arXiv subjects

Jia Yin

Publications and source records attributed to Jia Yin.

32 records · Page 2Linked to original sources

arXiv2021

Improved uniform error bounds on time-splitting methods for the long-time dynamics of the Dirac equation with small potentials

We establish improved uniform error bounds on time-splitting methods for the long-time dynamics of the Dirac equation with small electromagnetic potentials characterized by a dimensionless parameter $\varepsilon\in (0, 1]$ representing the amplitude of the potentials. We begin with a semi-discritization of the Dirac equation in time by a time-splitting method, and then followed by a full-discretization in space by the Fourier pseudospectral method. Employing the unitary flow property of the second-order time-splitting method for the Dirac equation, we prove uniform error bounds at $C(t)τ^2$ and $C(t)(h^m+τ^2)$ for the semi-discretization and full-discretization, respectively, for any time $t\in[0,T_\varepsilon]$ with $T_\varepsilon = T/\varepsilon$ for $T > 0$, which are uniformly for $\varepsilon \in (0, 1]$, where $τ$ is the time step, $h$ is the mesh size, $m\geq 2$ depends on the regularity of the solution, and $C(t) = C_0 + C_1\varepsilon t\le C_0+C_1T$ grows at most linearly with respect to $t$ with $C_0\ge0$ and $C_1>0$ two constants independent of $t$, $h$, $τ$ and $\varepsilon$. Then by adopting the regularity compensation oscillation (RCO) technique which controls the high frequency modes by the regularity of the solution and low frequency modes by phase cancellation and energy method, we establish improved uniform error bounds at $O(\varepsilonτ^2)$ and $O(h^m +\varepsilonτ^2)$ for the semi-discretization and full-discretization, respectively, up to the long-time $T_\varepsilon$. Numerical results are reported to confirm our error bounds and to demonstrate that they are sharp. Comparisons on the accuracy of different time discretizations for the Dirac equation are also provided.

math.NA↗

arXiv2021

Uniform error bounds of exponential wave integrator methods for the long-time dynamics of the Dirac equation with small potentials

Two exponential wave integrator Fourier pseudospectral (EWI-FP) methods are presented and analyzed for the long-time dynamics of the Dirac equation with small potentials characterized by $\varepsilon \in (0, 1]$ a dimensionless parameter. Based on the (symmetric) exponential wave integrator for temporal derivatives in phase space followed by applying the Fourier pseudospectral discretization for spatial derivatives, the EWI-FP methods are explicit and of spectral accuracy in space and second-order accuracy in time for any fixed $\varepsilon = \varepsilon_0$. Uniform error bounds are rigorously carried out at $O(h^{m_0}+τ^2)$ up to the time at $O(1/\varepsilon)$ with the mesh size $h$, time step $τ$ and $m_0$ an integer depending on the regularity of the solution. Extensive numerical results are reported to confirm our error bounds and comparisons of two methods are shown. Finally, dynamics of the Dirac equation in 2D are presented to validate the numerical schemes.

math.NA↗

arXiv2021

Analyzing and predicting non-equilibrium many-body dynamics via dynamic mode decomposition

Simulating the dynamics of a nonequilibrium quantum many-body system by computing the two-time Green's function associated with such a system is computationally challenging. However, we are often interested in the time diagonal of such a Green's function or time dependent physical observables that are functions of one time. In this paper, we discuss the possibility of using dynamic model decomposition (DMD), a data-driven model order reduction technique, to characterize one-time observables associated with the nonequilibrium dynamics using snapshots computed within a small time window. The DMD method allows us to efficiently predict long time dynamics from a limited number of trajectory samples. We demonstrate the effectiveness of DMD on a model two-band system. We show that, in the equilibrium limit, the DMD analysis yields results that are consistent with those produced from a linear response analysis. In the nonequilibrium case, the extrapolated dynamics produced by DMD is more accurate than a special Fourier extrapolation scheme presented in this paper. We point out a potential pitfall of the standard DMD method caused by insufficient spatial/momentum resolution of the discretization scheme. We show how this problem can be overcome by using a variant of the DMD method known as higher order DMD.

