分数阶双头分子马达的欠扩散输运现象

研究具有幂律记忆性的细胞液中双头分子马达的定向输运现象,选取幂函数作为广义Langevin方程的阻尼核函数,建立了分数阶过阻尼耦合Brown马达模型,讨论了阶数及耦合系数对双头分子马达定向输运速度的影响. 仿真结果表明,分数阶过阻尼双头分子马达也会产生定向输运现象,并且在某些阶数下会产生整数阶情形所不具有的反向定向流. 当噪声强度固定时,输运速度随着阶数以及耦合系数的变化均会出现广义随机共振现象. 特别地,研究发现双头分子马达在记忆闪烁棘轮势中具有某些单头分子马达所不具备的运动特性,定向流的大小和方向由噪声与双头间作用力相互耦合控制. 关键词： 分数阶双头分子马达 欠扩散 定向输运 广义随机共振     

分数阶布朗马达在闪烁棘齿势中的合作输运现象

引入分数阶微积分理论,建立耦合分数阶布朗马达在闪烁棘齿势中的合作输运模型, 利用分数阶差分法求得模型数值解并分析了模型参数对合作定向输运性质的影响. 发现在具有记忆性的分数阶棘齿系统中, 系统阶数与粒子间耦合强度不仅可影响粒子链输运速度, 还可使粒子链出现与整数阶方向相反的定向流; 在阶数固定下, 定向输运速度将随参数(噪声强度、耦合强度、棘齿势峰值高度)变化出现广义随机共振现象. 关键词： 分数阶布朗马达 闪烁棘齿势 合作定向输运 广义随机共振     

时间非对称外力驱动分数阶布朗马达的定向输运

本文研究了周期对称势中时间非对称外力驱动的布朗粒子输运现象, 建立了分数阶布朗马达输运模型. 其中外力是零均值的, 而分数阶阶数则刻画了客观环境的非均匀性程度. 通过将模型离散化进行数值模拟, 讨论了分数阶阶数、系统参量和外部参量与定向流之间的依赖关系. 研究表明, 即使没有倾斜势场的作用, 时间非对称外力也可以诱导系统产生定向输运; 输运速度随分数阶阶数的增大而单调递增; 当阶数固定时, 系统的输运速度会随着势垒高度、噪声强度非单调变化, 表现出广义随机共振现象. 分析指出, 分数阶郎之万方程所刻画的输运现象是在整数阶模型基础上的一个推广, 进而为输运现象提供了一个可能更为真实的模型.     

带反馈的分数阶耦合布朗马达的定向输运

研究具有幂律记忆性的带反馈耦合布朗马达的定向输运现象, 引入分数阶理论, 建立了带反馈的分数阶耦合布朗马达模型, 利用分数阶差分法求得模型数值解并分析了模型参数对合作定向输运性质的影响. 仿真结果表明, 系统的记忆性通过影响带反馈的棘齿势的打开和闭合而影响粒子的定向输运, 即当系统的阶数在较小的范围内, 系统的记忆性会使带反馈的棘齿势的开关频率增加, 从而增大定向流速; 当系统其他参数(势垒高度、噪声强度等)固定时, 输运速度随着阶数的变化出现广义随机共振现象.     

分数阶非对称耦合系统在对称周期势中的定向输运

在没有外力且周期势对称的情况下,对非对称耦合粒子链的运动,以具备更强刻画能力的分数阶微积分理论建立了分数阶模型,对其定向输运现象进行针对性研究,采用分数阶差分法进行数值求解并分析系统参数对定向输运速度的影响.相应仿真表明,分数阶非对称耦合系统在没有外力和噪声驱动的情况下仍能产生定向输运,且输运速度随阶数的增大而增大;当阶数固定时,粒子链平均速度随耦合强度和势垒高度非单调变化;当系统存在噪声时,粒子链平均速度出现了广义随机共振现象,且通过调节其他参数,可使得系统对噪声免疫甚至使噪声促进定向输运.     

