arXiv subjects
Publications and source records attributed to H. Jeong.
Universal quantum computation using optical coherent states is studied. A teleportation scheme for a coherent-state qubit is developed and applied to gate operations. This scheme is shown to be robust to detection inefficiency.
We consider a stochastic model for directed scale-free networks following power-laws in the degree distributions in both incoming and outgoing directions. In our model, the number of vertices grow geometrically with time with growth rate p. At each time step, (i) each newly introduced vertex is connected to a constant number of already existing vertices with the probability linearly proportional to the in-degree of a selected vertex, and (ii) each existing vertex updates its outgoing edges through a stochastic multiplicative process with mean growth rate of outgoing edges g and variance $σ^2$. Using both analytic treatment and numerical simulations, we show that while the out-degree exponent $γ_{\rm out}$ depends on the parameters, the in-degree exponent $γ_{\rm in}$ has two distinct values, $γ_{\rm in}=2$ for $p > g$ and 1 for $p < g$, independent of different parameters values. The latter case has logarithmic correction to the power-law. Since the vertex growth rate p is larger than the degree growth rate g for the world-wide web (www) nowadays, the in-degree exponent appears robust as $γ_{\rm in}=2$ for the www.
A central and long-standing issue in evolutionary theory is the origin of the biological variation upon which natural selection acts1. Some hypotheses suggest that evolutionary change represents an adaptation to the surrounding environment within the constraints of an organism's innate characteristics. Elucidation of the origin and evolutionary relationship of species has been complemented by nucleotide sequence and gene content analyses, with profound implications for recognizing life's major domains. Understanding of evolutionary relationships may be further expanded by comparing systemic higher-level organization among species. Here we employ multivariate analyses to evaluate the biochemical reaction pathways characterizing 43 species. Comparison of the information transfer pathways of Archaea and Eukaryotes indicates a close relationship between these domains. In addition, whereas eukaryotic metabolic enzymes are primarily of bacterial origin, the pathway-level organization of archaeal and eukaryotic metabolic networks is more closely related. Our analyses therefore suggest that during the symbiotic evolution of eukaryotes, incorporation of bacterial metabolic enzymes into the proto-archaeal proteome was constrained by the host's pre-existing metabolic architecture.
An entangled two-mode coherent state is studied within the framework of $2\times 2$ dimensional Hilbert space. An entanglement concentration scheme based on joint Bell-state measurements is worked out. When the entangled coherent state is embedded in vacuum environment, its entanglement is degraded but not totally lost. It is found that the larger the initial coherent amplitude, the faster entanglement decreases. We investigate a scheme to teleport a coherent superposition state while considering a mixed quantum channel. We find that the decohered entangled coherent state may be useless for quantum teleportation as it gives the optimal fidelity of teleportation less than the classical limit 2/3.
The fabrication of ZnSe/ZnTe superlattices grown by the process of rotating the substrate in the presence of an inhomogeneous flux distribution instead of successively closing and opening of source shutters is studied via Monte Carlo simulations. It is found that the concentration of each compound is sinusoidally modulated along the growth direction, caused by the uneven arrival of Se and Te atoms at a given point of the sample, and by the variation of the Te/Se ratio at that point due to the rotation of the substrate. In this way we obtain a ZnSe$_{1-x}$Te$_x$ alloy in which the composition $x$ varies sinusoidally along the growth direction. The period of the modulation is directly controlled by the rate of the substrate rotation. The amplitude of the compositional modulation is monotonous for small angular velocities of the substrate rotation, but is itself modulated for large angular velocities. The average amplitude of the modulation pattern decreases as the angular velocity of substrate rotation increases and the measurement position approaches the center of rotation. The simulation results are in good agreement with previously published experimental measurements on superlattices fabricated in this manner.
The co-authorship network of scientists represents a prototype of complex evolving networks. By mapping the electronic database containing all relevant journals in mathematics and neuro-science for an eight-year period (1991-98), we infer the dynamic and the structural mechanisms that govern the evolution and topology of this complex system. First, empirical measurements allow us to uncover the topological measures that characterize the network at a given moment, as well as the time evolution of these quantities. The results indicate that the network is scale-free, and that the network evolution is governed by preferential attachment, affecting both internal and external links. However, in contrast with most model predictions the average degree increases in time, and the node separation decreases. Second, we propose a simple model that captures the network's time evolution. Third, numerical simulations are used to uncover the behavior of quantities that could not be predicted analytically.
A key ingredient of current models proposed to capture the topological evolution of complex networks is the hypothesis that highly connected nodes increase their connectivity faster than their less connected peers, a phenomenon called preferential attachment. Measurements on four networks, namely the science citation network, Internet, actor collaboration and science coauthorship network indicate that the rate at which nodes acquire links depends on the node's degree, offering direct quantitative support for the presence of preferential attachment. We find that for the first two systems the attachment rate depends linearly on the node degree, while for the latter two the dependence follows a sublinear power law.
Many biological, ecological and economic systems are best described by weighted networks, as the nodes interact with each other with varying strength. However, most network models studied so far are binary, the link strength being either 0 or 1. In this paper we introduce and investigate the scaling properties of a class of models which assign weights to the links as the network evolves. The combined numerical and analytical approach indicates that asymptotically the total weight distribution converges to the scaling behavior of the connectivity distribution, but this convergence is hampered by strong logarithmic corrections.
