arXiv subjects

Qiang Luo

Publications and source records attributed to Qiang Luo.

78 records · Page 5Linked to original sources

arXiv2016

Local vibrational mode of impurity in a monatomic linear chain under open and periodic boundary conditions

In this paper, we revisit the lattice vibration of one-dimensional monatomic linear chain under open and periodic boundary conditions, and give the exact conditions for the emergence of the local vibration mode when one of the atoms is replaced by an impurity. Our motivation is twofold. Firstly, in deriving the dispersion relation of the atoms, periodic boundary condition is overwhelmingly utilized while open boundary condition is seldomly referred. Therefore we manage to obtain the dispersion relation under both boundary conditions simultaneously by Molinari formula. Secondly, in the presence of impurity, local vibration mode can emerge as long as the mass of the impurity $m'$ is smaller than the mass of the perfect atom $m$ to certain degree, which can be measured by the mass ratio $δ=\frac{m-m'}{m}$. At periodic boundary condition, the critical mass ratio is $0$ or $\frac{1}{N}$, depending on whether the length $N$ of the chain is even or odd. At open boundary condition, the critical mass ratio is $\frac{N}{2N-1}$ if the impurity locates at the end of the chain, while it is $\frac{N}{(2N_l+1)(2N_r+1)}$ with $N_l$ and $N_r$ be the number of atoms at the left and right hand sides of the impurity if the impurity locates at the middle.

cond-mat.mes-hall↗

arXiv2015

Numerical calculation of the Riemann zeta function at odd integer arguments: A direct formula method

In this article, we introduce a recurrence formula which only involves two adjacent values of the Riemann zeta function at integer arguments. Based on the formula, an algorithm to evaluate $ζ$-values(i.e. the values of Riemann zeta function) at odd-integers from the two nearest $ζ$-values at even-integers is posed and proved. The behavior of the error bound is $O(10^{-n})$ approximately where $n$ is the argument. Our method is especially powerful for the calculation of Riemann zeta function at large argument, while for smaller ones it can also reach spectacular accuracies such as more than ten decimal places.

math.NT↗

arXiv2015

A Padé approximant approach to two kinds of transcendental equations with applications in physics

In this paper, we obtain the analytical solutions of two kinds of transcendental equations with numerous applications in college physics by means of Lagrange inversion theorem, and rewrite them in the form of ratio of rational polynomials by second order Padé approximant afterwards from a practical and instructional perspective. Our method is illustrated in a pedagogical manner for the purpose that students at the undergraduate level will be beneficial. The approximate formulas introduced in the paper can be applied to abundant examples in physics textbooks, such as Fraunhofer single slit diffraction, Wien's displacement law and Schrödinger equation with single or double $δ$ potential. These formulas, consequently, can reach considerable accuracies according to the numerical results, therefore they promise to act as valuable ingredients in the standard teaching curriculum.

quant-ph↗

arXiv2013

Spatio-temporal Granger causality: a new framework

That physiological oscillations of various frequencies are present in fMRI signals is the rule, not the exception. Herein, we propose a novel theoretical framework, spatio-temporal Granger causality, which allows us to more reliably and precisely estimate the Granger causality from experimental datasets possessing time-varying properties caused by physiological oscillations. Within this framework, Granger causality is redefined as a global index measuring the directed information flow between two time series with time-varying properties. Both theoretical analyses and numerical examples demonstrate that Granger causality is a monotonically increasing function of the temporal resolution used in the estimation. This is consistent with the general principle of coarse graining, which causes information loss by smoothing out very fine-scale details in time and space. Our results confirm that the Granger causality at the finer spatio-temporal scales considerably outperforms the traditional approach in terms of an improved consistency between two resting-state scans of the same subject. To optimally estimate the Granger causality, the proposed theoretical framework is implemented through a combination of several approaches, such as dividing the optimal time window and estimating the parameters at the fine temporal and spatial scales. Taken together, our approach provides a novel and robust framework for estimating the Granger causality from fMRI, EEG, and other related data.

stat.AP↗

arXiv2008

$S$-wave pairing symmetry in non-centrosymmetric superconductor Re$_3$W

The alloys of non-centrosymmetric superconductor, Re$_3$W, which were reported to have an $α$-Mn structure [P. Greenfield and P. A. Beck, J. Metals, N. Y. \textbf{8}, 265 (1959)] with $T_\mathrm{c}=9 $K were prepared by arc melting. The ac susceptibility and low-temperature specific heat were measured on these alloys. It is found that there are two superconducting phases coexisting in the samples with $T_\mathrm{c1}\sim9 $K and $T_\mathrm{c2}\sim7 $K, both of which have a non-centrosymmetric structure as reported previously. By analyzing the specific heat data measured in various magnetic fields, we found that the absence of the inversion symmetry does not lead to the deviation from a s-wave pairing symmetry in Re$_3$W.

cond-mat.supr-con↗

arXiv2002

A Mean-field Calculation for the Three-Dimensional Holstein Model

A path integral representation appropriate for further Monte Carlo simulations is derived for the electron-phonon Holstein model in three spatial dimensions. The model is studied within mean-field theory. Charge density wave and superconducting phase transitions are discussed.

cond-mat.str-el↗