Quantum ratchets with few bands below the barrier

We investigate directed motion in nonadiabatically rocked ratchet systems sustaining few bands below the barrier. Upon restricting the dynamics to the lowest M bands, the total system-plus-bath Hamiltonian is mapped onto a discrete tight-binding model containing all the information both on the intrawell and interwell tunneling motion. A closed form for the current in the incoherent tunneling regime is obtained. In effective single-band ratchets, no current rectification occurs. We apply our theory to describe rectification effects in vortex quantum ratchets devices. Current reversals upon variation of the ac-field amplitude or frequency are predicted.     

Charging ratchets: Coulomb blockade and rectification

Discrete ratchets describe directed motion of a ‘reaction coordinate’ through a cycle of states in response to some varying external parameter. Such systems, in the simple, history-independent case, are described by a Markov process which in turn leads to a master equation with a transition matrix. Thus the ratchet property is reduced to a characteristic of the parameter-dependent symmetry of matrices. In the standard model of tunneling through a set of quantum dots in the Coulomb-blockade regime, a master equation is also used to describe the evolution through states in ‘dot-occupancy space’, leading to transport of electrons from a source to a drain. The symmetry of the transition matrix in this case is also a function of external parameters, notably the applied gate voltages and source–drain voltage, as well as depending on the configuration of dots and their tunnel couplings. We show that rectification and other ratchet behavior is a common feature of tunneling transport in the Coulomb-blockade regime. We also show that specific arrangements of dots and their tunnel couplings can be designed to enhance the ratchet effect. Finally, we show that the strong rectification of Coulomb-blockaded systems results from the reduction in phase space accessible to the system as it traverses the states in the reaction cycle. Received: 16 October 2001 / Accepted: 14 January 2002 / Published online: 22 April 2002     

SQUID ratchets: basics and experiments

Superconducting quantum interference devices (SQUIDs) are very well suited for experimental investigations of ratchet effects. This is due to the periodicity of the Josephson coupling energy with respect to the phase difference δ of the superconducting macroscopic wave function across a Josephson junction. We show first that, within the resistively and capacitively shunted junction model, the equation of motion for δ is equivalent to the motion of a particle in the so-called tilted washboard potential, and we derive the conditions which have to be satisfied to build a ratchet potential based on asymmetric dc SQUIDs. We then present results from numerical simulations and experimental investigations of dc SQUID ratchets with critical-current asymmetry under harmonic excitation (periodically rocking ratchets). We discuss the impact of important properties like damping or thermal noise on the operation of SQUID ratchets in various regimes, such as adiabatically slow or fast nonadiabatic excitation. Received: 22 November 2001 / Accepted: 14 January 2002 / Published online: 22 April 2002     

A Brownian-ratchet DNA pump with applications to single-nucleotide polymorphism genotyping

We have fabricated a micron-scale device capable of transporting DNA oligomers using Brownian ratchets. The ratchet potential is generated by applying a voltage difference to interdigitated electrodes. Cycling between the charged state and a discharged, free-diffusion state rectifies the Brownian motion of charged particles. The observed macroscopic transport properties agree with the transport rate predicted from microscopic parameters including the DNA diffusivity, the dimensions of the ratchet potential, and the cycling time. Applications to human genetics, primarily genotyping of single-nucleotide polymorphisms (SNPs), are discussed. Received: 7 November 2001 / Accepted: 14 January 2002 / Published online: 22 April 2002     

Quantum features of Brownian motors and stochastic resonance

We investigate quantum Brownian motion sustained transport in both, adiabatically rocked ratchet systems and quantum stochastic resonance (QSR). Above a characteristic crossover temperature T(0) tunneling events are rare; yet they can considerably enhance the quantum-noise-driven particle current and the amplification of signal output in comparison to their classical counterparts. Below T(0) tunneling prevails, thus yielding characteristic novel quantum transport phenomena. For example, upon approaching T=0 the quantum current in Brownian motors exhibits a tunneling-induced reversal, and tends to a finite limit, while the classical result approaches zero without such a change of sign. As a consequence, similar current inversions generated by quantum effects follow upon variation of the particle mass or of its friction coefficient. Likewise, in this latter regime of very low temperatures the tunneling dynamics becomes increasingly coherent, thus suppressing the semiclassically predicted QSR. Moreover, nonadiabatic driving may cause driving-induced coherences and quantized resonant transitions with no classical analog. (c) 1998 American Institute of Physics.     

