arXiv subjects
Publications and source records attributed to Jian Wang.
We prove that the operator $L_0=-(1+|x|)^β(-Δ)^{α/2}$ with $α\in(0,2)$, $d>α$ and $β\ge0$ generates a compact semigroup or resolvent on $L^2(\R^d;(1+|x|)^{-β}\,dx)$, if and only if $β>α$. When $β>α$, we obtain two-sided asymptotic estimates for high order eigenvalues, and sharp bounds for the corresponding heat kernel.
An intriguing observation on the quantum anomalous Hall effect (QAHE) in magnetic topological insulators (MTIs) is the dissipative edge states, where quantized Hall resistance is accompanied by nonzero longitudinal resistance. We numerically investigate this dissipative behavior of QAHE in MTIs with a three-dimensional tight-binding model and non-equilibrium Greens function formalism. It is found that, in clean samples, the geometric mismatch between the detecting electrodes and the MTI sample leads to additional scattering in the central Hall bar, which is similar to the effect of splitting gates in the traditional Hall effect. As a result, while the Hall resistance remains quantized, the longitudinal resistance deviates from zero due to such additional scattering. It is also shown that external magnetic fields as well as disorder scattering can suppress the dissipation of the longitudinal resistance. These results are in good agreement with previous experimental observations and provide insight on the fabrication of QAHE devices.
We provide a thermodynamically consistent description of energy, charge and spin transfers in a thermoelectric quantum-dot spin valve in the collinear configuration based on nonequilibrium Green's function and full counting statistics. We use the fluctuation theorem symmetry and the concept of entropy production to characterize the efficiency with which thermal gradients can transduce charges or spins against their chemical potentials, arbitrary far from equilibrium. Close to equilibrium, we recover the Onsager reciprocal relations and the connection to linear response notions of performance such as the figure of merit. We also identify regimes where work extraction is more efficient far then close from equilibrium.
We apply the probabilistic coupling approach to establish the spatial regularity of semigroups associated with Lévy type operators, by assuming that the martingale problem of Lévy type operators is well posed. In particular, we can prove the Lipschitz continuity of the semigroups under Hölder continuity of coefficients, even when the Lévy kernel corresponding to Lévy type operators is singular.
We investigate the rectification of heat current carried by electrons through a double quantum dot (DQD) system under a temperature bias. The DQD can be realized by molecules such as suspended carbon nanotube and be described by the Anderson-Holstein model in presence of electron-phonon interaction. Strong electron-phonon interaction can lead to formation of polaronic states in which electronic states are dressed by phonon cloud. Dressed tunneling approximation (DTA), which is nonperturbative in dealing with strong electron-phonon interaction, is employed to obtain the heat current expression. In DTA, self-energies are dressed by phonon cloud operator and are temperature dependent. The temperature dependency of imaginary part of dressed retarded self-energy gives rise to the asymmetry of the system and is the necessary condition of thermal rectification. On top of this, one can either tune DQD effective energy levels such that $|\barε_1|\neq |\barε_2|$ or have asymmetric dot-lead couplings to achieve thermal rectification. We numerically find that increasing electron-phonon coupling and reducing inter dot coupling can both improve thermal rectification effect, while the electronic heat current is reduced.
We observed a novel voltage peak in the proximity effect induced superconducting gold (Au) nanowire while cooling the sample through the superconducting transition temperature. The voltage peak turned into dip in the warming process. The voltage peak (or dip) was found to be closely related to the emergence (vanishing) of the proximity induced superconductivity in the Au nanowire. The amplitude of the voltage signal depends on the temperature scanning rate and it cannot be detected when the temperature is changed slower than 0.03 K/min. This transient feature suggests the non-equilibrium property of the effect. The voltage peak could be understood by Ginzburg-Landau model as a combined result of the emergence of Cooper pairs with relatively lower free energy in W contact and the non-equilibrium diffusion of Cooper pairs and quasiparticles.
Two dimensional (2D) superconducting systems are of great importance to exploring exotic quantum physics. Recent development of fabrication techniques stimulates the studies of high quality single crystalline 2D superconductors, where intrinsic properties give rise to unprecedented physical phenomena. Here we report the observation of Zeeman-type spin-orbit interaction protected superconductivity (Zeeman-protected superconductivity) in 4 monolayer (ML) to 6 ML crystalline Pb films grown on striped incommensurate (SIC) Pb layers on Si(111) substrates by molecular beam epitaxy (MBE). Anomalous large in-plane critical field far beyond the Pauli limit is detected, which can be attributed to the Zeeman-protected superconductivity due to the in-plane inversion symmetry breaking at the interface. Our work demonstrates that in superconducting heterostructures the interface can induce Zeeman-type spin-orbit interaction (SOI) and modulate the superconductivity.
