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![Color online) Biharmonic external ac driving G(t)=A[sin(Ωt)+ε sin(2Ωt+ϕ)] plotted for the amplitude A=1 and the frequency Ω=1, for four different second harmonic amplitude ε=0.1,0.5,1,2 and four phase shifts ϕ=0,π/2,1.65,2.41 which corresponds to the later commented figures (see Figs. 3, 4 for details).](profile/Lukasz-Machura/publication/49750627/figure/fig2/AS:272688442769418@1442025399577/Color-online-Biharmonic-external-ac-driving-GtAsinOt-esin2Ot-ph-plotted-for-the.png)
Color online) Biharmonic external ac driving G(t)=A[sin(Ωt)+ε sin(2Ωt+ϕ)] plotted for the amplitude A=1 and the frequency Ω=1, for four different second harmonic amplitude ε=0.1,0.5,1,2 and four phase shifts ϕ=0,π/2,1.65,2.41 which corresponds to the later commented figures (see Figs. 3, 4 for details).
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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 non...
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... A is the amplitude of the first harmonic, the factor scales the second harmonics, so that it has the resulting amplitude εA. The angular frequency Ω determines the time period T = 2π/Ω of the driving and φ controls the phase shift between two components of the biharmonic signal (5), see Fig. 1 for ...
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Citations
... In recent years, the phenomenon of negative transfer of a particle in an inertial ratchet has attracted considerable attention [1][2][3][4][5][6][7][8][9][10][11]. The second law of thermodynamics and Le Chatelier's principle rule out the negative mobility phenomenon for a system in an equilibrium state. ...
... The second law of thermodynamics and Le Chatelier's principle rule out the negative mobility phenomenon for a system in an equilibrium state. But the negative mobility phenomenon in an inertial ratchet system far away from the equilibrium state has been revealed by a lot of research [1][2][3][4][5][6][7][8][9][10][11]. The phenomenon of negative transfer is characterized by: the absolute negative mobility (ANM) phenomenon, that is, for a very small external force acting on a particle, the particle moves in the opposite direction of the external force; the negative nonlinear mobility (NNM) phenomenon, that is, when the force acting on the particle is very small, the particle transport direction and force is the same, then when the force increases, the motion of the particles and the force is the opposite; the negative differential mobility (NDM) phenomenon, that is, the particle transport direction and force is the same, but the particle's transport velocity decreases with an increase of the external force. ...
The influence of potential height on the absolute negative mobility of a particle in an inertial ratchet was investigated by the stochastic simulation method. The simulation results show: (1) When noise does not exist and the biasing force is small, there is no probability flow in the system, but when the biasing force is small, the noise on the heat balance disturbance can also make particles transport, and it can induce and eliminate the absolute negative mobility of the particle; (2) The absolute negative mobility of particle is eliminated by increasing the potential height. Study of the influence of barrier height on the absolute negative mobility of particle will provide a certain theoretical basis for the control of negative movement.
... First, the properties of ongoing fluctuations define the form of the generalized FDT holding for brain activity and, in fine, the way stimulus information is transferred to the brain. The presence of correlated noise affects the particle's transport properties and corresponding dynamics (Machura and łuczka, 2010), and information transfer is maximized when stimuli and brain fluctuations display similar scaling properties (Allegrini et al., 2007; Frontiers in Systems Neuroscience www.frontiersin.org June 2014 | Volume 8 | Article 112 | 3 West and Grigolini, 2010;Aquino et al., 2011). ...
Behavioural studies have shown that human cognition is characterized by properties such as temporal scale invariance, heavy-tailed non-Gaussian distributions, and long-range correlations at long time scales, suggesting models of how (non observable) components of cognition interact. On the other hand, results from functional neuroimaging studies show that complex scaling and intermittency may be generic spatio-temporal properties of the brain at rest. Somehow surprisingly, though, hardly ever have the neural correlates of cognition been studied at time scales comparable to those at which cognition shows scaling properties. Here, we analyze the meanings of scaling properties and the significance of their task-related modulations for cognitive neuroscience. It is proposed that cognitive processes can be framed in terms of complex generic properties of brain activity at rest and, ultimately, of functional equations, limiting distributions, symmetries, and possibly universality classes characterizing them.