Protein conformational fluctuations and free-energy transduction

Non-equilibrium fluctuations, whether imposed externally or driven by an energy-releasing chemical reaction, can cause a protein to cycle through several conformations. This cycling can drive a process thermodynamically uphill even though any one conformation considered independently catalyzes the process in the downhill direction. This is because the different conformations have different rate constants (energy barriers) between the states in the catalytic cycle. Even though each conformation individually obeys detailed balance, the flashing between different energy profiles gives rise to a ratchet effect. Further, by exploiting protein conformational dynamics, a single stochastic input can be converted into two phase-shifted internal parameters (e.g. a kinetic barrier height and a binding well energy). This allows the output process to be driven nearly adiabatically, explaining in part the very high efficiencies observed for some biological energy-transduction processes. The results apply equally to driving a biochemical reaction away from equilibrium by an enzyme, to formation of an osmotic gradient across a membrane by a molecular pump, or to motion and generation of force by a molecular motor. Received: 8 February 2002 / Accepted: 4 March 2002 / Published online: 22 April 2002     

反馈脉冲棘轮的能量转化效率研究

研究了反馈脉冲棘轮的定向输运及能量转化效率.详细讨论了弹簧自由长度、耦合强度及脉冲相位等参量对耦合布朗粒子定向输运性能的影响.研究发现,一定自由长度和耦合强度都能促进反馈脉冲棘轮的定向输运,并能使耦合粒子拖动负载做功时的能量转化效率达到最大.此外,通过调节脉冲相位能使反馈棘轮在一个演化周期内获得两次流反转,且合适的相位还能增强反馈棘轮的定向输运.所得结论不仅可为实验上设计合适的反馈脉冲作用来优化棘轮的定向输运性能,而且还能为生物医疗上药物的精准投放提供一定的理论参考.     

Double-dot quantum ratchet driven by an independently biased quantum point contact

We study a double quantum dot (DQD) coupled to a strongly biased quantum point contact (QPC), each embedded in independent electric circuits. For weak interdot tunneling we observe a finite current flowing through the Coulomb blockaded DQD in response to a strong bias on the QPC. The direction of the current through the DQD is determined by the relative detuning of the energy levels of the two quantum dots. The results are interpreted in terms of a quantum ratchet phenomenon in a DQD energized by a nearby QPC.     

Anomalous mobility and current reversals in inertial deterministic ratchets

We analyze the transport properties of inertial deterministic rocking ratchets in the presence of an external constant force. For small values of this load, we can obtain a positive current for a negative load, and vice versa. This phenomenon, in which the direction of the current is opposed to the sign of the external force, is a signature of anomalous negative mobility. We show that this anomalous mobility is possible in the deterministic case, and explain this phenomenon as current reversals associated to bifurcations in an inertial deterministic rocking ratchet in the presence of an external load.     

Resonant tunneling of electrons through single self-assembled InAs quantum dot studied by conductive atomic force microscopy

Resonant tunneling of electrons through a quantum level in single self-assembled InAs quantum dot (QD) embedded in thin AlAs barriers has been studied. The embedded InAs QDs are sandwiched by 1.7-nm-thick AlAs barriers, and surface InAs QDs, which are deposited on 8.3 nm-thick GaAs cap layer, are used as nano-scale electrodes. Since the surface InAs QD should be vertically aligned with a buried one, a current flowing via the buried QD can be measured with a conductive tip of an atomic force microscope (AFM) brought in contact with the surface QD-electrode. Negative differential resistance attributed to electron resonant tunneling through a quantized energy level in the buried QD is observed in the current–voltage characteristics at room temperature. The effect of Fermi level pinning around nano-scale QD-electrode on resonance voltage and the dependence of resonance voltage on the size of QD-electrodes are investigated, and it has been demonstrated that the distribution of the resonance voltages reflects the size variation of the embedded QDs.     

