Asymptotic solutions of continuous-time random walks

The continuous-time random walk of Montroll and Weiss has a complete separation of time (how long a walker will remain at a site) and space (how far a walker will jump when it leaves a site). The time part is completely described by a pausing time distribution(t). This paper relates the asymptotic time behavior of the probability of being at sitel at timet to the asymptotic behavior of(t). Two classes of behavior are discussed in detail. The first is the familiar Gaussian diffusion packet which occurs, in general, when at least the first two moments of(t) exist; the other occurs when(t) falls off so slowly that all of its moments are infinite. Other types of possible behavior are mentioned. The relationship of this work to solutions of a generalized master equation and to transient photocurrents in certain amorphous semiconductors and organic materials is discussed.This work was partially supported by NSF Grant No. 28501.     

There is more to be learned from the Lorentz model

The classical Lorentz model for charged noninteracting point particles in a perpendicular magnetic field is reconsidered in 2D. We show that the standard Boltzmann equation is not valid for this model, even in the Grad limit. We construct a generalized Boltzmann equation which is, and solve the corresponding initial value problem exactly. By an independent calculation, we find the same solution by directly constructing the Green function from the dynamics of the model in the Grad limit. From this solution an expression for the diffusion tensor, valid for arbitrary short-range forces, is derived. For hard disks we calculate the diffusion tensor explicitly. Away from the Grad limit a percolation problem arises. We determine numerically the percolation threshold and the corresponding geometric critical exponents. The numerical evidence strongly suggests that this continuum percolation model is in the universality class of 2D lattice percolation. Although we have explicitly determined a number of limiting properties of the model, several intriguing open problems remain.It is with great pleasure we include this paper in the issue honoring Matthieu Ernst, who not only shares our love for kinetic theory, but who also contributed so much to its modern development.     

Estimates for first exit times of non-Markovian Itô processes

First exit times and their path-wise dependence on trajectories are studied for non-Markovian Itô processes. Estimates of distances between two exit times are obtained. In particular, it follows that first exit times of two Itô processes are close if their trajectories are close.     

A hybrid formalism combining fluctuating hydrodynamics and generalized Langevin dynamics for the simulation of nanoparticle thermal motion in an incompressible fluid medium

A novel hybrid scheme based on Markovian fluctuating hydrodynamics of the fluid and a non-Markovian Langevin dynamics with the Ornstein-Uhlenbeck noise perturbing the translational and rotational equations of motion of the nanoparticle is employed to study the thermal motion of a nanoparticle in an incompressible Newtonian fluid medium. A direct numerical simulation adopting an arbitrary Lagrangian-Eulerian (ALE) based finite element method (FEM) is employed in simulating the thermal motion of a particle suspended in the fluid confined in a cylindrical vessel. The results for thermal equilibrium between the particle and the fluid are validated by comparing the numerically predicted temperature of the nanoparticle with that obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation function (VACF) and mean squared displacement (MSD) with well-known analytical results. For nanoparticle motion in an incompressible fluid, the fluctuating hydrodynamics approach resolves the hydrodynamics correctly but does not impose the correct equipartition of energy based on the nanoparticle mass because of the added mass of the displaced fluid. In contrast, the Langevin approach with an appropriate memory is able to show the correct equipartition of energy, but not the correct short- and long-time hydrodynamic correlations. Using our hybrid approach presented here, we show for the first time, that we can simultaneously satisfy the equipartition theorem and the (short- and long-time) hydrodynamic correlations. In effect, this results in a thermostat that also simultaneously preserves the true hydrodynamic correlations. The significance of this result is that our new algorithm provides a robust computational approach to explore nanoparticle motion in arbitrary geometries and flow fields, while simultaneously enabling us to study carrier adhesion mediated by biological reactions (receptor-ligand interactions) at the vessel wall at a specified finite temperature.     

