Failure of saturated ferromagnetism for the Hubbard model with two holes

We consider the Hubbard model on a finite set of sites with nonpositive hopping matrix elements and infinitely strong on-site repulsion. Nagaoka's theorem states that in this model the relative ground state in the sector with one unoccupied site is maximally ferromagnetic. We show that this phenomenon is a consequence of a combinatorial coincidence valid in the one-hole regime only. In the case of more than one hole there is no reason to expect maximally ferromagnetic ground states. We prove this claim for the case of two holes for models defined on a class of graphs which contains all tori that are not too small.     

Generic dissipation of entanglement

We find states for a multi-level system which are stable under a very general model of dissipation, one which is governed simply by generic rate parameters; in general such stable states are not entangled. We exhibit such a state explicitly for a two-qubit system. We then specialize to a more physical model of dissipation, one which is governed by pure dephasing. In such a case it is possible, by choice of the dephasing rates, to have a stable, and limiting, entangled state under the evolution governed by the free hamiltonian and pure decoherence. We exhibit such a choice explicitly which has a stable and limiting two-qubit state of maximum entanglement (Bell state).     

Attack Vulnerability of Network with Duplication-Divergence Mechanism

We study the attack vulnerability of network with duplication-divergence mechanism. Numerical results have shown that the duplication-divergence network with larger retention probability a is more robust against target attack relatively. Furthermore, duplication-divergence network is broken down more quickly than its counterpart BA network under target attack. Such result is consistent with the fact of WWW and Internet networks under target attack. So duplication-divergence model is a more realistic one for us to investigate the characteristics of the world wide web in future. We also observe that the exponent γ of degree distribution and average degree are important parameters of networks, reflecting the performance of networks under target attack. Our results are helpful to the research on the security of network.     

Bound States Energies of a Harmonic Oscillator Perturbed by Point Interactions

We determine explicitly the exact transcendental bound states energies equation for a one-dimensional harmonic oscillator perturbed by a single and a double point interactions via Green's function techniques using both momentum and position space representations. The even and odd solutions of the problem are discussed. The corresponding limiting cases are recovered. For the harmonic oscillator with a point interaction in more than one dimension,divergent series appear. We use to remove this divergence an exponential regulator and we obtain a transcendental equation for the energy bound states. The results obtained here are consistent with other investigations using different methods.     

Sparse Long Blocks and the Micro-structure of the Longuest Common Subsequences

Consider two random strings having the same length and generated by an iid sequence taking its values uniformly in a fixed finite alphabet. Artificially place a long constant block into one of the strings, where a constant block is a contiguous substring consisting only of one type of symbol. The long block replaces a segment of equal size and its length is smaller than the length of the strings, but larger than its square-root. We show that for sufficiently long strings the optimal alignment (OA) corresponding to a longest common subsequence (LCS) treats the inserted block very differently depending on the size of the alphabet. For two-letter alphabets, the long constant block gets mainly aligned with the same symbol from the other string, while for three or more letters the opposite is true and the block gets mainly aligned with gaps. We further provide simulation results on the proportion of gaps in blocks of various lengths. In our simulations, the blocks are “regular blocks” in an iid sequence, and are not artificially inserted. Nonetheless, we observe for these natural blocks a phenomenon similar to the one shown in case of artificially-inserted blocks: with two letters, the long blocks get aligned with a smaller proportion of gaps; for three or more letters, the opposite is true. It thus appears that the microscopic nature of two-letter OAs and three-letter OAs are entirely different from each other.     

Computing Quantum Bound States on Triply Punctured Two-Sphere Surface

We are interested in a quantum mechanical system on a triply punctured two-sphere surface with hyperbolicmetric.The bound states on this system are described by the Maass cusp forms(MCFs) which are smooth square integrable eigenfunctions of the hyperbolic Laplacian.Their discrete eigenvalues and the MCF are not known analytically.We solve numerically using a modified Hejhal and Then algorithm,which is suitable to compute eigenvalues for a surface with more than one cusp.We report on the computational results of some lower-lying eigenvalues for the triply punctured surface as well as providing plots of the MCF using GridMathematica.     

Evidence for out-of-equilibrium crystal nucleation in suspensions of oppositely charged colloids

We report a numerical study of the rate of crystal nucleation in a binary suspension of oppositely charged colloids. Two different crystal structures compete in the thermodynamic conditions under study. We find that the crystal phase that nucleates is metastable and, more surprisingly, its nucleation free-energy barrier is not the lowest one. This implies that, during nucleation, there is insufficient time for subcritical nuclei to relax to their lowest free-energy structure. Such behavior is in direct contradiction with the common assumption that the phase that crystallizes most readily is the one with the lowest free-energy barrier for nucleation. The phenomenon that we describe should be relevant for crystallization experiments where competing solid structures are not connected by an easy transformation.     

