arXiv subjects

Dan Li

Publications and source records attributed to Dan Li.

At least 253 records · Page 14Linked to original sources

arXiv2016

The Stiefel--Whitney theory of topological insulators

We study the topological band theory of time reversal invariant topological insulators and interpret the topological $\mathbb{Z}_2$ invariant as an obstruction in terms of Stiefel--Whitney classes. The band structure of a topological insulator defines a Pfaffian line bundle over the momentum space, whose structure group can be reduced to $\mathbb{Z}_2$. So the topological $\mathbb{Z}_2$ invariant will be understood by the Stiefel--Whitney theory, which detects the orientability of a principal $\mathbb{Z}_2$-bundle. Moreover, the relation between weak and strong topological insulators will be understood based on cobordism theory. Finally, the topological $\mathbb{Z}_2$ invariant gives rise to a fully extended topological quantum field theory (TQFT).

math-ph↗

arXiv2016

Generic Quantum Walks with Memory

Quantum walks with memory(QWM) are a type of modified quantum walks that record the walker's latest path. As we know, only two kinds of QWM are presented up to now. It is desired to design more QWM for research, so that we can explore the potential of QWM. In this work, through presenting the one-to-one correspondence between QWM on a regular graph and quantum walks without memory(QWoM) on line digraph of the regular graph, we construct a generic model of QWM on regular graphs. This construction gives a general scheme for building all possible standard QWM on regular graphs and makes it possible to study properties of different kinds of QWM. Here, by taking the simplest example which is QWM with 1 memory on the line, we analyze some properties of QWM, such as variance, occupancy rate and localization.

quant-ph↗

arXiv2015

Magnetic Field Structures in Star Forming Regions: Mid-Infrared Imaging Polarimetry of K3-50

We report new imaging polarimetry observations of the Galactic compact HII region K3-50 using CanariCam at the Gran Telescopio Canarias. We use a standard polarimetric analysis technique, first outlined by Aitken, to decompose the observed polarisation images centred at 8.7, 10.3, and 12.5 $μ$m into the emissive and absorptive components from silicate grains that are aligned with the local magnetic field. These components reveal the spatially-resolved magnetic field structures across the mid-infrared emission area of K3-50. We examine these structures and show that they are consistent with previously observed features and physical models of K3-50, such as the molecular torus and the ionised outflow. We propose a 3D geometry for all the structures seen at different wavelengths. We also compute relevant physical quantities in order to estimate the associated magnetic field strengths that would be implied under various physical assumptions. We compare these results with MHD simulations of protostar formation that predict the magnetic field strength and configuration. We find that the magnetic field may be dynamically important in the innermost 0.2 pc of the molecular torus, but that the torus is more likely to be rotationally-supported against gravity outside this radius. Similarly, magnetic fields are unlikely to dominate the {\em global} physics of the ionised outflow, but they may be important in helping confine the flow near the cavity wall in some locations. Ours is the first application of the Aitken technique to spatially-resolved magnetic field structures in multiple layers along the line of sight, effectively a method of "polarisation tomography."

astro-ph.SR↗

arXiv2015

Quantum walks on two kinds of two-dimensional models

In this paper, we numerically study quantum walks on two kinds of two-dimensional graphs: cylindrical strip and Mobius strip. The two kinds of graphs are typical two-dimensional topological graph. We study the crossing property of quantum walks on these two models. Also, we study its dependence on the initial state, size of the model. At the same time, we compare the quantum walk and classical walk on these two models to discuss the difference of quantum walk and classical walk.

quant-ph↗

arXiv2014

One dimensional lazy quantum walks and occupancy rate

Lazy quantum walks were presented by Andrew M. Childs to prove that the continuous-time quantum walk is a limit of the discrete-time quantum walk [Commun.Math.Phys.294,581-603(2010)]. In this paper, we discuss properties of lazy quantum walks. Our analysis shows that lazy quantum walks have $O(t^n)$ order of the n-th moment of the corresponding probability distribution, which is the same as that for normal quantum walks. Also, the lazy quantum walk with DFT (Discrete Fourier Transform) coin operator has a similar probability distribution concentrated interval to that of the normal Hadamard quantum walk. Most importantly, we introduce the concepts of occupancy number and occupancy rate to measure the extent to which the walk has a (relatively) high probability at every position in its range. We conclude that lazy quantum walks have a higher occupancy rate than other walks such as normal quantum walks, classical walks and lazy classical walks.