Ratchet patterns sort molecular shuttles

Molecular shuttles based on microtubules propelled by motor proteins can be guided on surfaces by adsorbing motors in chemical patterns or by using open guiding channels. While chemical patterns can guide microtubules based on a Brownian ratchet mechanism, the rigidity of the microtubules limits guiding to features with dimensions on the order of their persistence length (5 mm). To achieve guiding on micron-scale dimensions, physical barriers are required which can exploit the forces exerted by multiple motors to bend tubules into tight radii of curvature. Microtubule guiding is illustrated for the case of a special ratchet pattern that is capable of sorting microtubules on the basis of the direction of their motion. Received: 3 December 2001 / Accepted: 11 February 2002 / Published online: 22 April 2002     

过阻尼布朗棘轮的斯托克斯效率研究

根据随机能量理论解析得到阻尼环境中布朗粒子的概率流和斯托克斯效率,并进一步研究布朗粒子的输运性能.详细讨论了空间的不对称性、外偏置力及外势结构等对棘轮定向输运的影响.研究发现,合适的外偏置力能使棘轮的定向输运达到最强.通过调节外势的不对称性可使棘轮中粒子的运动反向,当选择合适的空间不对称性时布朗粒子的反向输运可获得最强.此外,一定条件下合适的外势高度也能增强棘轮输运,且能使粒子克服黏滞阻力的斯托克斯效率达到最大.所得结论能够启发实验上设计合适的外势及外偏置来优化布朗棘轮的定向输运性能,并为生物纳米器件的研制提供一定的理论参考.     

Analytical solution to transport in Brownian ratchets via the gambler's ruin model

We present an analogy between the classic gambler's ruin problem and the thermally activated dynamics in periodic Brownian ratchets. By considering each periodic unit of the ratchet as a site chain, we calculated the transition probabilities and mean first passage time for transitions between energy minima of adjacent units. We consider the specific case of Brownian ratchets driven by Markov dichotomous noise. The explicit solution for the current is derived for any arbitrary temperature, and is verified numerically by Langevin simulations. The conditions for current reversal in the ratchet are obtained and discussed.     

Force generation by polymerizing microtubules

Polymerization ratchets formed by the assembly of actin filaments and microtubules are possibly the simplest realizations of biological thermal ratchets. A variety of experimental evidence exists that significant forces are generated by these processes, but quantitative studies lag far behind similar studies for molecular motors such as kinesin and myosin. Here we present a discussion of the theory of polymerization ratchets as well as experimental techniques used in our laboratory for the study of forces generated by single growing microtubules. Data obtained with these techniques provide us with valuable information that may eventually allow us to distinguish between different models for the growth of microtubules. Received: 15 January 2002 / Accepted: 11 February 2002 / Published online: 22 April 2002     

Functional fractionation-ratchets

Electrophoretic ratchets have been developed for both analytical and preparative electrophoresis. These ratchets use a new type of pulsed field. The quality of the fractionations meets the usual standards for biochemistry-based electrophoresis. The supporting medium is either an agarose gel or a capillary-contained polymer solution. The electrophoretic ratchets are effective with a particle that has an electrophoretic mobility (μ=velocity/electrical field) that varies as the electrical field varies. A ratchet developed for DNA molecules is effective because μ increases in magnitude as the electrical field increases in magnitude. Ratchets developed for both DNA–protein complexes and spheres are effective because of the opposite dependence of μ on the electrical field. Ratchet-based gel electrophoresis can be performed in a continuous, preparative mode. Ratchet-based capillary electrophoresis provides a necessary component for cyclic capillary electrophoresis. Cyclic capillary electrophoresis of DNA is a procedure for analyzing a DNA profile in several segments. These segments are separated by electrophoretic enhancements of the DNA profile. Cyclic capillary electrophoresis is being developed for increasing both the length and the accuracy of the analysis of a DNA-sequencing ladder. Received: 16 October 2001 / Accepted: 14 January 2002 / Published online: 22 April 2002     

