逾渗分立时间量子行走的传输及纠缠特性

在一维分立时间量子行走中,通过静态和动态两种方式随机地断开连接边引入无序效应,研究了静态逾渗和动态逾渗对量子行走传输特性以及位置自由度和硬币自由之间纠缠的影响.随着演化时间的增加,静态逾渗会使得量子行走从弹道传输转变为安德森局域化,而动态逾渗则会使之转变为经典扩散.理想情况下,量子纠缠在较短的时间内就达到一个常数值E_0.静态逾渗量子行走的纠缠减小,并随着时间做无规振荡,而动态逾渗量子行走的纠缠则会随着时间光滑地增加,并在某一时间超过理想情况下的常数值,表现出动态逾渗增强量子纠缠的特性.     

Optimal disorder for segregation in annealed small worlds

We study a model for microscopic segregation in a homogeneous system of particles moving on a one-dimensional lattice. Particles tend to separate from each other, and evolution ceases when at least one empty site is found between any two particles. Motion is a mixture of diffusion to nearest-neighbour sites and long-range jumps, known as annealed small-world propagation. The long-range jump probability plays the role of the small-world disorder. We show that there is an optimal value of this probability, for which the segregation process is fastest. Moreover, above a critical probability, the time needed to reach a fully segregated state diverges for asymptotically large systems. These special values of the long-range jump probability depend crucially on the particle density. Our system is a novel example of the rare dynamical processes with critical behaviour at a finite value of the small-world disorder.     

Continuity and Anomalous Fluctuations in Random Walks in Dynamic Random Environments: Numerics,Phase Diagrams and Conjectures

We perform simulations for one dimensional continuous-time random walks in two dynamic random environments with fast (independent spin-flips) and slow (simple symmetric exclusion) decay of space-time correlations, respectively. We focus on the asymptotic speeds and the scaling limits of such random walks. We observe different behaviors depending on the dynamics of the underlying random environment and the ratio between the jump rate of the random walk and the one of the environment. We compare our data with well known results for static random environment. We observe that the non-diffusive regime known so far only for the static case can occur in the dynamical setup too. Such anomalous fluctuations give rise to a new phase diagram. Further we discuss possible consequences for more general static and dynamic random environments.     

A generalization of random walk models to correlations over two jumps

Using published results on continuous time random walk theories, we show that the random walk theory of Gissler and Rother is equivalent to a master equation with jumps to further neighbor sites. We extend the theory to include time correlations over two jumps. No special assumptions are made in the analysis, so that the theory may be applied to any lattice type with a general time probability distribution for jumps; a generalized second-order differential equation is given for the results. In the special case of an exponential time probability density, a simple homogeneous second order differential equation is obtained which is shown to be equivalent to a certain two-state master equation model.     

Generalized pricing formulas for stochastic volatility jump diffusion models applied to the exponential Vasicek model

Path integral techniques for the pricing of financial options are mostly based on models that can be recast in terms of a Fokker-Planck differential equation and that, consequently, neglect jumps and only describe drift and diffusion. We present a method to adapt formulas for both the path-integral propagators and the option prices themselves, so that jump processes are taken into account in conjunction with the usual drift and diffusion terms. In particular, we focus on stochastic volatility models, such as the exponential Vasicek model, and extend the pricing formulas and propagator of this model to incorporate jump diffusion with a given jump size distribution. This model is of importance to include non-Gaussian fluctuations beyond the Black-Scholes model, and moreover yields a lognormal distribution of the volatilities, in agreement with results from superstatistical analysis. The results obtained in the present formalism are checked with Monte Carlo simulations.     

Directional quantum random walk induced by coherence

Quantum walk (QW), which is considered as the quantum counterpart of the classical random walk (CRW), is actually the quantum extension of CRW from the single-coin interpretation. The sequential unitary evolution engenders correlation between different steps in QW and leads to a non-binomial position distribution. In this paper, we propose an alternative quantum extension of CRW from the ensemble interpretation, named quantum random walk (QRW), where the walker has many unrelated coins, modeled as two-level systems, initially prepared in the same state. We calculate the walker's position distribution in QRW for different initial coin states with the coin operator chosen as Hadamard matrix. In one-dimensional case, the walker's position is the asymmetric binomial distribution. We further demonstrate that in QRW, coherence leads the walker to perform directional movement. For an initially decoherenced coin state, the walker's position distribution is exactly the same as that of CRW. Moreover, we study QRW in 2D lattice, where the coherence plays a more diversified role in the walker's position distribution.     

Localization of quantum walks on finite graphs

We analyze the localization of quantum walks on a one-dimensional finite graph using vector-distance. We first vectorize the probability distribution of a quantum walker in each node. Then we compute out the probability distribution vectors of quantum walks in infinite and finite graphs in the presence of static disorder respectively, and get the distance between these two vectors. We find that when the steps taken are small and the boundary condition is tight, the localization between the infinite and finite cases is greatly different. However, the difference is negligible when the steps taken are large or the boundary condition is loose. It means quantum walks on a one-dimensional finite graph may also suffer from localization in the presence of static disorder. Our approach and results can be generalized to analyze the localization of quantum walks in higher-dimensional cases.     