quant-ph↗

arXiv2014

Mid-IR Spectra of Type Ia SN 2014J in M82 Spanning the First Four Months

We present a time series of 8 - 13 $μ$m spectra and photometry for SN 2014J obtained 57, 81, 108, and 137 d after the explosion using CanariCam on the Gran Telescopio Canarias. This is the first mid-IR time series ever obtained for a Type Ia supernova. These observations can be understood within the framework of the delayed detonation model and the production of $\sim$0.6 $\rm M_\odot$ of $^{56}$Ni, consistent with the observed brightness, the brightness decline relation, and the $γ$-ray fluxes. The [Co III] line at 11.888 $μ$m is particularly useful for evaluating the time evolution of the photosphere and measuring the amount of $^{56}$Ni and thus the mass of the ejecta. Late-time line profiles of SN 2014J are rather symmetric and not shifted in the rest frame. We see Argon emission, which provides a unique probe of mixing in the transition layer between incomplete burning and nuclear statistical equilibrium. We may see [Fe III] and [Ni IV] emission, both of which are observed to be substantially stronger than indicated by our models. If the latter identification is correct, then we are likely observing stable Ni, which might imply central mixing. In addition, electron capture, also required for stable Ni, requires densities larger than $\sim$$1 \times 10^9$ g cm$^{-3}$, which are expected to be present only in white dwarfs close to the Chandrasekhar limit. This study demonstrates that mid-IR studies of Type Ia supernovae are feasible from the ground and provide unique information, but it also indicates the need for better atomic data.

astro-ph.SR↗

arXiv2014

The Immediate Environments of Two Herbig Be Stars: MWC 1080 and HD 259431

Deep mid-infrared (10-20 $μ$m) images with sub-arcsec resolution were obtained for two Herbig Be stars, MWC 1080 and HD 259431, to probe their immediate environments. Our goal is to understand the origin of the diffuse nebulosities observed around these two very young objects. By analyzing our new mid-IR images and comparing them to published data at other wavelengths, we demonstrate that the well extended emission around MWC 1080 traces neither a disk nor an envelope, but rather the surfaces of a cavity created by the outflow from MWC 1080A, the primary star of the MWC 1080 system. In the N-band images, the filamentary nebulosities trace the hourglass-shaped gas cavity wall out to $\sim$0.15 pc. This scenario reconciles the properties of the MWC 1080 system revealed by a wide range of observations. Our finding confirms that the environment around MWC 1080, where a small cluster is forming, is strongly affected by the outflow from the central Herbig Be star. Similarities observed between the two subjects of this study suggest that the filamentary emission around HD 259431 may arise from a similar outflow cavity structure, too.

astro-ph.SR↗

arXiv2013

Search for $C=+$ charmonium states in $e^+e^-\to γ+~X$ at BEPCII/BESIII

We extend our original study in Ref. [1] on the production of $C=+$ charmonium states $X=η_c(1S/2S)$ and $χ_{cJ}(1P/2P)$ in $e^+e^-\toγ~+~X$ at B factories to the BEPCII/BESIII energy region with $\sqrt{s}=4.0\mbox{-}5.0$ GeV. In the framework of nonrelativistic QCD factorization, the cross sections are estimated to be as large as $0.1\mbox{-}0.9$ pb. The results could be used to search for the missing $2P$ charmonium states or to estimate the continuum backgrounds in the resonance region.

hep-ph↗

arXiv2013

Harper operators, Fermi curves, and Picard-Fuchs equations

This paper is a continuation of the work on the spectral problem of Harper operator using algebraic geometry. We continue to discuss the local monodromy of algebraic Fermi curves based on Picard-Lefschetz formula. The density of states over approximating components of Fermi curves satisfies a Picard-Fuchs equation. By the property of Landen transformation, the density of states has a Lambert series as the quarter period. A $q$-expansion of the energy level can be derived from a mirror map as in the B-model.

math-ph↗

arXiv2013

GreenDCN: a General Framework for Achieving Energy Efficiency in Data Center Networks

