Fixation of advantageous mutations in an off-equilibrium population

We investigate the evolution of asexual populations subject to a large supply of deleterious mutations such that Muller's ratchet operates. In this regime, the accumulation of deleterious mutations takes place continuously with the resulting loss of the least-loaded class of individuals. In the current work, we study the effect of the supply of beneficial mutations on the ratchet's speed. We also examine how the rate of substitution of favorable mutations as well as the mean selective effect of favorable mutations that reach fixation is compared to those assuming a population at equilibrium. We observe that under Muller's ratchet, the rate of fixation of advantageous mutations is higher than that predicted for an equilibrium population. The difference between the rate supposing an equilibrium regime and that for the non-equilibrium case becomes larger as we increase the rate of deleterious mutations. On the other hand, the mean selective effect of beneficial mutations that reach fixation is smaller than the expected value for the equilibrium situation.     

Rectification in Luttinger liquids

We investigate the rectification of an ac bias in Luttinger liquids in the presence of an asymmetric potential (the ratchet effect). We show that a strong repulsive electron interaction enhances the ratchet current in comparison with Fermi-liquid systems, and the dc I-V curve is strongly asymmetric in the low-voltage regime even for a weak asymmetric potential. At higher voltages the ratchet current exhibits an oscillatory voltage dependence.     

Dynamics of matter-wave solitons in a ratchet potential

We study the dynamics of bright solitons formed in a Bose-Einstein condensate with attractive atomic interactions perturbed by a weak bichromatic optical lattice potential. The lattice depth is a biperiodic function of time with a zero mean, which realizes a flashing ratchet for matter-wave solitons. We find that the average velocity of a soliton and the soliton current induced by the ratchet depend on the number of atoms in the soliton. As a consequence, soliton transport can be induced through scattering of different solitons. In the regime when matter-wave solitons are narrow compared to the lattice period the dynamics is well described by the effective Hamiltonian theory.     

Transport and dynamical properties of inertial ratchets

In this paper we discuss the dynamics and transport properties of a massive particle in a ratchet type potential immersed in a dissipative environment. The directional currents and characteristics of the motion are studied as the specific frictional coefficient varies, finding that the stationary regime is strongly dependent on this parameter. The maximal Lyapunov exponent and the current show large fluctuations and inversions, therefore for some range of the control parameter, this inertial ratchet could originate a mass separation device. Also an exploration of the effect of a random force on the system is performed.     

周期驱动玻色-爱因斯坦凝聚系统的棘齿效应

研究了周期脉冲驱动下的玻色-爱因斯坦凝聚体系（BEC）的动力学演化.其中着重考虑了BEC原子间的非线性相互作用对量子棘齿效应的影响.数值计算结果表明,较弱的非线性相互作用可以减弱定向动量流的强度.而较强的非线性相互作用则会使量子棘齿效应消失甚至发生反转,即系统会出现反向的定向动量流,而且随着时间的演化,动量流会表现出微弱的饱和趋势.计算还发现,高阶量子共振下系统的棘齿效应变得很不明显,而且外部驱动势的周期噪声很容易破坏体系的棘齿效应. 关键词： 玻色-爱因斯坦凝聚 量子混沌 量子共振 棘齿效应     

涨落作用下周期驱动的分数阶过阻尼棘轮模型的混沌输运现象

考虑涨落作用下周期驱动的过阻尼分数阶棘轮模型, 通过模型的数值求解, 研究确定性棘轮的混沌特性与噪声的作用对输运行为的影响, 进而讨论过阻尼分数阶分子马达反向输运的机理. 分析表明: 随着势垒高度、 势不对称性与模型记忆性的变化, 随机棘轮的反向输运并不必然地要求确定性棘轮也反向输运; 随着模型阶数的减小, 亦即分数阻尼介质记忆性的增强, 确定性棘轮在反向输运之前会经历一个周期倍化导致的混沌状态, 但在噪声作用下, 反向流的发生会提前, 即混沌状态的确定性棘轮在噪声的作用下即可进行反向输运. 也就是说, 噪声能定性地改变棘轮的输运状态: 从无噪声时的混沌运动到有噪声时的定向输运. 这是过阻尼随机棘轮反向输运的一种机理, 也是噪声在定向输运过程中发挥积极作用的一个体现.     