Phase control of two-dimensional probe gain-absorption spectra in semiconductor quantum wells

We investigate the two-dimensional gain and absorption of a weak probe field via two orthogonal standing-wave lasers in a four-level inverted-Y asymmetric quantum well system. We find that, due to the spatial-dependent quantum interference effect, the spatial distribution of the 2D gain and absorption spectra can be easily controlled by adjusting the system parameters. More importantly, the probe gain-absorption spectrum can be controlled at a particular position and the 2D localization effect is indeed achieved efficiently. Thus, our scheme shows the underlying probability for the formation of the 2D localization effect by using a QW structure.     

Relationships between a roller and a dynamic pressure distribution in circular hydraulic jumps

We investigated numerically the relation between a roller and the pressure distribution to clarify the dynamics of the roller in circular hydraulic jumps. We found that a roller which characterizes a type II jump is associated with two high pressure regions after the jump, while a type I jump (without the roller) is associated with only one high pressure region. Our numerical results show that building up an appropriate pressure field is essential for a roller.     

Resonant elastic scattering of light from single quantum wells in semiconductor multilayers

A theory is developed for steady-state elastic scattering of light via quasi-2D excitons from a quantum well (QW) whose interfaces are randomly rough. The study is mainly focused on the angle dependences of radiation giving direct information about static disorder responsible for the elastic scattering. A nonlocal excitonic susceptibility is expressed in terms of random profile functions of QW interfaces. Treated is elastic scattering of light from a disordered QW in the following actual dielectric environments: (i) a uniform background, (ii) a Fabry–Perot film with rough boundaries, and (iii) a semiconductor microcavity. The cross-sections are derived analytically for scattering of linearly polarized light to the lowest (Born's) approximation with arbitrary roughness statistics. The spectral and angle dependencies of scattering intensity are analyzed numerically in the absolute-value scale with Gaussian correlation of interface roughness. The probability 10⁻² was found for the exciton-mediated scattering of a photon from a QW interface roughness whose root-mean-square height is on the level of 2×10⁻¹ nm. This probability is shown to exceed by two orders of magnitude that is typical of resonant scattering from either a single semiconductor surface or rough boundaries of a semiconductor Fabry–Perot film containing the QW. The scattering spectrum of a QW placed in a microcavity is predicted to have a doublet structure whose components are associated with the cavity exciton–polaritons.     

Asymptotic distributions of continuous-time random walks: A probabilistic approach

We provide a systematic analysis of the possible asymptotic distributions o one-dimensional continuous-time random walks (CTRWs) by applying the limit theorems of probability theory. Biased and unbiased walks of coupled and decoupled memory are considered. In contrast to previous work concerning decoupled memory and Lévy walks, we deal also with arbitrary coupled memory and with jump densities asymmetric about its mean, obtaining asymmetric Lévy-stable limits. Suprisingly, it is found that in most cases coupled memory has no essential influence on the form of the limiting distribution. We discuss interesting properties of walks with an infinite mean waiting time between successive jumps.     

The noisy Hegselmann-Krause model for opinion dynamics

In the model for continuous opinion dynamics introduced by Hegselmann and Krause, each individual moves to the average opinion of all individuals within an area of confidence. In this work we study the effects of noise in this system. With certain probability, individuals are given the opportunity to change spontaneously their opinion to another one selected randomly inside the opinion space with different rules. If the random jump does not occur, individuals interact through the Hegselmann-Krause’s rule. We analyze two cases, one where individuals can carry out opinion random jumps inside the whole opinion space, and other where they are allowed to perform jumps just inside a small interval centered around the current opinion. We found that these opinion random jumps change the model behavior inducing interesting phenomena. Using pattern formation techniques, we obtain approximate analytical results for critical conditions of opinion cluster formation. Finally, we compare the results of this work with the noisy version of the Deffuant et al. model [G. Deffuant, D. Neu, F. Amblard, G. Weisbuch, Adv. Compl. Syst. 3, 87 (2000)] for continuous-opinion dynamics.     

The effect of an NH tautomerism on the structure and vibrational states of chlorin

A random sequence (path) of counts of an ideal detector, selective for energy states of an atom, at the output of a one-atom maser is simulated numerically by the Monte Carlo method. Fragments of a path for the cases in which a micromaser undergoes quantum jumps with an increase (jump up) or a decrease in the average number of photons in a mode are obtained. An idealized dynamic model of a quantum jump is formulated on the basis of the concept of a critical fluctuation, when several tens of atoms in the same state are detected successively. Approximate formulas for the dependence of the average number of photons and the rate of its change on the number of atoms passing through a cavity along a jump path are obtained. The probability of a quantum jump in the idealized model is estimated. It is shown that accounting for the nonideality of a jump increases its probability by several orders of magnitude. The high rate of a quantum jump up (the superpump effect) is attributed to the possibility of redistribution of photons between subensembles of the mode states. The probability of a nonideal quantum jump and the most likely number of interruptions (opposite escapes) in an ideal jump path are estimated.     