The popularization of cloud computing has raised concerns over the energy consumption that takes place in data centers. In addition to the energy consumed by servers, the energy consumed by large numbers of network devices emerges as a significant problem. Existing work on energy-efficient data center networking primarily focuses on traffic engineering, which is usually adapted from traditional networks. We propose a new framework to embrace the new opportunities brought by combining some special features of data centers with traffic engineering. Based on this framework, we characterize the problem of achieving energy efficiency with a time-aware model, and we prove its NP-hardness with a solution that has two steps. First, we solve the problem of assigning virtual machines (VM) to servers to reduce the amount of traffic and to generate favorable conditions for traffic engineering. The solution reached for this problem is based on three essential principles that we propose. Second, we reduce the number of active switches and balance traffic flows, depending on the relation between power consumption and routing, to achieve energy conservation. Experimental results confirm that, by using this framework, we can achieve up to 50 percent energy savings. We also provide a comprehensive discussion on the scalability and practicability of the framework.

cs.NI↗

arXiv2012

The Mineralogy and Structure of the Inner Debris Disk of β Pictoris

We observed the edge-on, planet-bearing disk of β Pictoris using T-ReCS at Gemini to clarify and extend previous observations and conclusions about this unique system. Our spectroscopy and spectral modeling of the 10-micron silicate feature constrain the spatial distributions of three representative dust components (0.1-micron/2.0-micron glassy olivine and crystalline forsterite) across the inner 20-AU of the disk. We confirm that the 2.0-micron glassy olivine is strongly peaked in the disk center and that the 0.1-micron glassy olivine does not show this concentration, but rather is double peaked, with the peaks on either side of the star. However, we do not see the strong difference in brightness between those two peaks reported in a previous study. Although the spatial distribution of the 0.1-micron dust is consistent with the scenario of a dust-replenishing planetesimal belt embedded in the disk, we note an alternative interpretation that can explain the spatial distributions of the 0.1-micron and 2.0-micron grains simultaneously and does not require the planetesimal belt. In addition to the spectroscopy, we also obtained a new 11.7 micron image of the β Pic disk. By comparing this image with that acquired in 2003, we confirm the existence and overall shape of the dusty clump at 52 AU in the SW disk. We speculate that the clump's projected spatial displacement of ~2.0 AU, a 3.6-σ result, between two epochs separated by seven years is due to the Keplerian motion of the clump at an orbital radius of $54.3^{+2.0}_{-1.2}$ AU.

astro-ph.EP↗

arXiv2012

The Ponzano-Regge model and parametric representation

We give a parametric representation of the effective noncommutative field theory derived from a $κ$-deformation of the Ponzano-Regge model and define a generalized Kirchhoff polynomial with $κ$-correction terms, obtained in a $κ$-linear approximation. We then consider the corresponding graph hypersurfaces and the question of how the presence of the correction term affects their motivic nature. We look in particular at the tetrahedron graph, which is the basic case of relevance to quantum gravity. With the help of computer calculations, we verify that the number of points over finite fields of the corresponding hypersurface does not fit polynomials with integer coefficients, hence the hypersurface of the tetrahedron is not polynomially countable. This shows that the correction term can change significantly the motivic properties of the hypersurfaces, with respect to the classical case.

math-ph↗

arXiv2011

Saying HelloWorld with QVTR-XSLT - A Solution to the TTC 2011 Instructive Case

In this short paper we present our solution for the Hello World case study of the Transformation Tool Contest (TTC) 2011 using the QVTR-XSLT tool. The tool supports editing and execution of the graphical notation of QVT Relations language. The case study consists of a set of simple transformation tasks which covers the basic functions required for a transformation language, such as creating, reading/querying, updating and deleting of model elements. We design a transformation for each of the tasks.

cs.SE↗

arXiv2011

Solving the TTC 2011 Compiler Optimization Case with QVTR-XSLT

In this short paper we present our solution for the Compiler Optimization case study of the Transformation Tool Contest (TTC) 2011 using the QVTR-XSLT tool. The tool supports editing and execution of the graphical notation of QVT Relations language

cs.SE↗

arXiv2011

The algebraic geometry of Harper operators

Following an approach developed by Gieseker, Knörrer and Trubowitz for discretized Schrödinger operators, we study the spectral theory of Harper operators in dimension two and one, as a discretized model of magnetic Laplacians, from the point of view of algebraic geometry. We describe the geometry of an associated family of Bloch varieties and compute their density of states. Finally, we also compute some spectral functions based on the density of states. We discuss the difference between the cases with rational or irrational parameters: for the two dimensional Harper operator, the compactification of the Bloch variety is an ordinary variety in the rational case and an ind-pro-variety in the irrational case. This gives rise, at the algebro-geometric level of Bloch varieties, to a phenomenon similar to the Hofstadter butterfly in the spectral theory. In dimension two, the density of states can be expressed in terms of period integrals over Fermi curves, where the resulting elliptic integrals are independent of the parameters. In dimension one, for the almost Mathieu operator, with a similar argument we find the usual dependence of the spectral density on the parameter, which gives rise to the well known Hofstadter butterfly picture.