... 32−36 Quantum mechanical effects may also play a role because ratchet systems must be of microscopic size to rectify the fluctuating motion. 37−47 A Fokker−Planck approach 48 and a Langevin approach 49 have been used in classical studies of ratchets, while varieties of equation of motion approaches have been employed for quantum mechanical studies. 37 −47 In the quantum mechanical case, dissipative systems are commonly modeled as potential systems coupled to heat-bath degrees of freedom at finite temperature. ...
... shown that not only the strength of the ac force but also its phase is of experimental relevance [20,21]. The generalization of the monochromatic ac force to a multifrequency ac force leads to nontrivial results in ultra-cold-atom dynamics [22][23][24][25][26][27][28][29][30][31][32][33]. The relationship between symmetries and transport was explored for a cold-atom ratchet with multifrequency driving [25]. ...
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... [32,33,34,35,36] Quantum mechanical effects may also play a role, because ratchet systems must be of microscopic size to rectify the fluctuating motion. [37,38,39,40,41,42,43,44,45,46,47] A Fokker-Planck approach [48] and a Langevin approach [49] have been used in classical studies of ratchets, while varieties of equation of motion approaches have been employed for quantum mechanical studies. [37,38,39,40,41,42,43,44,45,46,47] In quantum mechanical case, dissipative systems are commonly modeled as potential systems coupled to heat-bath degrees of freedom at finite temperature. ...
... We introduced the counter term j a 2 jq 2 /2m j ω 2 j to maintain the translational symmetry of the Hamiltonian for U (q; 0) = 0. Here, we consider a reflectionsymmetric potential system driven by a biharmonic force. [14,15,16,17,18,19,45,46,47,48,49] This force prevents the system from reaching equilibrium and breaks the spatio-temporal symmetry. We write the potential as U (q; t) = U (q) −qF (t), where U (q) is static, reflectionsymmetric potential, and −qF (t) is the dynamic potential. ...
... where U 0 is the barrier height, κ is the wave number, and F 1 , F 2 , Ω and θ denote the amplitudes, frequency, and the phase difference of the biharmonic forces, respectively. [14,15,16,17,18,19,45,46,47,48,49] Experimentally, such a situation has been realized for fluxons in long ...
We rigorously investigate the quantum dissipative dynamics of a ratchet system described by a periodic potential model based on the Caldeira-Leggett Hamiltonian with a biharmonic force. In this model, we use the reduced hierarchy equations of motion in the Wigner space representation. These equations represent a generalization of the Gaussian-Markovian quantum Fokker-Planck equation introduced by Tanimura and Wolynes (1991), which was formulated to study non-Markovian and non-perturbative thermal effects at finite temperature. This formalism allows us to treat both the classical limit and the tunneling regimes, and it is helpful for identifying purely quantum mechanical effects through the time evolution of the Wigner distribution. We carried out extensive calculations of the classical and quantum currents for various temperatures, coupling strengths, and barrier heights. Our results reveal that at low temperature, while the quantum current is larger than the classical current in the case of a high barrier, the opposite is true in the case of a low barrier. We find that this behavior results from the fact that the tunneling enhances the current in the case of a high barrier, while it suppresses the current in the case of a low barrier. This is because the effect of the ratchet potential is weak in the case of a low barrier, due to the large dispersion of the distribution introduced by tunneling. This causes the spatio-temporal asymmetry, which is necessary for ratchet current, to be weak, and as a result, the net current is suppressed.
... 5,6 Most of the previous investigations have focused on the transport of the overdamped Brownian particles in which the inertial term due to the finite mass of the particles is neglected. However, some transport phenomena of the underdamped Brownian particles (i.e., inertial Brownian motors) in ratchet systems were observed, [7][8][9] such as the anomalous transport properties induced by transient chaos, 10 absolute negative mobility induced by thermal equilibrium fluctuations 11 and colored thermal fluctuations, 12 facilitated transport driven by a load, 13 and multiple current reversal induced by correlation time of thermal fluctuations 14 and so on. On the other hand, thermal diffusion also plays a prominent role for particle selection and separation tasks in a tilted periodic potential. ...
... In this subsection, we show the impacts of the noise correlation and systemic parameters (i.e., k; a, Q, x, and a) on the current through Eq. (13) in Figs. 1-5, respectively, and then the impact of the noise correlation on the effective diffusion coefficient is shown in Fig. 6 through Eq. (14) with (13). ...