We obtain the boundedness in $L^p$ spaces for all $1<p<\infty$ of the so-called vertical Littlewood--Paley functions for non-local Dirichlet forms in the metric measure space under some mild assumptions. For $1<p\le 2$, the pseudo-gradient is introduced to overcome the difficulty that chain rules are not available for non-local operators, and then the Mosco convergence is used to pave the way from the finite jumping kernel case to the general case, while for $2\le p<\infty$, the Burkholder--Davis--Gundy inequality is effectively applied. The former method is analytic and the latter one is probabilistic. The results extend those ones for pure jump symmetric Lévy processes in Euclidean spaces.
We study the electronic waiting time distributions (WTDs) in a non-interacting quantum dot spin valve by varying spin polarization and the noncollinear angle between the magnetizations of the leads using scattering matrix approach. Since the quantum dot spin valve involves two channels (spin up and down) in both the incoming and outgoing channels, we study three different kinds of WTDs, which are two-channel WTD, spin-resolved single-channel WTD and cross-channel WTD. We analyze the behaviors of WTDs in short times, correlated with the current behaviors for different spin polarizations and noncollinear angles. Cross-channel WTD reflects the correlation between two spin channels and can be used to characterize the spin transfer torque process. We study the influence of the earlier detection on the subsequent detection from the perspective of cross-channel WTD, and define the influence degree quantity as the cumulative absolute difference between cross-channel WTDs and first passage time distributions to quantitatively characterize the spin flip process. The influence degree shows a similar behavior with spin transfer torque and can be a new pathway to characterize spin correlation in spintronics system.
Bendable light beams have recently seen tremendous applications in optical manipulation, optical imaging, optical routing, micromachining, plasma generation and nonlinear optics. By exploiting curved light beams instead of traditional Gaussian beam for line-of-sight light communications, here we propose and demonstrate the viability of free-space data-carrying bendable light communications along arbitrary trajectories with multiple functionalities. By employing 39.06-Gbit/s 32-ary quadrature amplitude modulation (32-QAM) discrete multi-tone (DMT) signal, we demonstrate free-space bendable light intensity modulated direct detection (IM-DD) communication system under 3 different curved light paths. Moreover, we characterize multiple functionalities of free-space bendable light communications, including bypass obstructions transmission, self-healing transmission, self-broken trajectory transmission, and movable multi-receiver transmission. The observed results indicate that bendable light beams can make free-space optical communications more flexible, more robust and more multifunctional. The demonstrations may open a door to explore more special light beams enabling advanced free-space light communications with enhanced flexibility, robustness and functionality.
We consider SDEs driven by multiplicative pure jump Lévy noises, where Lévy processes are not necessarily comparable to $α$-stable-like processes. By assuming that the SDE has a unique solution, we obtain gradient estimates of the associated semigroup when the drift term is locally Hölder continuous, and we establish the ergodicity of the process both in the $L^1$-Wasserstein distance and the total variation, when the coefficients are dissipative for large distances. The proof is based on a new explicit Markov coupling for SDEs driven by multiplicative pure jump Lévy noises, which is derived for the first time in this paper.
In this paper, we propose a comprehensive Polar coding solution that integrates reliability calculation, rate matching and parity-check coding. Judging a channel coding design from the industry's viewpoint, there are two primary concerns: (i) low-complexity implementation in application-specific integrated circuit (ASIC), and (ii) superior \& stable performance under a wide range of code lengths and rates. The former provides cost- \& power-efficiency which are vital to any commercial system; the latter ensures flexible and robust services. Our design respects both criteria. It demonstrates better performance than existing schemes in literature, but requires only a fraction of implementation cost. With easily-reproducible code construction for arbitrary code rates and lengths, we are able to report "1-bit" fine-granularity simulation results for thousands of cases. The released results can serve as a baseline for future optimization of Polar codes.
Semiconductor lasers capable of generating a vortex beam with a specific orbital angular momentum (OAM) order are highly attractive for applications ranging from nanoparticle manipulation, imaging and microscopy to fibre and quantum communications. In this work, an electrically pumped OAM laser operating at telecom wavelengths is fabricated by monolithically integrating an optical vortex emitter with a distributed feedback (DFB) laser on the same InGaAsP/InP epitaxial wafer. A single-step dry etching process is adopted to complete the OAM emitter, equipped with specially designed top gratings. The vortex beam emitted by the integrated laser is captured, and its OAM mode purity characterized. The electrically pumped OAM laser eliminates the external laser required by silicon- or silicon-on-insulator (SOI)-based OAM emitters, thus demonstrating great potential for applications in communication systems and quantum domain.