Vortex-rectification effects in films with periodic asymmetric pinning

We study the transport of vortices excited by an ac current in an Al film with an array of nanoengineered asymmetric antidots. The vortex response to the ac current is investigated by detailed measurements of the voltage output as a function of ac current amplitude, magnetic field, and temperature. The measurements revealed pronounced voltage rectification effects which are mainly characterized by the two critical depinning forces of the asymmetric potential. The shape of the net dc voltage as a function of the excitation amplitude indicates that our vortex ratchet behaves in a way very different from standard overdamped models. Rather, the repinning force, necessary to stop vortex motion, is considerably smaller than the depinning force, resembling the behavior of the so-called inertia ratchets. Calculations based on an underdamped ratchet model provide a very good fit to the experimental data.     

Soliton ratchets out of point-like inhomogeneities

We introduce and study a novel design for a ratchet potential for soliton excitations. The potential is implemented by means of an array of point-like (delta) inhomogeneities in an otherwise homogeneous potential. We use collective coordinates which predict that the effective potential acting on the soliton is periodic but asymmetric and gives rise to the ratchet effect. Numerical simulations fully confirm this prediction; quantitative agreement is reached by an improved version of the theory. Although we specifically show that it is most interesting for building Josephson junction ratchets capable to rectify time-symmetric ac forces, the proposed mechanism is very general and can appear in many contexts, including biological systems.Received: 25 November 2003, Published online: 19 February 2004PACS: 05.45.Yv Solitons - 05.60.-k Transport processes - 63.20.Pw Localized modes     

Fano-type spin-flip mesoscopic transport through an Aharonov-Bohm interferometer

We have investigated the mesoscopic transport properties of a quantum dot embedded Aharonov-Bohm (AB) interferometer applied with a rotating magnetic field. The spin-flip effect is induced by the rotating magnetic field, and the tunneling current is sensitive to the spin-flip effect. The spin-flipped electrons tunneling from the direct channel and the resonant channel interfere with each other to form spin-polarized tunneling current components. The non-resonant tunneling (direct transmission) strength and the AB phase φ play important roles. When the non-resonant tunneling (background transmission) exists, the spin and charge currents form asymmetric peaks and valleys, which exhibit Fano-type line shapes by varying the source-drain bias voltage, or gate voltage. The AB oscillations of the spin and charge currents exhibit distinct dependence on the magnetic flux and direct tunneling strength.     

Transport reversal in a delayed feedback ratchet

Feedback flashing ratchets are thermal rectifiers that use information on the state of the system to operate the switching on and off of a periodic potential. They can induce directed transport even with symmetric potentials thanks to the asymmetry of the feedback protocol. We investigate here the dynamics of a feedback flashing ratchet when the asymmetry of the ratchet potential and of the feedback protocol favor transport in opposite directions. The introduction of a time delay in the control strategy allows one to nontrivially tune the relative relevance of the competing asymmetries leading to an interesting dynamics. We show that the competition between the asymmetries leads to a current reversal for large delays. For small ensembles of particles current reversal appears as the consequence of the emergence of an open-loop like dynamical regime, while for large ensembles of particles it can be understood as a consequence of the stabilization of quasiperiodic solutions. We also comment on the experimental feasibility of these feedback ratchets and their potential applications.     

Negative excess noise in quantum conductors

We predict that in quantum conductors the excess noise can be absent or even negative provided the energy dependence of the electron transmission probability at the Fermi energy is sufficiently sharp. In other words the current (or voltage) fluctuations under transport conditions can be less than in equilibrium. As examples for this surprising behavior we consider resonant tunneling, ballistic point contacts and the integer quantum Hall effect.Work performed within the research program of the Sonderforschungsbereich 341, Köln-Aachen-Jülich