cond-mat.stat-mech↗

arXiv2021

A fourth-order compact time-splitting method for the Dirac equation with time-dependent potentials

In this paper, we present an approach to deal with the dynamics of the Dirac equation with time-dependent electromagnetic potentials using the fourth-order compact time-splitting method ($S_\text{4c}$). To this purpose, the time-ordering technique for time-dependent Hamiltonians is introduced, so that the influence of the time-dependence could be limited to certain steps which are easy to treat. Actually, in the case of the Dirac equation, it turns out that only those steps involving potentials need to be amended, and the scheme remains efficient, accurate, as well as easy to implement. Numerical examples in 1D and 2D are given to validate the scheme.

math.NA↗

arXiv2021

Census of Variable Stars toward Serpens Main

We have monitored a 3 deg2 area toward Serpens Main in the Pan-STARRS1 r, i, and z bands from 2016 April to September. Light curves of more than 11,000 stars in each band were obtained, and 143 variables have been identified. Among those, 119 variables are new discoveries, while 24 variables were previously known. We present variability classes and periods of 99 stars. Of these, 81 are located in the upper giant branch, displaying long periods, while the remaining 18 variables are pre-main-sequence objects with short periods. We also identify eight eclipsing binary systems, including the known binary V0623 Ser, and derive their physical parameters. According to a clustering analysis of Gaia DR2 stars in the observed field, there are 10 variable members in Serpens Main, where six members have been classified as young stellar objects in previous studies. Here we provide color-magnitude and color-color diagrams for these variables. The color variability of most variables in the color-magnitude diagrams produce the expected displacements, while the movements of cluster members point in different directions; this behavior may be associated with accretion spots or circumstellar disks.

astro-ph.SR↗

arXiv2021

Spatial resolution of different discretizations over long-time for the Dirac equation with small potentials

We compare the long-time error bounds and spatial resolution of finite difference methods with different spatial discretizations for the Dirac equation with small electromagnetic potentials characterized by $\varepsilon \in (0, 1]$ a dimensionless parameter. We begin with the simple and widely used finite difference time domain (FDTD) methods, and establish rigorous error bounds of them, which are valid up to the time at $O(1/\varepsilon)$. In the error estimates, we pay particular attention to how the errors depend explicitly on the mesh size $h$ and time step $τ$ as well as the small parameter $\varepsilon$. Based on the results, in order to obtain "correct" numerical solutions up to the time at $O(1/\varepsilon)$, the $\varepsilon$-scalability (or meshing strategy requirement) of the FDTD methods should be taken as $h = O(\varepsilon^{1/2})$ and $τ= O(\varepsilon^{1/2})$. To improve the spatial resolution capacity, we apply the Fourier spectral method to discretize the Dirac equation in space. Error bounds of the resulting finite difference Fourier pseudospectral (FDFP) methods show that they exhibit uniform spatial errors in the long-time regime, which are optimal in space as suggested by the Shannon's sampling theorem. Extensive numerical results are reported to confirm the error bounds and demonstrate that they are sharp.

math.NA↗

arXiv2021

Error estimates of finite difference methods for the Dirac equation in the massless and nonrelativistic regime

We present four frequently used finite difference methods and establish the error bounds for the discretization of the Dirac equation in the massless and nonrelativistic regime, involving a small dimensionless parameter $0< \varepsilon \ll 1$ inversely proportional to the speed of light. In the massless and nonrelativistic regime, the solution exhibits rapid motion in space and is highly oscillatory in time. Specifically, the wavelength of the propagating waves in time is at $O(\varepsilon)$, while in space it is at $O(1)$ with the wave speed at $O(\varepsilon^{-1}).$ We adopt one leap-frog, two semi-implicit, and one conservative Crank-Nicolson finite difference methods to numerically discretize the Dirac equation in one dimension and establish rigorously the error estimates which depend explicitly on the time step $τ$, mesh size $h$, as well as the small parameter $\varepsilon$. The error bounds indicate that, to obtain the `correct' numerical solution in the massless and nonrelativistic regime, i.e. $0<\varepsilon\ll1$, all these finite difference methods share the same $\varepsilon$-scalability as time step $τ=O(\varepsilon^{3/2})$ and mesh size $h=O(\varepsilon^{1/2})$. A large number of numerical results are reported to verify the error estimates.

