Ratchet effect in an underdamped periodic potential and its characterisation

We investigate an overdamped Brownian motion in symmetric periodic potential switching by Markovian dichotomous noise between two configurations. Second configuration differs from the first one by the half of spatial period displacement when the maxima of a potential profile become the minima and vice versa. We establish a validity of the formula for effective diffusion constant previously obtained in the case of fixed periodic potentials and, thus, reduce the problem to calculation of mean first-passage times (MFPTs). At the same time the MFPT in this formula should be substituted for the semi-sum of MFPTs regarding two initial configurations of potential profile. A set of equations for MFPTs in flipping potentials can be solved for the sawtooth periodic potential. As a result, after cumbersome calculations we obtain the exact complex expression for effective diffusion coefficient of Brownian particles in such a medium which is valid for arbitrary mean frequency of potential switchings. We detect the acceleration of diffusion in comparison with the case of fixed sawtooth potential profile as it was demonstrated for a symmetric periodic potential modulating by external Gaussian white noise.

Defect modes are studied in parity-time (PT) symmetric periodic complex potentials for both positive and negative defects. Such new kinds of linear localized modes may conserve their energy or endure gain or loss upon propagating. The existence domain of the conserved modes would be prolonged by positive defects or shortened by negative defects, and the dissipative modes would appear before the phase transition point of the PT symmetric potential at stronger negative defects.

Chaos-like properties such as noise or fluctuations arising from quantum effects have recently investigated on a single barrier potential and on a one-dimensional periodic potential barrier. They used either the planewave of light or a wavepacket (pulse) passing through the potential barrier, demonstrating the chaos created by the bounded one-dimensional multibarrier potential (Bar and Horwitz, 2002; Hondou and Sawada, 1995), and proved it is an ordered and periodic phenomenon. Also another group demonstrated unexpected behavior of a dissipative particle in simple multiscale systems subject to chaotic noise and clarified the reason for the particular behavior because it is under a periodic potential (Chialvo et al., 1997). They concluded the occurrence of drift in a symmetric periodic potential would be expected to be a common feature of noise-driven systems. Essentially this effect is quite similar to the problem of a particle placed in a potential well of finite barrier (Cohen-Tannoudji et al., 1977) and the present issue of the photon distribution on a crystallite surface. When the crystallite size decreases to a few nanometers, the light absorption or photoluminescence in air moves to the direction of smaller wavelength, which is known as the blueshift (Kale and Lokhande, 2000; Nanda et al., 1999; Tsunekawa et al., 2003; Von Behren et al., 2000). The basic theory for this phenomenon is the quantum confinement effect (Andersen et al., 2002; Sharma et al., 2005). According to this theory the number of photons confined in each unit cell increases with the decreasing crystallite size. It is also said to enlarge the band gap between the valence band and the conduction band. Another approach is to take crystalline unit cells as numerical elements and employ different potential energies over a unit cell (Choi, 2007; Choi and Kim, 2007), realizing light intensity fluctuations. The effect of the film thickness on the blueshift was investigated by one of the authors (Choi and Pyun, 2008) about cellular crystalline surfaces with periodic potential, getting the blueshift numerically demonstrated in good agreement with experiments. In this paper we deal with surface nanostructures and try to prove the blueshift numerically by predicting the location of absorption wavelength. One of the best ways to uphold the present numerical method would be to demonstrate the blueshift phenomenon observed widely experimentally (Lu et al., 2008; Miyake et al., 1999; Tan et al., 2005; Tsunekawa et al., 2000). They demonstrated experimentally the dependence of the blueshift on the crystallite size for CeO and CdS. One of the authors has been studying this problem recently, publishing a few papers (Choi, 2007; Choi and Kim, 2007; Choi and Pyun, 2008), and this paper may be taken as an extension of these consecutive efforts. Another publication (Choi and Choi, 2009) predicting the blueshift with respect to the shell layer thickness has been already accomplished and led the present investigation to be made. 17

Fundamental, dipole, and vortex solitons in fractional nonlinear Schrödinger equation with a parity-time-symmetric periodic potential

The ratchet effect [1–3] is the rectification of fluctuations in a periodic potential in the absence of net applied bias forces. In this way directed motion along a macroscopically flat structure is obtained. The archetypal of a ratchet consists of Brownian particles in a periodic potential. In order to obtain directed motion, two main requirements have to be fulfilled. First, the system has to be driven out of equilibrium, so to overcome the limitations imposed by the second principle of thermodynamics. Second, the relevant symmetries of the system, which would otherwise prevent the generation of a current, have to be broken. Among the different possible implementations of the ratchet effect, we mention here the flashing ratchet [1–3], the rocking ratchet [1–3], and the more recently introduced gating ratchet [4–6]. In the rocking ratchet set-up, Brownian particles in a periodic potential experience an additional time-dependent applied force F(t), which is homogeneous and has zero time-average. The oscillating applied force plays a double role. On one hand, it drives the system out of thermodynamic equilibrium, thus avoiding the restrictions imposed by the second principle of thermodynamics. On the other hand, the temporal symmetry properties of the applied force, together with the spatial symmetry properties of the periodic potential, control the directed motion.

