Asymptotics of the Charlier polynomials via difference equation methods

We derive uniform and non-uniform asymptotics of the Charlier polynomials by using difference equation methods alone. The Charlier polynomials are special in that they do not fit into the framework of the turning point theory, despite the fact that they are crucial in the Askey scheme. In this paper, asymptotic approximations are obtained respectively in the outside region, an intermediate region, and near the turning points. In particular, we obtain uniform asymptotic approximation at a pair of coalescing turning points with the aid of a local transformation. We also give a uniform approximation at the origin by applying the method of dominant balance and several matching techniques.Comment: 31 pages, 1 figure (in two separated files

High frequency limit for single-electron pumping operations

In this Letter, we study the transient electron transfer phenomena of single-electron devices with alternating external gate voltages. We obtain a high frequency limit for pumping electrons one at a time in single-electron devices. Also, we find that in general the electrical current is not proportional to the frequency of the external signals in the single-electron devices, due to the strong quantum coherence tunneling effect.Comment: 4 pages 5 figure

Real-time dynamics of single-electron pumping

In this Letter, we study the real-ime dynamics of single-electron pumpings. We modulate the left tunneling barrier along with the dot level but slightly changing the right barrier to operate the single-electron pumping device at zero bias. We show the adiabatic to the non-adiabatic transition in pumping operations. We also find that the relation $I=e\omega/2\pi$ is only valid in the low operating frequency adiabatic regime.Comment: 4 pages, 5 figure

Master equation approach to transient quantum transport incorporating with initial correlations

In this paper, the exact transient quantum transport of non-interacting nanostructures is investigated in the presence of initial system-lead correlations and initial lead-lead correlations for a device system coupled to general electronic leads. The exact master equation incorporating with initial correlations is derived through the extended quantum Langevin equation. The effects of the initial correlations are manifested through the time-dependent fluctuations contained explicitly in the exact master equation. The transient transport current incorporating with initial correlations is obtained from the exact master equation. The resulting transient transport current can be expressed in terms of the single-particle propagating and correlation Green functions of the device system. We show that the initial correlations can affect quantum transport not only in the transient regime, but also in the steady-state limit when system-lead couplings are strong enough so that electron localized bound states occur in the device system.Comment: 13pages, 4figure

Transient Current-Current Correlations and Noise Spectra

In this paper, we present an exact formalism for transient current-current correlations and transient noise spectra. The exact solution of transient current correlations in both the time domain and the frequency domain are obtained. Without taking the wide band limit, we investigate transient current-current correlations with different bias voltages and different finite temperatures. Transient noise spectra over the whole frequency range are calculated and that in the steady-state limit are also reproduced. From transient current-current correlations and noise spectra, we analyze the frequency-dependence of electron transport for the system evolving far away from equilibrium to the steady state. Various time scales associated with the energy structure of the nanosystem are also obtained from the transient current-current correlations and transient noise spectra.Comment: 10 pages, 7 figure

Enhancing the geometric quantum discord in the Heisenberg {\it XX} chain by Dzyaloshinsky-Moriya interaction

We studied the trance distance, the Hellinger distance, and the Bures distance geometric quantum discords (GQDs) for a two-spin Heisenberg {\it XX} chain with the Dzyaloshinsky-Moriya (DM) interaction and the external magnetic fields. We found that considerable enhancement of the GQDs can be achieved by introducing the DM interaction, and their maxima were obtained in the limiting case $D\rightarrow \infty$. The external magnetic fields and the increase of the temperature can also enhance the GQDs to some extent for certain special cases.Comment: 6 pages, 4 figure

Detecting Adversarial Attacks on Neural Network Policies with Visual Foresight

Deep reinforcement learning has shown promising results in learning control policies for complex sequential decision-making tasks. However, these neural network-based policies are known to be vulnerable to adversarial examples. This vulnerability poses a potentially serious threat to safety-critical systems such as autonomous vehicles. In this paper, we propose a defense mechanism to defend reinforcement learning agents from adversarial attacks by leveraging an action-conditioned frame prediction module. Our core idea is that the adversarial examples targeting at a neural network-based policy are not effective for the frame prediction model. By comparing the action distribution produced by a policy from processing the current observed frame to the action distribution produced by the same policy from processing the predicted frame from the action-conditioned frame prediction module, we can detect the presence of adversarial examples. Beyond detecting the presence of adversarial examples, our method allows the agent to continue performing the task using the predicted frame when the agent is under attack. We evaluate the performance of our algorithm using five games in Atari 2600. Our results demonstrate that the proposed defense mechanism achieves favorable performance against baseline algorithms in detecting adversarial examples and in earning rewards when the agents are under attack.Comment: Project page: http://yclin.me/RL_attack_detection/ Code: https://github.com/yenchenlin/rl-attack-detectio

Simulation of beam gas coulomb scattering in HALS

In conventional research on the beam gas coulomb scattering (BGCS), only the related beam lifetime using the analytical method is studied. In this paper, using the PIC-MCC method, we not only simulated the beam lifetime but also explored the effect of BGCS on the beam distribution. In order to better estimate the effect on particle distribution, we study the ultra-low emittance electron beam, here we choose the HeFei Advanced Light Source (HLAS). By counting the lost particles in a certain time, the corresponding beam lifetime we simulated is 5.1078h/14.5507h in x/y, which is very close to the theoretic value (5.0555h /13.7024h in x/y). By counting the lost particles relative to the collided particles, the simulated value of the loss probability of collided particles is 1.3228e-04, which is also very close to the theoretical value (1.3824e-04). Besides, the simulation shows there is a tail in the transverse distribution due to the BGCS. The close match of the simulation with theoretic value in beam lifetime and loss probability indicates our simulation is reliable

The Extent of In Situ Urbanisation in China’s County Areas

By developing and using indexes reflecting “quasi-urban” status, this paper attempts to quantitatively estimate the “invisible” contribution of in situ urbanisation to the overall urbanisation process in the county areas of Fujian Province. The results show that the urbanisation level of the county areas in Fujian Province would be significantly increased if the urban characteristics resulting from in situ urbanisation were fully reflected, suggesting that the conventional urban statistics seriously underestimate the true extent of rural-urban transformation in the county areas. Furthermore, such underestimation is more serious in the coastal areas with most dynamic socioeconomic development, and thus distorts the true picture of the spatial pattern of rural-urban transformation. The paper explores the implications of the above results for the understanding of China’s urbanisation process, suggesting that rural-urban transformation and the corresponding planning practice in China should be conceptualised in the context of blurred rural-urban distinction and more important roles for rural areas in the urbanisation process

Single-electron turnstile pumping with high frequencies

In this Letter, we present a theoretical analysis to single-electron pumping operation in a large range of driving frequencies through the time-dependent tunneling barriers controlled by external gate voltages. We show that the single-electron turnstile works at the frequency lower than the characteristic frequency which is determined by the mean average electron tunneling rate. When the driving frequency is greater than the characteristic frequency of electron tunnelings, fractional electron pumping occurs as an effect of quantum coherence tunneling.Comment: 4 pages, 5 figure