math.NA↗

arXiv2021

Uniform error bounds of time-splitting methods for the nonlinear Dirac equation in the nonrelativistic regime without magnetic potential

Super-resolution of the Lie-Trotter splitting ($S_1$) and Strang splitting ($S_2$) is rigorously analyzed for the nonlinear Dirac equation without external magnetic potentials in the nonrelativistic regime with a small parameter $0<\varepsilon\leq 1$ inversely proportional to the speed of light. In this regime, the solution highly oscillates in time with wavelength at $O(\varepsilon^2)$. The splitting methods surprisingly show super-resolution, i.e. the methods can capture the solution accurately even if the time step size $τ$ is much larger than the sampled wavelength at $O(\varepsilon^2)$. Similar to the linear case, $S_1$ and $S_2$ both exhibit $1/2$ order convergence uniformly with respect to $\varepsilon$. Moreover, if $τ$ is non-resonant, i.e. $τ$ is away from certain region determined by $\varepsilon$, $S_1$ would yield an improved uniform first order $O(τ)$ error bound, while $S_2$ would give improved uniform $3/2$ order convergence. Numerical results are reported to confirm these rigorous results. Furthermore, we note that super-resolution is still valid for higher order splitting methods.

math.NA↗

arXiv2020

Super-resolution of time-splitting methods for the Dirac equation in the nonrelativistic regime

We establish error bounds of the Lie-Trotter splitting ($S_1$) and Strang splitting ($S_2$) for the Dirac equation in the nonrelativistic limit regime in the absence of external magnetic potentials, with a small parameter $0<\varepsilon\leq 1$ inversely proportional to the speed of light. In this limit regime, the solution propagates waves with $O(\varepsilon^2)$ wavelength in time. Surprisingly, we find out that the splitting methods exhibit super-resolution, in the sense of breaking the resolution constraint under the Shannon's sampling theorem, i.e. the methods can capture the solutions accurately even if the time step size $τ$ is much larger than the sampled wavelength at $O(\varepsilon^2)$. $S_1$ shows $1/2$ order convergence uniformly with respect to $\varepsilon$, by establishing that there are two independent error bounds $τ+ \varepsilon$ and $τ+ τ/\varepsilon$. Moreover, if $τ$ is non-resonant, i.e. $τ$ is away from certain region determined by $\varepsilon$, $S_1$ would yield an improved uniform first order $O(τ)$ error bound. In addition, we show $S_2$ is uniformly convergent with 1/2 order rate for general time step size $τ$ and uniformly convergent with $3/2$ order rate for non-resonant time step size. Finally, numerical examples are reported to validate our findings.

math.NA↗

arXiv2020

Site testing campaign for the Large Optical/infrared Telescope of China: Overview

The Large Optical/infrared Telescope (LOT) is a ground-based 12m diameter optical/infrared telescope which is proposed to be built in the western part of China in the next decade. Based on satellite remote sensing data, along with geographical, logistical and political considerations, three candidate sites were chosen for ground-based astronomical performance monitoring. These sites include: Ali in Tibet, Daocheng in Sichuan, and Muztagh Ata in Xinjiang. Up until now, all three sites have continuously collected data for two years. In this paper, we will introduce this site testing campaign, and present its monitoring results obtained during the period between March 2017 and March 2019.

astro-ph.IM↗

arXiv2018

A fourth-order compact time-splitting Fourier pseudospectral method for the Dirac equation