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     

Magnetic ratchet effects in a two-dimensional electron gas

The effect of the magnetic field on the generation of an electric current in a two-dimensional electronic ratchet is theoretically studied. Mechanisms of the formation of magnetically induced photocurrent are proposed for a structure with a two-dimensional electron gas (quantum well, graphene, or topological insulator) with a lateral asymmetric superlattice consisting of metallic strips on the external surface of the structure. The ratchet with the spatially oscillating magnetic field generated by the ferromagnetic lattice, as well as the nonmagnetic ratchet placed in the uniform magnetic field both classically weak and strong quantizing, is considered. It is established that the ratio of the amplitude of the magnetic oscillations of photocurrent to the ratchet photocurrent in zero field can exceed two orders of magnitude.     

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

Current-driven dynamics of Josephson junction networks (JJNs) is studied using numerical simulations. We consider a JJN with an asymmetric and periodic potential of vortices, which is realized by saw-tooth modulation of junction critical currents. When external ac currents are applied to the JJN in a magnetic field, there appears a ratchet effect, and then directed motion of vortices is induced in certain system parameter regimes. A ratchet behavior is observed even for JJNs with weak structural disorder. We clarify the vortex pinning and dynamics in the JJN as a ratchet system.     

Feedback control in a coupled Brownian ratchet

On the basis of the double-well ratchet potential which can be calculated theoretically and implemented experimentally, the influences of the time delay, the coupling constant, and the asymmetric parameter of the potential on the performance of a delayed feedback ratchet consisting of two Brownian particles coupled mutually with a linear elastic force are investigated. The centre-of-mass velocity of two coupled Brownian particles, the average effective diffusion coefficient, and the Pe number are calculated. It is found that the parameters are affected by not only the time delay and coupling constant but also the asymmetric parameter of the double-well ratchet potential. It is also found that the enhancement of the current may be obtained by varying the coupling constant of the system for the weak coupling case. It is expected that the results obtained here may be observed in some physical and biological systems.     

Adaptive walks and extreme value theory

We study biological evolution in a high-dimensional genotype space in the regime of rare mutations and strong selection. The population performs an uphill walk which terminates at local fitness maxima. Assigning fitness randomly to genotypes, we show that the mean walk length is logarithmic in the number of initially available beneficial mutations, with a prefactor determined by the tail of the fitness distribution. This result is derived analytically in a simplified setting where the mutational neighborhood is fixed during the adaptive process, and confirmed by numerical simulations.     

Collective Transport of Coupled Brownian Motors with Low Randomness

The transport properties of coupled Brownian motors in rocking ratchet are investigated via solving Langevin equation. By means of velocity, diffusion coefficient, and their ratio （Peclet number）, different features from a single particle have been found. In the regime of low-to-moderate D, the average velocity of elastically coupled Brownian motors is larger than that of a single Brownian particles; the Peclet number of elastically coupled Brownian motors is peaked functions of intensity of noise D but the Peclet number of a single Brownian motor decreases monotonously with the increase of a single Brownian motor. The results exhibit an interesting cooperative behavior between coupled particles subjected to a rocking force, which can generate directed transport with low randomness or high transport coherence in symmetrical periodic potential.     

Relativistic graphene ratchet on semidisk Galton board

Using extensive Monte Carlo simulations we study numerically and analytically a photogalvanic effect, or ratchet, of directed electron transport induced by a microwave radiation on a semidisk Galton board of antidots in graphene. A comparison between usual two-dimensional electron gas (2DEG) and electrons in graphene shows that ratchet currents are comparable at very low temperatures. However, a large mean free path in graphene should allow to have a strong ratchet transport at room temperatures. Also in graphene the ratchet transport emerges even for unpolarized radiation. These properties open promising possibilities for room temperature graphene based sensitive photogalvanic detectors of microwave and terahertz radiation.     

Chaotic Ratchet Effect for Bose-Einstein Condensed Atoms in 1D Optical Lattices

The chaotic ratchet effect for Bose-Einstein condensed atoms in an optical lattice is investigated. By using the direct perturbation method we obtain the chaotic solution of the condensed system. Theoretical analysis reveals that the transport of the condensed atoms in the ratchet potential is a chaotic one, and corresponding numerical results agree well with the theoretical results.     