We construct a complete and minimal basis of subleading-power N-jet operators in position-space soft-collinear effective theory (SCET) and discuss how the Low-Burnett-Kroll amplitude is recovered in this framework. We begin a systematic investigation of the anomalous dimension of next-to-leading power N-jet operators in view of resummation of logarithmically enhanced terms in partonic cross sections and discuss the explicit result at the one-loop order for fermion-number two N-jet operators at the second order in the power expansion parameter of SCET.
Proxima Centauri is known as the closest star from the Sun. Recently, radial velocity observations revealed the existence of an Earth-mass planet around it. With an orbital period of ~11 days, the surface of Proxima Centauri b is temperate and might be habitable. We took a photometric monitoring campaign to search for its transit, using the Bright Star Survey Telescope at the Zhongshan Station in Antarctica. A transit-like signal appearing on 2016 September 8th, is identified tentatively. Its midtime, $T_{C}=2,457,640.1990\pm0.0017$ HJD, is consistent with the predicted ephemeris based on RV orbit in a 1$σ$ confidence interval. Time-correlated noise is pronounced in the light curve of Proxima Centauri, affecting detection of transits. We develop a technique, in a Gaussian process framework, to gauge the statistical significance of potential transit detection. The tentative transit signal reported here, has a confidence level of $2.5σ$. Further detection of its periodic signals is necessary to confirm the planetary transit of Proxima Centauri b. We plan to monitor Proxima Centauri in next Polar night at Dome A in Antarctica, taking the advantage of continuous darkness. \citet{Kipping17} reported two tentative transit-like signals of Proxima Centauri b, observed by the Microvariability and Oscillation of Stars space Telescope in 2014 and 2015, respectively. The midtransit time of our detection is 138 minutes later than that predicted by their transit ephemeris. If all the signals are real transits, the misalignment of the epochs plausibly suggests transit timing variations of Proxima Centauri b induced by an outer planet in this system.
The growth of the number of people in the monitoring scene may increase the probability of security threat, which makes crowd counting more and more important. Most of the existing approaches estimate the number of pedestrians within one frame, which results in inconsistent predictions in terms of time. This paper, for the first time, introduces a quadratic programming model with the network flow constraints to improve the accuracy of crowd counting. Firstly, the foreground of each frame is segmented into groups, each of which contains several pedestrians. Then, a regression-based map is developed in accordance with the relationship between low-level features of each group and the number of people in it. Secondly, a directed graph is constructed to simulate constraints on people's flow, whose vertices represent groups of each frame and arcs represent people moving from one group to another. Then, the people flow can be viewed as an integer flow in the constructed digraph. Finally, by solving a quadratic programming problem with network flow constraints in the directed graph, we obtain consistency in people counting. The experimental results show that the proposed method can reduce the crowd counting errors and improve the accuracy. Moreover, this method can also be applied to any ultramodern group-based regression counting approach to get improvements.
Support recovery of sparse signals from noisy measurements with orthogonal matching pursuit (OMP) has been extensively studied. In this paper, we show that for any $K$-sparse signal $\x$, if a sensing matrix $\A$ satisfies the restricted isometry property (RIP) with restricted isometry constant (RIC) $δ_{K+1} < 1/\sqrt {K+1}$, then under some constraints on the minimum magnitude of nonzero elements of $\x$, OMP exactly recovers the support of $\x$ from its measurements $\y=\A\x+\v$ in $K$ iterations, where $\v$ is a noise vector that is $\ell_2$ or $\ell_{\infty}$ bounded. This sufficient condition is sharp in terms of $δ_{K+1}$ since for any given positive integer $K$ and any $1/\sqrt{K+1}\leq δ<1$, there always exists a matrix $\A$ satisfying the RIP with $δ_{K+1}=δ$ for which OMP fails to recover a $K$-sparse signal $\x$ in $K$ iterations. Also, our constraints on the minimum magnitude of nonzero elements of $\x$ are weaker than existing ones. Moreover, we propose worst-case necessary conditions for the exact support recovery of $\x$, characterized by the minimum magnitude of the nonzero elements of $\x$.
We begin a systematic investigation of the anomalous dimension of subleading power N-jet operators in view of resummation of logarithmically enhanced terms in partonic cross sections beyond leading power. We provide an explicit result at the one-loop order for fermion-number two N-jet operators at the second order in the power expansion parameter of soft-collinear effective theory.