On the Application of Gluon to Heavy Quarkonium Fragmentation Functions

We analyze the uncertainties induced by different definitions of the momentum fraction $z$ in the application of gluon to heavy quarkonium fragmentation function. We numerically calculate the initial $g \to J / \psi$ fragmentation functions by using the non-covariant definitions of $z$ with finite gluon momentum and find that these fragmentation functions have strong dependence on the gluon momentum $\vec{k}$. As $| \vec{k} | \to \infty$, these fragmentation functions approach to the fragmentation function in the light-cone definition. Our numerical results show that large uncertainties remains while the non-covariant definitions of $z$ are employed in the application of the fragmentation functions. We present for the first time the polarized gluon to $J/\psi$ fragmentation functions, which are fitted by the scheme exploited in this work.Comment: 11 pages, 7 figures;added reference for sec.

General Relationship Between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States

We consider (2+1)-dimensional topological quantum states which possess edge states described by a chiral (1+1)-dimensional Conformal Field Theory (CFT), such as e.g. a general quantum Hall state. We demonstrate that for such states the reduced density matrix of a finite spatial region of the gapped topological state is a thermal density matrix of the chiral edge state CFT which would appear at the spatial boundary of that region. We obtain this result by applying a physical instantaneous cut to the gapped system, and by viewing the cutting process as a sudden "quantum quench" into a CFT, using the tools of boundary conformal field theory. We thus provide a demonstration of the observation made by Li and Haldane about the relationship between the entanglement spectrum and the spectrum of a physical edge state.Comment: 7 pages, 2 figures. A presentation of this work can be found in the following talk at KITP: http://online.itp.ucsb.edu/online/compqcm10/qi

Two monotonic functions involving gamma function and volume of unit ball

In present paper, we prove the monotonicity of two functions involving the gamma function $\Gamma(x)$ and relating to the $n$-dimensional volume of the unit ball $\mathbb{B}^n$ in $\mathbb{R}^n$.Comment: 7 page

Monotonicity and logarithmic convexity relating to the volume of the unit ball

Let $\Omega_n$ stand for the volume of the unit ball in $\mathbb{R}^n$ for $n\in\mathbb{N}$. In the present paper, we prove that the sequence $\Omega_{n}^{1/(n\ln n)}$ is logarithmically convex and that the sequence $\frac{\Omega_{n}^{1/(n\ln n)}}{\Omega_{n+1}^{1/[(n+1)\ln(n+1)]}}$ is strictly decreasing for $n\ge2$. In addition, some monotonic and concave properties of several functions relating to $\Omega_{n}$ are extended and generalized.Comment: 12 page

Quantum simulation of artificial Abelian gauge field using nitrogen-vacancy center ensembles coupled to superconducting resonators

We propose a potentially practical scheme to simulate artificial Abelian gauge field for polaritons using a hybrid quantum system consisting of nitrogen-vacancy center ensembles (NVEs) and superconducting transmission line resonators (TLR). In our case, the collective excitations of NVEs play the role of bosonic particles, and our multiport device tends to circulate polaritons in a behavior like a charged particle in an external magnetic field. We discuss the possibility of identifying signatures of the Hofstadter "butterfly" in the optical spectra of the resonators, and analyze the ground state crossover for different gauge fields. Our work opens new perspectives in quantum simulation of condensed matter and many-body physics using hybrid spin-ensemble circuit quantum electrodynamics system. The experimental feasibility and challenge are justified using currently available technology.Comment: 6 papes+supplementary materia

Quantum master equation scheme of time-dependent density functional theory to time-dependent transport in nano-electronic devices

In this work a practical scheme is developed for the first-principles study of time-dependent quantum transport. The basic idea is to combine the transport master-equation with the well-known time-dependent density functional theory. The key ingredients of this paper include: (i) the partitioning-free initial condition and the consideration of the time-dependent bias voltages which base our treatment on the Runge-Gross existence theorem; (ii) the non-Markovian master equation for the reduced (many-body) central system (i.e. the device); and (iii) the construction of Kohn-Sham master equation for the reduced single-particle density matrix, where a number of auxiliary functions are introduced and their equations of motion (EOM) are established based on the technique of spectral decomposition. As a result, starting with a well-defined initial state, the time-dependent transport current can be calculated simultaneously along the propagation of the Kohn-Sham master equation and the EOM of the auxiliary functions.Comment: 9 pages, no figure

Quantifying dynamic sensitivity of optimization algorithm parameters to improve hydrological model calibration

It is widely recognized that optimization algorithm parameters have significant impacts on algorithm performance, but quantifying the influence is very complex and difficult due to high computational demands and dynamic nature of search parameters. The overall aim of this paper is to develop a global sensitivity analysis based framework to dynamically quantify the individual and interactive influence of algorithm parameters on algorithm performance. A variance decomposition sensitivity analysis method, Analysis of Variance (ANOVA), is used for sensitivity quantification, because it is capable of handling small samples and more computationally efficient compared with other approaches. The Shuffled Complex Evolution method developed at the University of Arizona algorithm (SCE-UA) is selected as an optimization algorithm for investigation, and two criteria, i.e., convergence speed and success rate, are used to measure the performance of SCE-UA. Results show the proposed framework can effectively reveal the dynamic sensitivity of algorithm parameters in the search processes, including individual influences of parameters and their interactive impacts. Interactions between algorithm parameters have significant impacts on SCE-UA performance, which has not been reported in previous research. The proposed framework provides a means to understand the dynamics of algorithm parameter influence, and highlights the significance of considering interactive parameter influence to improve algorithm performance in the search processes.National Natural Science Foundation of ChinaChina Scholarship Counci

Coexistence of hexatic and isotropic phases in two-dimensional Yukawa systems

We have performed Brownian dynamics simulations on melting of two-dimensional colloidal crystal in which particles interact with Yukawa potential. The pair correlation function and bond-orientational correlation function was calculated in the Yukawa system. An algebraic decay of the bond orientational correlation function was observed. By ruling out the coexistence region, only a unstable hexatic phase was found in the Yukawa systems. But our work shows that the melting of the Yukawa systems is a two-stage melting not consist with the KTHNY theory and the isotropic liquid and the hexatic phase coexistence region was found. Also we have studied point defects in two-dimensional Yukawa systems.Comment: 9 pages, 8 figures. any comments are welcom