Quantum Ratchet in Disordered Quantum Walk

Symmetrically evolving discrete quantum walk results in dynamic localization with zero mean displacement when the standard evolution operations are replaced by a temporal disorder evolution operation. In this work we show that the quantum ratchet action, that is, a directed transport in standard or disordered discrete‐time quantum walk can be realized by introducing a pawl like effect realized by using a fixed coin operation at marked positions that is, different from the ones used for evolution at other positions. We also show that the combination of standard and disordered evolution operations can be optimized to get the mean displacement of order ∝ t (number of walk steps). This model of quantum ratchet in quantum walk is defined using only a set of entangling unitary operators resulting in the coherent quantum transport.     

二维耦合定向输运模型研究

建立了外部驱动力及噪声作用下的二维耦合定向输运模型, 其中的一个维度上为周期性分段棘齿势, 另一垂直维度上为周期性对称非棘齿势, 外部驱动力及噪声加在周期对称非棘齿势方向上, 而棘齿势方向不加任何驱动, 采用非平衡统计及非线性动力学理论研究了过阻尼情况下耦合系统在两个维度上的输运性质. 结果显示, 棘齿势与非棘齿势方向均可产生定向输运, 其中棘齿势方向的系统平均速度对耦合强度、噪声强度、驱动力强度及粒子数目均有明显的依赖性, 合适的耦合强度、噪声强度、驱动力强度或粒子数目下均可产生最大输运速度. 而非棘齿势方向的系统平均速度受非棘齿势势垒高度影响显著, 但随耦合强度、驱动力强度、驱动力初相位差及粒子数目的变化均出现波动现象, 表现出平均速度对这些参量的依赖性较弱.     

Random Evolutionary Dynamics Driven by Fitness and House-of-Cards Mutations: Sampling Formulae

We first revisit the multi-allelic mutation-fitness balance problem, especially when mutations obey a house of cards condition, where the discrete-time deterministic evolutionary dynamics of the allelic frequencies derives from a Shahshahani potential. We then consider multi-allelic Wright–Fisher stochastic models whose deviation to neutrality is from the Shahshahani mutation/selection potential. We next focus on the weak selection, weak mutation cases and, making use of a Gamma calculus, we compute the normalizing partition functions of the invariant probability densities appearing in their Wright–Fisher diffusive approximations. Using these results, generalized Ewens sampling formulae (ESF) from the equilibrium distributions are derived. We start treating the ESF in the mixed mutation/selection potential case and then we restrict ourselves to the ESF in the simpler house-of-cards mutations only situation. We also address some issues concerning sampling problems from infinitely-many alleles weak limits.     

Dynamics of quantum Fisher information in a two-level system coupled to multiple bosonic reservoirs

We consider the optimal parameter estimation for a two-level system coupled to multiple bosonic reservoirs. By using quantum Fisher information(QFI), we investigate the effect of the Markovian reservoirs' number N on QFI in both weak and strong coupling regimes for a two-level system surrounded by N zero-temperature reservoirs of field modes initially in the vacua. The results show that the dynamics of QFI non-monotonically decays to zero with revival oscillations at some time in the weak coupling regime depending on the reservoirs' parameters. Furthermore, we also present the relations between the QFI flow, the flows of energy and information, and the sign of the decay rate to gain insight into the physical processes characterizing the dynamics.     

Regular and Chaotic Spatial Distribution of Bose-Einstein Condensed Atoms in a Ratchet Potential

We study the regular and chaotic spatial distribution of Bose-Einstein condensed atoms with a space-dependent nonlinear interaction in a ratchet potential. There exists in the system a space-dependent atomic current that can be tuned via Feshbach resonance technique. In the presence of the space-dependent atomic current and a weak ratchet potential, the Smale-horseshoe chaos is studied and the Melnikov chaotic criterion is obtained. Numerical simulations show that the ratio between the intensities of optical potentials forming the ratchet potential, the wave vector of the laser producing the ratchet potential or the wave vector of the modulating laser can be chosen as the controlling parameters to result in or avoid chaotic spatial distributional states.