Two Speed TASEP

We consider the TASEP on ? with two blocks of particles having different jump rates. We study the large time behavior of particles’ positions. It depends both on the jump rates and the region we focus on, and we determine the complete process diagram. In particular, we discover a new transition process in the region where the influence of the random and deterministic parts of the initial condition interact. Slow particles may create a shock, where the particle density is discontinuous and the distribution of a particle’s position is asymptotically singular. We determine the diffusion coefficient of the shock without using second class particles. We also analyze the case where particles are effectively blocked by a wall moving with speed equal to their intrinsic jump rate.     

Jumps in icosahedral quasicrystals

Atomic jumps in icosahedral (AlCu)Li quasicrystals and related structures have been studied by molecular dynamics simulations. In quasicrystalline structures jumps exists with jump vectors much shorter than an average nearest neighbor distance. This is a consequence of the phasonic degree of freedom. The jumps therefore are called flips and the sites connected by the jump vector are denoted alternative positions. We find that the atoms in the quasicrystal structures studied here do not flip to alternative positions as proposed and observed in decagonal or dodecagonal quasicrystals but jump to sites which are at least an ordinary interatomic distance apart. Furthermore we observe two diffusion regimes: below about 55% of the melting temperature only small (AlCu) atoms carry out ring processes whereas at higher temperatures both kinds of atoms contribute to long-range diffusion. Received 21 July 1999     

Optical properties of type-II InGaN/GaAsN/GaN quantum wells

Optical properties of type-II InGaN/GaNAs QW light-emitting diodes are investigated by using the multiband effective mass theory. These results are compared with those of conventional InGaN/GaN QW structures. The type-II InGaN/GaNAs/GaN QW structure shows much larger spontaneous emission and optical gain than that of a conventional QW structure. This can be explained by the fact that, in the case of the type-II QW structure, the effective well width is greatly reduced. A type-II QW structure shows that the peak position at a high carrier density is similar to that (530 nm) at a low carrier density. On the other hand, in the case of a conventional QW structure, the peak position is largely blueshifted at a high carrier density.     

Multiple avalanches across the metal-insulator transition of vanadium oxide nanoscaled junctions

The metal-insulator transition of nanoscaled VO2 devices is drastically different from the smooth transport curves generally reported. The temperature driven transition occurs through a series of resistance jumps ranging over 2 decades in magnitude, indicating that the transition is caused by avalanches. We find a power law distribution of the jump sizes, demonstrating an inherent property of the VO2 films. We report a surprising relation between jump magnitude and device size. A percolation model captures the general transport behavior, but cannot account for the statistical behavior.     

Unfolding pathway and its identifiability in heterogeneous chains of bistable units

We investigate the behavior of a chain of bistable units with an heterogeneous distribution of energy jumps between the folded and unfolded states. For homogeneous chains, loaded by soft or hard devices, all units at each switching occurrence have the same probability to unfold and it is therefore impossible to identify an unfolding pathway. Conversely, the heterogeneity represents a quenched disorder from the statistical mechanics point of view, and is able to break the symmetry eventually generating an unfolding pathway. We prove that the most probable pathway is realized by arranging the energy jumps in ascending order. Hence, the mechanics of this system is able to implement a statistical sorting procedure. We quantitatively evaluate the identifiability of the obtained unfolding pathway in terms of the variance of the heterogeneous energy jumps and the temperature. This concept is applied to both deterministic and random distributions of energy jumps within the chain.     

Non-Markovian dynamics and quantum jumps

Experiments with trapped particles have demonstrated the existence of quantum jumps and the discrete nature of single-system dynamics in quantum mechanics. The concept of jumps is also a powerful tool for simulating and understanding open quantum systems. In non-Markovian systems jump probabilities can become negative due to memory effects between the system and its environment. We discuss a recently presented method that can handle both positive and negative probabilities and provides powerful insight into the dynamics of open systems with memory. The key element is a reversed quantum jump to a system state that was, in principle, already destroyed by an earlier normal jump. Instead of using artificial extensions of the system or exploiting hidden variables we take advantage of the information stored in the quantum ensemble itself.     

Localization stabilized by noise

We present a model which describes a quantum two-state system interacting with the environment represented by stochastic noise. We show that coherent tunneling between the two states survives if the interaction with the environment is weak. On the contrary, a strong interaction destroys quantum coherence and the system randomly jumps from one state to the other. Moreover, the jump probability rate becomes extremely small for very strong noise. The model is relevant for understanding the quantum properties of some mesoscopic systems.