Capture of DNA in microfluidic channel using magnetic beads: Increasing capture efficiency with integrated microfluidic mixer

We have studied the hybridization of target DNA in solution with probe DNA on magnetic beads immobilized on the channel sidewalls in a magnetic bead separator. The hybridization is carried out under a liquid flow and is diffusion limited. Two systems are compared: one with a straight microfluidic channel and one with an integrated staggered herringbone mixer. Fluorescence microscopy studies show that the hybridization is much more efficient in the system with the integrated mixer. The results, which are discussed in terms of a simple model, are relevant for any diffusion-limited reaction taking place on the surface in a microfluidic system.     

Interlaced solitons and vortices in coupled DNLS lattices

In the present work, we propose a new set of coherent structures that arise in nonlinear dynamical lattices with more than one component, namely interlaced solitons. In the anti-continuum limit of uncoupled sites, these are waveforms whose one component has support where the other component does not. We illustrate systematically how one can combine dynamically stable unary patterns to create stable ones for the binary case of two-components. For the one-dimensional setting, we provide a detailed theoretical analysis of the existence and stability of these waveforms, while in higher dimensions, where such analytical computations are far more involved, we resort to corresponding numerical computations. Lastly, we perform direct numerical simulations to showcase how these structures break up, when they are exponentially or oscillatorily unstable, to structures with a smaller number of participating sites.     

Models of collective cell motion for cell populations with different aspect ratio: Diffusion,proliferation and travelling waves

Continuum, partial differential equation models are often used to describe the collective motion of cell populations, with various types of motility represented by the choice of diffusion coefficient, and cell proliferation captured by the source terms. Previously, the choice of diffusion coefficient has been largely arbitrary, with the decision to choose a particular linear or nonlinear form generally based on calibration arguments rather than making any physical connection with the underlying individual-level properties of the cell motility mechanism. In this work we provide a new link between individual-level models, which account for important cell properties such as varying cell shape and volume exclusion, and population-level partial differential equation models. We work in an exclusion process framework, considering aligned, elongated cells that may occupy more than one lattice site, in order to represent populations of agents with different sizes. Three different idealisations of the individual-level mechanism are proposed, and these are connected to three different partial differential equations, each with a different diffusion coefficient; one linear, one nonlinear and degenerate and one nonlinear and nondegenerate. We test the ability of these three models to predict the population-level response of a cell spreading problem for both proliferative and nonproliferative cases. We also explore the potential of our models to predict long time travelling wave invasion rates and extend our results to two-dimensional spreading and invasion. Our results show that each model can accurately predict density data for nonproliferative systems, but that only one does so for proliferative systems. Hence great care must be taken to predict density data with varying cell shape.     

The statistics of lines in natural images and implications for visual detection

As borders between different regions, lines are an important element of natural images. Already at the level of the mammalian primary visual cortex (V1), neurons respond best to oriented bars. We reduce a set of images to linear segments and analyze their statistical properties. In particular, appropriately defined Fourier spectra show more power in their transverse component than in the longitudinal one. We then characterize filters that are best suited for extracting information from such images, and find some qualitative consistency with neural connections in V1. We also demonstrate that such filters are efficient in reconstructing missing lines in an image.     

Theorem of Levinson via the Spectral Density

We deduce Levinson’s theorem in non-relativistic quantum mechanics in one dimension as a sum rule for the spectral density constructed from asymptotic data. We assume a self-adjoint Hamiltonian which guarantees completeness; the potential needs not to be isotropic and a zero-energy resonance is automatically taken into account. Peculiarities of this one-dimension case are explained because of the “critical” character of the free case u(x) = 0, in the sense that any attractive potential forms at least a bound state. We believe this method is more general and direct than the usual one in which one proves the theorem first for single wave modes and performs analytical continuation.     

The radial flow, equation of state and freeze-out phenomena

This is a status report on the on-going work [1] aiming at producing new hydro-based event generator HKM (the hydro-kinetic model) which incorporates such features as EOS with the QCD phase transition. We discuss whether data on radial flow can help us to restrict EOS. We argue that the usual fixed-T freeze-out condition is too crude and a more sophisticated one is needed: the “local” one is studied in details. Comparison with RQMD shows that the results for heavy ions agree well, while for medium one hydro overpredicts flow. Both RQMD and HKM reproduce magnitude of radial flow at SPS, but need additional repulsion between baryons (relative to resonance gas [13]) to reproduce it at AGS. New ideas related with event-per-event fluctuations are discussed, which can help better measure matter properties at the freeze-out.     