math-ph↗

arXiv2011

$χ_{cJ}$ production associated with a $c\bar c$ pair at hadron colliders

$χ_{cJ}$ (J=0,1,2) production associated with a charm quark pair in hadron collisions is calculated in the framework of nonrelativistic QCD at the Tevatron and LHC. It is found that the color-singlet contribution is small and the color-octet contribution may be dominant in the large $p_T$ region. The differential cross section of $p\bar p\toχ_c+c\bar{c}$ is at least one order of magnitude smaller than the next-to-leading order result of $χ_{cJ}$ inclusive production $p\bar p\toχ_c+X$, therefore $χ_{cJ}$ production in $p\bar p\toχ_c+c\bar{c}$ may have negligible influence on the ratio $R_{χ_c}=\frac{σ_{χ_{c2}}}{σ_{χ_{c1}}}$ measured by CDF at the Tevatron. The feeddown contribution from $χ_{cJ}+c+\bar{c}$ to $J/ψ+c+\bar{c}$ is found to be large compared with $J/ψ$ direct production and may have important influence on the measurement of $J/ψ+c+\bar{c}$. The validity of fragmentation approximation for the process is also discussed.

hep-ph↗

arXiv2011

Global analysis of data on the spin-orbit coupled $A^{1}Σ_{u}^{+}$ and $b^{3}Π_{u}$ states of Cs2

We present experimentally derived potential curves and spin-orbit interaction functions for the strongly perturbed $A^{1}Σ_{u}^{+}$ and $b^{3}Π_{u}$ states of the cesium dimer. The results are based on data from several sources. Laser-induced fluorescence Fourier transform spectroscopy (LIF FTS) was used some time ago in the Laboratoire Aimé Cotton primarily to study the $X ^{1}Σ_{g}^{+}$ state. More recent work at Tsinghua University provides information from moderate resolution spectroscopy on the lowest levels of the $b^{3}Π_{0u}^{\pm}$ states as well as additional high resolution data. From Innsbruck University, we have precision data obtained with cold Cs$_{2}$ molecules. Recent data from Temple University was obtained using the optical-optical double resonance polarization spectroscopy technique, and finally, a group at the University of Latvia has added additional LIF FTS data. In the Hamiltonian matrix, we have used analytic potentials (the Expanded Morse Oscillator form) with both finite-difference (FD) coupled-channels and discrete variable representation (DVR) calculations of the term values. Fitted diagonal and off-diagonal spin-orbit functions are obtained and compared with {\it ab initio} results from Temple and Moscow State universities.

physics.atom-ph↗

arXiv2009

Search for $C=+$ charmonium and bottomonium states in $e^+e^-\to γ+ X$ at B factories

We study the production of $C=+$ charmonium states $X$ in $e^+e^-\to γ+ X$ at B factories with $X=η_c(nS)$ (n=1,2,3), $χ_{cJ}(mP)$ (m=1,2), and $^1D_2(1D)$. In the S and P wave case, contributions of tree-QED with one-loop QCD corrections are calculated within the framework of nonrelativistic QCD(NRQCD) and in the D-wave case only the tree-QED contribution are considered. We find that in most cases the QCD corrections are negative and moderate, in contrast to the case of double charmonium production $e^+e^-\to J/ψ+ X$, where QCD corrections are positive and large in most cases. We also find that the production cross sections of some of these states in $e^+e^-\to γ+ X$ are larger than that in $e^+e^-\to J/ψ+ X$ by an order of magnitude even after the negative QCD corrections are included. So we argue that search for the X(3872), X(3940), Y(3940), and X(4160) in $e^+e^-\to γ+ X$ at B factories may be helpful to clarify the nature of these states. For completeness, the production of bottomonium states in $e^+e^-$ annihilation is also discussed.

hep-ph↗