Current-driven dynamics in Josephson junction networks with an asymmetric potential

We study numerically dynamical frictional phenomena using the Frenkel-Kontorova model with impurities.Even in the presence of randomness sliding states have a quasi long range order, which changes with the sliding velocity.Such an order affects the velocity dependence of the kinetic frictional force and produces peculiar transverse pinning effects.We discuss them in the relation with the moving Bragg glass theory developed for vortex lattices in type II superconductors.

Collective directional transport of particles in symmetric periodic potentials is studied. An example is given to reveal the directed motion of a single particle in a symmetric periodic potential and subject to an asymmetric ac force with zero mean. It is then shown that the asymmetric coupling can give rise to a directed transport. The transport failure (pinning of the lattice) is related to the phase delocalization (crisis) in the circle map. For symmetric couplings, it is found that a train of plane wave can also lead to a directed transport. The mode-locking steps of the transport velocity is found and analyzed. The collective transport can be well optimized by adjusting parameters in the system.

Near-surface Brownian motor with synchronously fluctuating symmetric potential and applied force

We report a systematic study of barrier-crossing dynamics of self-propelled particles (SPPs) across a periodic ratchet potential U0(x), which is fabricated on a ratchet-microgroove-patterned polydimethylsiloxane substrate. From the measured steady-state probability density function P(x;F0) of the SPPs with different self-propulsion forces F0, we find that the escape dynamics of slow-rotating SPPs over the asymmetric ratchet potential can be well described by an activity-dependent potential, U±(x;F0) ≃ U0(x) ∓ aF0x, for the forward (+) and backward (-) moving particles with aF0 being the amplitude of their self-propulsion force projected along the x axis. By a thorough analysis of a large volume of the SPP trajectories obtained from both the spatially symmetric and asymmetric potentials, we delineate two experimental conditions under which the ratchet effect of SPPs is realized without involving a time-dependent rectification, and directed particle transport with a steady flux is observed. This work thus provides an effective statistical approach to describe the non-equilibrium transport of SPPs across ratchet potentials.

We investigate the motion of an overdamped Brownian particle in a periodicpotential with weak thermal noise and a time-periodic unbiased (i.e. ⟨F(t)⟩ = 0) external driving force F(t). By introducingappropriate “waiting-periods”, where F(t) vanishes, an arbitrarily strongenhancement of diffusion in a symmetric potential is possible. In asymmetric periodic potentials (ratchets) the net flux of particles can be directed in both directions, even in the absence of thermal noise. For finite temperatures we observe and explain additional, pure-noise–induced flux reversal phenomena.

The one-dimensional dynamics of a dimer consisting of two harmonically coupled components is considered. The mutual distance between the dimer components plays the role of an internal degree of freedom. Both components are in contact with the same heat bath and are coupled to a spatially periodic, symmetric potential, whose amplitude is modulated periodically in time and whose coupling strength is different for the two components. In the absence of any external bias, a ratchet effect (directed transport) arises generically unless the mutual coupling of the dimer components tends to zero or infinity. In other words, the ratchet effect is generated by the internal degree of freedom. An accurate analytical approximation for the dimer's velocity and diffusion coefficient is obtained. The velocity of the system is maximized by adding an optimal amount of noise and by tuning the driving frequency to an optimal value. Furthermore, there exists an optimal coupling strength at which the velocity is the largest.

We analyze the impact of temperature on the diffusion coefficient of an inertial Brownian particle moving in a symmetric periodic potential and driven by a symmetric time-periodic force. Recent studies have revealed the low-friction regime in which the diffusion coefficient shows giant damped quasiperiodic oscillations as a function of the amplitude of the time-periodic force [I. G. Marchenko et al., Chaos 32, 113106 (2022)1054-150010.1063/5.0117902]. We find out that when temperature grows the diffusion coefficient increases at its minima; however, it decreases at the maxima within a finite temperature window. This curious behavior is explained in terms of the deterministic dynamics perturbed by thermal fluctuations and mean residence time of the particle in the locked and running trajectories. We demonstrate that temperature dependence of the diffusion coefficient can be accurately reconstructed from the stationary probability to occupy the running trajectories.

Biological molecular motors drive unidirectional transport and transduce chemical energy to mechanical work. In order to identify this energy conversion which is a common feature of molecular motors, many workers have studied various physical models, which consist of Brownian particles in spatially periodic potentials. Most of the models are, however, based on “single-particle” dynamics and too simple as models for biological motors, especially for actin-myosin motors, which cause muscle contraction. In this paper, particles coupled by elastic strings in an asymmetric periodic potential are considered as a model for the motors. We investigate the dynamics of the model and calculate the efficiency of energy conversion with the use of molecular dynamical method. In particular, we find that the velocity and efficiency of the elastically coupled particles where the natural length of the springs is incommensurable with the period of the periodic potential are larger than those of the corresponding single particle model.

Transport of the Brownian particles driven by Lévy flights coexisting with subdiffusion in asymmetric periodic potentials is investigated in the absence of any external driving forces. Using the Langevin-type dynamics with subordination techniques, we obtain the group velocity which can measure the transport. It is found that the group velocity increases monotonically with the subdiffusive index and there exists an optimal value of the Lévy index at which the group velocity takes its maximal value. There is a threshold value of the subdiffusive index below which the ratchet effects will disappear. The nonthermal character of the Lévy flights and the asymmetry of the potential are necessary to obtain the directed transport. Some peculiar phenomena induced by the competition between Lévy flights and subdiffusion are also observed. The pseudonormal diffusion will appear on the level of the median.