arXiv subjects
Publications and source records attributed to Xing Huang.
In this paper, the well-posedness for one-dimensional path dependent McKean-Vlasov SDEs with $α$($α\geq \frac{1}{2}$)-Hölder continuous diffusion is investigated. Moreover, the associated quantitative propagation of chaos in the sense of Wasserstein distance, total variation distance as well as relative entropy is studied.
We first derive the boundary theory from the U(1) Chern-Simons theory. The boundary action on an $n$-sheet manifold appears from its back-reaction of the Wilson line. The reason is that the U(1) Chern-Simons theory can provide an exact effective action when introducing the Wilson line. The Wilson line in the pure AdS$_3$ Einstein gravity is equivalent to entanglement entropy in the boundary theory up to classical gravity. The U(1) Chern-Simons theory deviates by a self-interaction term from the gauge formulation on the boundary. We also compare the Hayward term in the SL(2) Chern-Simons formulation to the Wilson line approach. Introducing two wedges can reproduce the entanglement entropy for a single interval at the classical level. We propose quantum generalization by combining the bulk and Hayward terms. The quantum correction of the partition function vanishes. In the end, we calculate the entanglement entropy for a single interval. The pure AdS$_3$ Einstein gravity theory shows a shift of central charge by 26 at the one-loop level. The U(1) Chern-Simons theory does not show a shift from the quantum effect. The result is the same in the weak gravitational constant limit. The non-vanishing quantum correction shows that the Hayward term is incorrect.
In this paper, the discrete parameter expansion is adopted to investigate the estimation of heat kernel for Euler-Maruyama scheme of SDEs driven by α-stable noise, which implies krylov's estimate and khasminskii's estimate. As an application, the convergence rate of Euler-Maruyama scheme of a class of multidimensional SDEs with singular drift( in aid of Zvonkin's transformation) is obtained.
We report the synthesis and characterization of a Si-based ternary semiconductor Mg$_3$Si$_2$Te$_6$, which exhibits a quasi-two-dimensional structure, where the trigonal Mg$_2$Si$_2$Te$_6$ layers are separated by Mg ions. Ultraviolet-visible absorption spectroscopy and density functional theory calculations were performed to investigate the electronic structure. The experimentally determined direct band gap is 1.39 eV, consistent with the value of the density function theory calculations. Our results reveal that Mg$_3$Si$_2$Te$_6$ is a direct gap semiconductor with a relatively narrow gap, which is a potential candidate for infrared optoelectronic devices.
The propagation of light in moving media is dragged by atomic motion. The light-drag effect can be dramatically enhanced by reducing the group velocity with electro-magnetically induced transparency (EIT). We develop a systematic procedure to accurately reconstruct the complex wavefront of the slow light with single-shot measurements, enabling precise, photon shot-noise limited spectroscopic measurements of atomic response across EIT even in presence of generic atomic number fluctuations. Applying the technique to an expanding cloud of cold atoms, we demonstrate simultaneous inference of the atomic density distribution and the velocity field from the complex imaging data. This inline imaging technique may assist a wide range of cold atom experiments to access spectroscopic and phase space information with in situ and minimally destructive measurements.
By using distribution dependent Zvonkin's transforms and Malliavin calculus, the Bismut type formula is derived for the intrinisc/Lions derivatives of distribution dependent SDEs with singular drifts, which generalizes the corresponding results derived for classical SDEs and regular distribution dependent SDEs.
By using Zvonkin's transformation and a two-step fixed point argument in distributions, the well-posedness and regularity estimates are derived for singular McKean-Vlasov SDEs with distribution dependent noise, where the drift contains a term growing linearly in space and distribution and a locally integrable term independent of distribution, while the noise coefficient is weakly differentiable in space and Lipschitz continuous in distribution with respect to the sum of Wasserstein and weighted variation distances. The main results extend existing ones derived for noise coefficients either independent of distribution, or having nice linear functional derivatives in distribution. Singular reflecting SDEs with distribution dependent noise are also studied.