二维势场中弹性耦合粒子的定向输运研究

建立了二维势场中弹性耦合粒子的输运模型, 其中一维上加交流驱动及噪声, 另一维上不加驱动及噪声, 分析讨论了过阻尼情形下系统和外部参量对定向流的影响. 结果表明, 粒子可以通过相互耦合使一个方向上输入的驱动能量转化到垂直方向上, 从而使无能量输入的方向产生定向流. 适当的弹簧自由长度及耦合强度可以使定向流达到极值, 特别是当耦合强度及噪声强度固定时, 定向流会随弹簧自由长度的变化而振荡, 出现多峰现象. 研究还发现, 定向流随噪声强度的变化出现随机共振现象. 当产生定向流方向上的势的不对称度达到一定程度时会出现流反转现象. 关键词： 弹性耦合 定向输运 随机共振 流反转     

耦合分数阶布朗马达在非对称势中的输运

讨论了分数阶Frenkel-Kontorova模型的物理意义, 并应用该模型刻画了耦合粒子链在记忆性介质中的输运现象, 研究了各参数对粒子链运动状态的影响. 数值仿真结果表明: 系统的记忆性对粒子链的运动有显著影响, 尤其出现了在非记忆性情况下所不具有的反向流. 同时发现粒子链的平均流速会随耦合强度、分数阶的阶数变化而产生广义共振; 此外, 平均流速还会随噪声强度的变化出现广义随机共振现象. 关键词： 分数阶Frenkel-Kontorova模型 记忆性介质 随机共振 定向输运反向流     

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.     

过阻尼分数阶Langevin方程及其随机共振

通过对广义Langevin方程阻尼核函数的适当选取,在过阻尼的情形下, 推导出分数阶Langevin方程.给合反常扩散理论和分数阶导数的记忆性, 讨论了分数阶Langevin方程的物理意义,进而得出分数阶Langevin方程产生随机共振的内在机理.数值模拟表明,在一定的阶数范围内,分数阶Langevin方程可以产生随机共振, 并且分数阶下的信噪比增益好于整数阶情形.     

双频驱动下分数阶过阻尼马达在空间对称势中的定向输运

从阻尼对历史加速度记忆的角度出发,对阶数p∈(0,2)的分数阶阻尼物理意义给出了统一的合理解释,具体分析了不同阶数下的阻尼记忆特性,在此基础上研究了空间对称势中分数阶单分子马达在无偏置双频简谐激励下的输运问题,通过数值方法分析了输运速度与模型各参数的关系以及分数阶阻尼对输运现象的影响机理.研究表明,在不同阶数下历史加速度对当前时刻阻尼力的贡献与距当前时刻的时间长度呈单增或单减关系;在适当参数下输运速度随空间势深和外力频率的增大均会出现广义共振现象,特别地,在存在输运且阻尼阶数较大的情况下输运速度随势深增大出现阶梯状变化而与外力频率呈正比例关系;输运速度及方向对外力波形十分敏感,在不同外力下阻尼力的记忆性会分别促进或阻碍粒子跃迁,甚至引发与整数阶方向相反的定向流.     

Spin-resolved polarized transport through a quasi one-dimensional mesoscopic quantum ring-shaped conductor with local Rashba spin-orbit interaction

We propose a quasi one-dimensional quantum ring-shaped model associated with Rashba spin-orbit (SO) interaction and Aharomov-Bohm flux to study a spin-dependent quantum transport. It is a possible candidate for spintronic current modulators. By tuning SO coupling strength and Fermi energy, we find there is a broad energy range of small vanishing spin transmission in the resonance and antiresonance interferences. More interestingly, the large on/off spin-resolved polarized conductance ratios are robust even in the presence of strong random on-site Anderson-type disorder in devices, which suggests a potential application in the real system.     

Kapitza resistance in basic chain models with isolated defects

We explore numerically the boundary Kapitza resistance in one-dimensional chain models with isotopic and/or coupling defects for variety of the inter-particle potentials. In linear models, the Kapitza resistance is well-defined and size-independent (contrary to the bulk heat conduction coefficient), but depends on the parameters of thermostats used in the simulation. For β-FPU model one also encounters the dependence on the thermostats; in addition, the simulated boundary resistance strongly depends on the total system size. Finally, in the models characterized by convergent bulk heat conductivity (chain of rotators, Frenkel-Kontorova model) the boundary resistance is thermostat- and size-independent. In linear chains, the Kapitza resistance is temperature-independent; thus, its temperature dependence allows one to judge on significance of the nonlinear interactions in the phonon scattering processes at the interface.     

Phase coherence of the electron and hole in a ferromagnetic film in proximity with a superconductor

The scattering matrix approach between the clean and dirty limits is developed for the study of tunneling spectra in a ferromagnetic film in proximity to a superconductor. The minigap and the damped oscillation from ``0" to ``π" state in tunneling conductance are attributed to the phase coherence of the electrons and the corresponding Andreev-reflected holes in the ferromagnetic film. The calculated results provide a reasonable explanation for the behavior observed in recent experiments.     