Collective excitations of harmonically trapped ideal gases

We theoretically study the collective excitations of an ideal gas confined in an isotropic harmonic trap. We give an exact solution to the Boltzmann-Vlasov equation; as expected for a single-component system, the associated mode frequencies are integer multiples of the trapping frequency. We show that the expressions found by the scaling ansatz method are a special case of our solution. Our findings are most useful in case the trap contains more than one phase: we demonstrate how to obtain the oscillation frequencies in case an interface is present between the ideal gas and a different phase.     

Frequency-selective response of FitzHugh-Nagumo neuron networks via changing random edges

We consider a network of FitzHugh-Nagumo neurons; each neuron is subjected to a subthreshold periodic signal and independent Gaussian white noise. The firing pattern of the mean field changes from an internal-scale dominant pattern to an external-scale dominant one when more and more edges are added into the network. We find numerically that (a) this transition is more sensitive to random edges than to regular edges, and (b) there is a saturation length for random edges beyond which the transition is no longer sharpened. The influence of network size is also investigated.     

苯基分子器件 量子相干输运第一性原理研究

摘要：分子器件在纳米尺度下,电子的相干性将对体系的电导产生重大影响。本文基于第一性原理计算研究了苯分子连接于一维金属电极下的电荷输运性质。发现一维金电极连接下,不同的连接方式（para与meta）体系下的电导将会有显著差别,而一维铂电极连接下,体系的电导差别不大。我们通过计算电极的能带,发现金电极与铂电极在费米面处的散射态数目有差别。 当量子相干效应导致散射态局域化发生改变时,由于铂电极的通道数较多,电子依然可以通过扩展的通道输运,因此不同连接方式下的电导变化不明显。     

System Temperatures, Single Versus Double Sideband Operation, and Optimum Receiver Performance

This paper discusses the relative observing efficiency of single sideband (SSB) and double sideband (DSB) receiver systems in the presence of atmospheric and antenna losses. We use the antenna parameters currently specified for the NRAO Millimeter Array (MMA) antennas and atmospheric opacities appropriate to an excellent site such as Mauna Kea or the MMA site on the Llano de Chajnantor in northern Chile. We find that for spectroscopic observations in one sideband, SSB measurements are always more efficient. Below 400 GHz, the observing time advantage is 50-80%. Above 400 GHz, the advantage is over a factor of 2, indicating that SSB-mode observing is more efficient even if spectral lines of interest are present in both sidebands. We discuss the goals for the ultimate, practical receiver performance that one should aim for in the presence of atmospheric and telescope losses. Observing efficiencies are displayed as a function of frequency using atmospheric opacity models as input. We also develop some analytic expressions for SSB and DSB observing.     

Geometry and Elasticity of Strips and Flowers

We solve several problems that involve imposing metrics on surfaces. The problem of a strip with a linear metric gradient is formulated in terms of a Lagrangian similar to those used for spin systems. We are able to show that the low energy state of long strips is a twisted helical state like a telephone cord. We then extend the techniques used in this solution to two–dimensional sheets with more general metrics. We find evolution equations and show that when they are not singular, a surface is determined by knowledge of its metric, and the shape of the surface along one line. Finally, we provide numerical evidence by minimizing a suitable energy functional that once these evolution equations become singular, either the surface is not differentiable, or else the metric deviates from the target metric.     

Monte Carlo simulation of quantum statistical lattice models

In this article we review recent developments in computational methods for quantum statistical lattice problems. We begin by giving the necessary mathematical basis, the generalized Trotter formula, and discuss the computational tools, exact summations and Monte Carlo simulation, that will be used to examine explicit examples. To illustrate the general strategy, the method is applied to an analytically solvable, non-trivial, model: the one-dimensional Ising model in a transverse field. Next it is shown how to generalized Trotter formula most naturally leads to different path-integral representations of the partition function by considering one-dimensional fermion lattice models. We show how to analyze the different representations and discuss Monte Carlo simulation results for one-dimensional fermions. Then Monte Carlo work on one- and two-dimensional spin-$\text{1}\text{2}$ models based upon the Trotter formula approach is reviewed and the more dedicated Handscomb Monte Carlo method is discussed. We consider electron-phonon models and discuss Monte Carlo simulation data on the Molecular Crystal Model in one, two and three dimensions and related one-dimensional polaron models. Exact numerical results are presented for free fermions and free bosons in the canonical ensemble. We address the main problem of Monte Carlo simulations of fermions in more than one dimension: the cancellation of large contributions. Free bosons on a lattice are compared with bosons in a box and the effects of finite size on Bose-Einstein condensation are discussed.