In a cell or microorganism the processes that generate mass, energy, information transfer, and cell fate specification are seamlessly integrated through a complex network of various cellular constituents and reactions. However, despite the key role these networks play in sustaining various cellular functions, their large-scale structure is essentially unknown. Here we present the first systematic comparative mathematical analysis of the metabolic networks of 43 organisms representing all three domains of life. We show that, despite significant variances in their individual constituents and pathways, these metabolic networks display the same topologic scaling properties demonstrating striking similarities to the inherent organization of complex non-biological systems. This suggests that the metabolic organization is not only identical for all living organisms, but complies with the design principles of robust and error-tolerant scale-free networks, and may represent a common blueprint for the large-scale organization of interactions among all cellular constituents.
We study the tilt dependence of the pinning-depinning transition for an interface described by the anisotropic quenched Kardar-Parisi-Zhang equation in 2+1 dimensions, where the two signs of the nonlinear terms are different from each other. When the substrate is tilted by m along the positive sign direction, the critical force F_c(m) depends on m as F_c(m)-F_c(0) \sim -|m|^{1.9(1)}. The interface velocity v near the critical force follows the scaling form v \sim |f|^θΨ_{\pm}(m^2 /|f|^{θ+ϕ}) with θ= 0.9(1) and ϕ= 0.2(1), where f \equiv F-F_c(0) and F is the driving force.
Recently it was experimentally demonstrated that sputtering under normal incidence leads to the formation of spatially ordered uniform nanoscale islands or holes. Here we show that these nanostructures have inherently nonlinear origin, first appearing when the nonlinear terms start to dominate the surface dynamics. Depending on the sign of the nonlinear terms, determined by the shape of the collision cascade, the surface can develop regular islands or holes with identical dynamical features, and while the size of these nanostructures is independent of flux and temperature, it can be modified by tuning the ion energy.
Many morphological features of sputter eroded surfaces are determined by the balance between ion induced linear instability and surface diffusion. However, the impact of the nonlinear terms on the morphology is less understood. We demonstrate that while at short times ripple formation is described by the linear theory, after a characteristic time the nonlinear terms determine the surface morphology by either destroying the ripples, or generating a new rotated ripple structure. We show that the morphological transitions induced by the nonlinear effects can be detected by monitoring the surface width and the erosion velocity.
We perform Monte Carlo simulations on stochastic models such as the Wolf-Villain (WV) model and the Family model in a modified version to measure mean separation $\ell$ between islands in submonolayer regime and damping time $\tilde t$ of layer-by-layer growth oscillations on one dimension. The stochastic models are modified, allowing diffusion within interval $r$ upon deposited. It is found numerically that the mean separation and the damping time depend on the diffusion interval $r$, leading to that the damping time is related to the mean separation as ${\tilde t} \sim \ell^{4/3}$ for the WV model and ${\tilde t} \sim \ell^2$ for the Family model. The numerical results are in excellent agreement with recent theoretical predictions.
The quenched Kardar-Parisi-Zhang (QKPZ) equation with negative non-linear term shows a first order pinning-depinning (PD) transition as the driving force $F$ is varied. We study the substrate-tilt dependence of the dynamic transition properties in 1+1 dimensions. At the PD transition, the pinned surfaces form a facet with a characteristic slope $s_c$ as long as the substrate-tilt $m$ is less than $s_c$. When $m s_c$. We explain these features from a pinning mechanism involving a localized pinning center and the self-organized facet formation.
We reexamine the density of two dimensional islands in the submonolayer regime of a homoepitaxially growing surface using the coarse grained Monte Carlo simulation with random sequential updating rather than parallel updating. It turns out that the power law dependence of the density of islands on the deposition rate agrees much better with the theoretical prediction than previous data obtained by other methods if random sequential instead of parallel updating is used.
We analyze the anisotropic Kardar-Parisi-Zhang equation in general substrate dimensions $d'$ with spatially correlated noise, $\langle\tilde η({\bf{k}},ω)\rangle=0$ and $\langle\tilde η({\bf{k}},ω) \tilde η({\bf{k}}',ω')\rangle$ $=2D(k)δ^{d'}({\bf{k}}+{\bf{k}}')δ(ω+ω')$ where $D(k)=D_0+D_ρk^{-2ρ}$, using the dynamic renormalization group (RG) method. When the signs of the nonlinear terms in parallel and perpendicular directions are opposite, a novel finite stable fixed point is found for $d'< d'_c \equiv 2+2ρ$ within one-loop order. The roughening exponent $α$ and the dynamic exponent $z$ associated with the stable fixed point are determined as $α={2 \over 3}\big(ρ-{{d'-2}\over 2}\big)$, and $z=2-α$. For $d' > d'_c$, the RG transformations flow to the fixed point of the weak-coupling limit, so that the dynamic exponent becomes $z=2$.
We present numerical data of the height-height correlation function and of the avalanche size distribution for the three dimensional Toom interface. The height-height correlation function behaves samely as the interfacial fluctuation width, which diverges logarithmically with space and time for both unbiased and biased cases. The avalanche size defined by the number of changing sites caused by a single noise process, exhibits an exponentially decaying distribution, which is in contrast to power-law distributions appearing in typical self-organized critical phenomena. We also generalize the Toom model into arbitrary dimensions.
We introduce a novel three dimensional Toom model on bcc lattice, and study its physical properties. In low-noise limit, the model leads to an effective solid-on-solid-type model, which exhibits a stationary interface via depositions and evaporations with avalanche process. We find that the model is described by the Edwards-Wilkinson equation for unbiased case and the anisotropic-Kardar-Parisi-Zhang equation in the weak-coupling limit for biased case. Thus the square of the surface width diverges logarithmically with space and time for both unbiased and biased cases.