Fast quantum search driven by environmental engineering

Studies have demonstrated that a joined complete graph is a typical mathematical model that can support a fast quantum search. In this paper, we study the implementation of joined complete graphs in atomic systems and realize a quantum search of runtime $O(\sqrt{N})$ based on this implementation with a success probability of 50%. Even though the practical systems inevitably interact with the surrounding environment, we reveal that a successful quantum search can be realized through delicately engineering the environment itself. We consider that our study will bring about a feasible way to realize quantum information processing including quantum algorithms in reality.     

Deterministic controlled bidirectional remote state preparation in dissipative environments

It is a significant subject to explore effective quantum communication protocol and enhance the efficiency of the transmission process in noisy environments. In this paper, we investigate the bidirectional controlled remote preparation of an arbitrary single-qubit state in the presence of dissipative environments by using two EPR states as the entanglement source. We first construct the quantum circuit of our scheme by means of unitary matrix decomposition procedure, then the effects of the Markovian and non-Markovian environmental noises acting on the EPR states are considered through the analytical derivation and numerical calculations of the corresponding average fidelity. Moreover, we adopt two methods of weak measurement reversal (WMR) and detuning modulation to improve the average fidelity. Our results show that the average fidelity can be remarkably enhanced under appropriate conditions of the WMR strength and the detuning. Compared with the average fidelity behaviors in dissipative environments, it is also shown that the two methods for fidelity improvement are more efficient in the non-Markovian regime than in the Markovian regime.     

The squeezing dynamics of two independent atoms by detuning in two non-Markovian environments

The squeezing dynamics of two independent two-level atoms off-resonantly coupled to two non-Markovian reservoirs is studied by the time-convolutionless master-equation approach. We find that the squeezing of two atoms is dependent on both detuning and the non-Markovian effect. Our results show that, in the non-Markovian regime, the bigger the detuning and the stronger the non-Markovian effect are, the larger the strength of the squeezing is. And the squeezing of two atoms can be effectively protected for a long time when both the non-Markovian effect and detuning are present simultaneously. The physical mechanism is that the detuning not only can promote the feedback of information from the environment into the atomic system but also can greatly suppress the atomic decay in the non-Markovian regime.     

Feedback of Non-Markovian Quantum Dynamics in Dimer System: the Effect of Correlated Environments and Temperature

In this work, we research the non-Markovian dynamical process of the dimer system and the effect of the interactional environments for the information feedback under different temperature T. Not only the functional relation of the trace distance and the fidelity are obtained, but also the changing properties of the fidelity and the measure quantity N (φ) which are used to quantify the degree of the non-Markovian process are discussed as a function of the interactional strength q between the environments. These results show a possible method which can preserve the information and enhance the distinguishability of the pair of states in decohering environments.     

Quantum coherence preservation of atom with a classical driving field under non-Markovian environment

The exact dynamics of an open quantum system consisting of one qubit driven by a classical driving field is investigated. Our attention is focused on the influences of single-and two-photon excitations on the dynamics of quantum coherence and quantum entanglement. It is shown that the atomic coherence can be improved or even maintained by the classical driving field, the non-Markovian effect, and the atom-reservoir detuning. The interconversion between the atomic coherence and the atom-reservoir entanglement exists and can be controlled by the appropriate conditions. The conservation of coherence for different partitions is explored, and the dynamics of a system with two-photon excitations is different from the case of single-photon excitation.     

周期场中非各态历经布朗运动

将自由状态下呈弹道扩散的非各态历经系统置于周期场中,进而将非各态历经布朗运动分为两类.第一类是阻尼核的Laplace变换的低频为零的系统,当温度远大于势垒高度时,系统平均能量的动能部分依赖粒子的初始速度分布;随温度降低,系统的各态历经性得到恢复.然后将第一类系统的稳定速度变量作为一个内部噪声,再去驱动一个自由布朗粒子,则阻尼核的Laplace变换在零频时为无穷大.结果发现,粒子扩散系数随温度的增加而趋于零,显示一种经典局域化特征,系统的渐进分布依赖于初始坐标分布.这是第二类非各态历经性运动,不能通过外加势而恢复. 关键词： 非各态历经 非Markov布朗运动 扩散系数 噪声谱