundreds of megabytes for typical case Classification: 4.3, 23. External routines: The NVIDIA CUDA Random Number Generation library (cuRAND) Nature of problem: Graphics processing unit accelerated numerical simulation of stochastic differential equation. Solution method: The jump-adapted simplified weak order 2.0 predictor–corrector method is employed to integrate the Langevin equation of motion. Ensemble-averaged quantities of interest are obtained through averaging over multiple independent realizations of the system generated by means of the Monte Carlo method. Unusual features: The actual numerical simulation runs exclusively on the graphics processing unit using the CUDA environment. This allows for a speedup as large as about 3000 when compared to a typical CPU. Running time: A few seconds

Quantum diffusion in biased washboard potentials: Strong friction limit

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.

Optimal strategy for controlling transport in inertial Brownian motors

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.

Transport driven by biharmonic forces: impact of correlated thermal noise.

We study an inertial brownian particle moving in a symmetric periodic substrate, driven by a zero-mean biharmonic force and correlated thermal noise. The brownian motion is described in terms of a generalized Langevin equation with an exponentially correlated gaussian noise term, obeying the fluctuation-dissipation theorem. We analyze impact of nonzero correlation time of thermal noise on transport properties of the brownian particle. We identify regimes where the increase of the correlation time intensifies long-time transport of the brownian particle. The opposite effect is also found: longer correlation time reduces the stationary velocity of the particle. The correlation time induced multiple current reversal is detected. We reveal that thermal noise of nonzero correlation time can radically enhance long-time velocity of the brownian particle in regimes where in the white noise limit the velocity is extremely small. All transport properties can be tested in the setup consisting of a resistively and capacitively shunted Josephson junction device.

Inertial Brownian motors driven by biharmonic signals

We study transport properties of an inertial Brownian particle moving in viscous symmetric periodic structures and driven by an oscillating signal of two harmonic components. We analyze the influence of symmetric, antisymmetric and asymmetric signals on directed transport and reveal the shift symmetry of the stationary averaged velocity of the Brownian particle with respect to the relative phase of two components of the signal. The shift symmetry holds true in all regimes.