... 49,50 Therefore, for generation of directed transport, the breaking of at least one of these symmetries is necessary. Fig. 6 displays the effective diffusion coefficient D as a function of the intensity k of the correlation between two noises through Eq. (14) with (13). It is shown that the effective diffusion coefficient D increases first and then decreases, exhibiting a maximum at k ' 0 with the increase of k. ...
Transport and diffusion of Brownian particles in a symmetrical periodic potential were investigated for both overdamped and underdamped cases, where the ratchet potential is driven by an external unbiased time periodic force and correlation between thermal and potential fluctuations. It is shown that the correlation between two noises breaks the symmetry of the potential to generate motion of the Brownian particles in particular direction, and the current can reverse its direction by changing the sign of the noise correlation. For the overdamped case, the systemic parameters only induce the directed current, and the noise correlation suppresses the diffusion of the overdamped Brownian particles. However for the underdamped case, the current reverses its direction multiple times with increasing the systemic parameters, i.e., the multiple current reversal is observed, and the noise negative correlation suppresses the diffusion of the underdamped Brownian particles, while the noise positive correlation enhances it.
Based on micromagnetic simulation and analysis of Thiele's equation, in this work we demonstrate that ratchet motion of a skyrmion can be induced by a biharmonic in-plane magnetic field hx(t)=h1sin(mωt)+h2sin(nωt+φ), provided that integers m and n are coprime and that m+n is odd. Remarkably, the speed and direction of the ratchet motion can be readily adjusted by the field amplitude, frequency, and phase, with the maximum speed being over 5 m/s and the direction rotatable over 360°. The origin of the skyrmion ratchet motion is analyzed by tracing the excitation spectra of the dissipation parameter D and the skyrmion position R, and it shows that the dissipative force plays a key role in the appearance of ratchet motion. Such a ratchet motion of a skyrmion is distinguished from those caused by single-frequency ac drives reported in the literature, and from that driven by pulsed magnetic fields as also predicted in this work. Our results show that skyrmion ratchet effect under biharmonic forces shares some common features with those found in many soliton systems, and the facile controllability of both the skyrmion speed and direction should be useful in practice.
We study miniaturized noncontact rack and pinion composed of a corrugated plate and a corrugated cylinder intermeshed via the lateral Casimir force. We assume that the rack position versus time is a periodic multi-harmonic signal. The axle of the pinion is subject to Casimir torque, frictional torque, load torque, and random Gaussian torque. A Fokker-Planck rather than Langevin description of the pinion dynamics allows us to explore a huge parameter space in a reasonable computational time. We show that even at the room temperature, the device acts as a mechanical rectifier: The pinion rotates with a nonzero average velocity and lifts up an external load. For typical values of parameters, we find that the pinion rotates with an average angular velocity . The thermal noise may even facilitate the device operation.
We study transport properties of an inertial Brownian motor which moves in a deformable Remoissenet-Peyrad periodic potential and is subjected to both a static bias force and time periodic driving biharmonic force. By modifying the shape of the potential, the anomalous transport is identified for a particular set of the system parameters. For a particular potential shape, the mean velocity of a particle is modified by going from negative to positive values according to the external bias force. These features also depend on both the biharmonic parameter and the phase-lag of two signals. A remarkable transition of the negative velocity depending on the shape of the potential is observed. We also focus on the efficiency of the motor and discuss velocity fluctuation. In addition, within selected system parameters, different types of diffusion particle such as subdiffusion, superdiffusion, normal diffusion, ballistic diffusion, hyperdiffusion and dispersionless transport phenomena are generated in the system.
Effects of non-Gaussian noise on negative mobility in an inertial ratchet were investigated by means of stochastic simulation method. The absolute negative mobility (ANM), negative nonlinear mobility (NDM), and negative differential mobility (NNM) were simulated, separately. Results indicate that: (i) non-Gaussian noise can either enhance or diminish the phenomena of ANM, and non-Gaussian noise also can induce NDM and NNM in regions of parameter space. (ii) The average velocity-correlation time characteristics shift towards small value of correlation time. (iii) The absolute value of negative-valued minima decreases as the non-Gaussian noise parameter q increases.