We propose a new fourth-order compact time-splitting ($S_\text{4c}$) Fourier pseudospectral method for the Dirac equation by splitting the Dirac equation into two parts together with using the double commutator between them to integrate the Dirac equation at each time interval. The method is explicit, fourth-order in time and spectral order in space. It is unconditional stable and conserves the total density in the discretized level. It is called a compact time-splitting method since, at each time step, the number of sub-steps in $S_\text{4c}$ is much less than those of the standard fourth-order splitting method and the fourth-order partitioned Runge-Kutta splitting method. Comparison among $S_\text{4c}$ and many other existing time-splitting methods for the Dirac equation are carried out in terms of accuracy and efficiency as well as long time behavior. Numerical results demonstrate the advantage in terms of efficiency and accuracy of the proposed $S_\text{4c}$. Finally we report the spatial/temporal resolutions of $S_\text{4c}$ for the Dirac equation in different parameter regimes including the nonrelativistic limit regime, the semiclassical limit regime, and the simultaneously nonrelativisic and massless limit regime.

math.NA↗

arXiv2016

Error estimates of numerical methods for the nonlinear Dirac equation in the nonrelativistic limit regime

We present several numerical methods and establish their error estimates for the discretization of the nonlinear Dirac equation in the nonrelativistic limit regime, involving a small dimensionless parameter $0<\varepsilon\ll 1$ which is inversely proportional to the speed of light. In this limit regime, the solution is highly oscillatory in time, i.e. there are propagating waves with wavelength $O(\varepsilon^2)$ and $O(1)$ in time and space, respectively. We begin with the conservative Crank-Nicolson finite difference (CNFD) method and establish rigorously its error estimate which depends explicitly on the mesh size $h$ and time step $τ$ as well as the small parameter $0<\varepsilon\le 1$. Based on the error bound, in order to obtain `correct' numerical solutions in the nonrelativistic limit regime, i.e. $0<\varepsilon\ll 1$, the CNFD method requests the $\varepsilon$-scalability: $τ=O(\varepsilon^3)$ and $h=O(\sqrt{\varepsilon})$. Then we propose and analyze two numerical methods for the discretization of the nonlinear Dirac equation by using the Fourier spectral discretization for spatial derivatives combined with the exponential wave integrator and time-splitting technique for temporal derivatives, respectively. Rigorous error bounds for the two numerical methods show that their $\varepsilon$-scalability is improved to $τ=O(\varepsilon^2)$ and $h=O(1)$ when $0<\varepsilon\ll 1$ compared with the CNFD method. Extensive numerical results are reported to confirm our error estimates.

math.NA↗

arXiv2015

Beam transport experiment with a new kicker control system on the HIRFL-CSR

The kicker control system was used for beam extraction and injection between two cooling storage rings (CSRs) at the Heavy Ion Research Facility in Lanzhou (HIRFL). To meet the requirements of special physics experiments, the kicker controller was upgraded. The new controller was designed based on ARM+DSP+FPGA technology and monolithic circuit architecture, which can achieve a precision time delay of 2.5 ns. In September 2014, the new kicker control system was installed in the kicker field, and the test experiment using the system was completed. In addition, a pre-trigger signal was provided by the controller, which was designed to synchronize the beam diagnostic system and physics experiments. Experimental results indicate that the phenomena of "missed kick" and "inefficient kick" were not observed, and the multichannel trigger signals' delay could be adjusted individually for kick power supplies in digitization; thus, the beam transport efficiency was improved compared with that of the original system. The fast extraction and injection experiment was successfully completed based on the new kicker control systems for HIRFL-CSR.

physics.acc-ph↗

arXiv2013

The Development of Single Star Scidar for Tibet and Dome A

A Single Star Scidar system(SSS) has been developed for remotely sensing atmospheric turbulence profiles. The SSS consists of computing the spatial auto/cross-correlation functions of short exposure images of the scintillation patterns produced by a single star, and provides the vertical profiles of optical turbulence intensity C2n(h) and wind speed V(h). The SSS needs only a 40 cm aperture telescope, so that can be portable and equipped easily to field candidate sites. Some experiments for the SSS have been made in Beijing last year, successfully retrieving atmospheric turbulence and wind profiles from the ground to 30 km. The SSS observations has recently been made at the Xinglong station of NAOC, characterizing atmospheric parameters at this station. We plan to automatize SSS instrument and run remote observation via internet; a more friendly auto-SSS system will be set up and make use at the candidate sites in Tibet and Dome A.

astro-ph.IM↗