束流输运理论的新表述（II）——线性力的检验

 用数值方法在恒定和周期线性力情况下对纯粹和混合系统检验了我们在文献[1]中所提出的输运理论框架的可靠性和优越性。结果表明，该理论的数值计算和常用的粒子跟踪模拟完全一致，但计算时间少，误差涨落小。     

Spin Polarizations of Electron with Rashba Couplings in T-Shaped Devices: A Finite Element Approach

A generalized finite element formulation is proposed for the study of the spin-dependent ballistic transport of electron through the two-dimensional quantum structures with Rashba spin-orbit interactions (SOI). Thetransmission coefficient, conductance, the total and local polarization are numerically calculated and discussed as the Rashba coefficient, the geometric sizes, and incident energy are changed in the T-shaped devices. Some interesting features are found in the proper parameter regime. The polarization has an enhancement as the Rashba coefficient becomes stronger. The polarization valley is rigid in the regime of the conductance plateaus since the local interference among the polarized multi-wave modes. The Rashba interactions coupling to geometry in sizes could form the structure-induced Fano-Rashba resonance. In the wider stub, the localized spin lattice of electron could be produced. The conductance plateaus correspond to weakpolarizations. Strong polarizations appear when the stub sizes, incident energy, and the Rashba coupling coefficient are matched. The resonances are formed in a wide Fermi energy segment easily.     

Electrical conductance at initial stage in epitaxial growth of Pb on modified Si(1 1 1) surface

The electrical conductance and RHEED intensities as a function of the coverage have been measured during Pb depositions at 105 K on Si(1 1 1)-(6 × 6)Au with up to 4.2 ML of annealed Pb. The experiments show the strong influence of used substrates on the behavior of the conductance during the epitaxy of Pb atoms, especially for very initial stage of growth. Oscillations of the conductance during the layer-by-layer growth are correlated with RHEED intensity oscillations. The analysis of the conductance behavior is made according to the theory described by Trivedi and Aschcroft [N. Trivedi, N. Aschcroft, Phys. Rev. B 38 (1988) 12298].     

Linear and nonlinear transports of coupled quantum dots

Series of double quantum dots each with a size around 400 × 400nm² have been realized by delineating a 2DEG in modulation-doped AlGaAs/GaAs with 100 nm wide Schottky split gates fabricated by an electron-beam lithography and a lift-off technique. The split gate in the middle of the double dot allows us to control interdot coupling widely. The charging diagram obtained from linear transports in the Coulomb blockade regime shows that the isolated dots merge into a single composite dot with increase of interdot coupling. A clear Coulomb staircase has been observed in the double-dot system at a limited high-bias condition.     

A bond bending model for negative differential resistance in transport through single molecules

We develop a model for transport through benzene-based single molecules with an NO₂ side-group, which incorporates bond bending between the NO₂ and the adjacent benzene ring and successfully reproduces the experimentally observed strong negative differential resistance. Transport through the molecule is assumed to be incoherent and is treated using photon assisted tunnelling.     

Memory Effects in Nonequilibrium Transport for Deterministic Hamiltonian Systems

We consider nonequilibrium transport in a simple chain of identical mechanical cells in which particles move around. In each cell, there is a rotating disc, with which these particles interact, and this is the only interaction in the model. It was shown in Ref. 1 that when the cells are weakly coupled, to a good approximation, the jump rates of particles and the energy-exchange rates from cell to cell follow linear profiles. Here, we refine that study by analyzing higher-order effects which are induced by the presence of external gradients for situations in which memory effects, typical of Hamiltonian dynamics, cannot be neglected. For the steady state we propose a set of balance equations for the particle number and energy in terms of the reflection probabilities of the cell and solve it phenomenologically. Using this approximate theory we explain how these asymmetries affect various aspects of heat and particle transport in systems of the general type described above and obtain in the infinite volume limit the deviation from the theory in Ref. 1 to first-order. We verify our assumptions with extensive numerical simulations.     

Quantum Transport of Particles and Entropy

A unified view on macroscopic thermodynamics and quantum transport is presented. Thermodynamic processes with an exchange of energy between two systems necessarily involve the flow of other balancable quantities. These flows are first analyzed using a simple drift-diffusion model, which includes the thermoelectric effects, and connects the various transport coefficients to certain thermodynamic susceptibilities and a diffusion coefficient. In the second part of the paper, the connection between macroscopic thermodynamics and quantum statistics is discussed. It is proposed to employ not particles, but elementary Fermi- or Bose-systems as the elementary building blocks of ideal quantum gases. In this way, the transport not only of particles but also of entropy can be derived in a concise way, and is illustrated both for ballistic quantum wires, and for diffusive conductors. In particular, the quantum interference of entropy flow is in close correspondence to that of electric current.