In digital circuit designs, sequential components such as flip-flops are used to synchronize signal propagations. Logic computations are aligned at and thus isolated by flip-flop stages. Although this fully synchronous style can reduce design efforts significantly, it may affect circuit performance negatively, because sequential components can only introduce delays into signal propagations but never accelerate them. In this paper, we propose a new timing model, VirtualSync+, in which signals, specially those along critical paths, are allowed to propagate through several sequential stages without flip-flops. Timing constraints are still satisfied at the boundary of the optimized circuit to maintain a consistent interface with existing designs. By removing clock-to-q delays and setup time requirements of flip-flops on critical paths, the performance of a circuit can be pushed even beyond the limit of traditional sequential designs. In addition, we further enhance the optimization with VirtualSync+ by fine-tuning with commercial design tools, e.g., Design Compiler from Synopsys, to achieve more accurate result. Experimental results demonstrate that circuit performance can be improved by up to 4% (average 1.5%) compared with that after extreme retiming and sizing, while the increase of area is still negligible. This timing performance is enhanced beyond the limit of traditional sequential designs. It also demonstrates that compared with those after retiming and sizing, the circuits with VirtualSync+ can achieve better timing performance under the same area cost or smaller area cost under the same clock period, respectively.
Very recently, we proposed an explanation of the discrepancy between the measured anomalous magnetic moment of the muon and the Standard Model (SM) prediction in which the dominant contribution to $(g-2)_μ$ originates in Kaluza-Klein (KK) excitations (of the lepton gauge boson) which do not mix with quarks (to lowest order) and therefore can be quite light avoiding LHC constraints. In this addendum we reexamine the bounds on 4-fermion contact interactions from precise electroweak measurements and show that the constraints on KK masses and couplings are more severe than earlier thought. However, we demonstrate that our explanation remains plausible if a few KK modes are lighter than LEP energy, because if this were the case the contribution to the 4-fermion scattering from the internal propagator would be dominated by the energy and not by the mass. To accommodate the $(g-2)_μ$ discrepancy we assume that the lepton number $L$ does not partake in the hypercharge and propagates in one extra dimension (transverse to the SM branes): for a mass of the lowest KK excitation of 60 GeV (lower than the LEP energy), the string scale is roughly 10 TeV while the $L$ gauge coupling is of order $\sim 10^{-1}$.
We demonstrate a simple method to obtain accurate optical waveforms with a GHz-level programmable modulation bandwidth and Watt-level output power for wideband optical control of free atoms and molecules. Arbitrary amplitude and phase modulations are transferred from microwave to light with a low-power fiber electro-optical modulator. The sub-milliWatt optical sideband is co-amplified with the optical carrier in a power-balanced fashion through a tapered semiconductor amplifier (TSA). By automatically keeping TSA near saturation in a quasi-continuous manner, typical noise channels associated with pulsed high-gain amplifications are efficiently suppressed. As an example application, we demonstrate interleaved cooling and trapping of two rubidium isotopes with coherent nanosecond pulses.
The existence and uniqueness are established for McKean-Vlasov SDEs driven by Lévy processes. By using an approximation technique and coupling by change of measures, Harnack inequalities are investigated for McKean-Vlasov SDEs driven by subordinate Brownian motions.
In this paper, Wang's log-Harnack inequality and exponential ergodicity are derived for two types of distribution dependent SDEs: one is the CKLS model, where the diffusion coefficient is a power function of order $θ$ with $θ\in[\frac{1}{2},1)$; the other one is Vasicek model, where the diffusion coefficient only depends on distribution. Both models in the distribution independent case can be used to characterize the interest rate in mathematical finance.
In this paper, by utilizing Wang's Harnack inequality with power and the Banach fixed point theorem, the weak well-posedness for McKean-Vlasov SDEs with integrable drift is investigated. In addition, using the decoupled method, some regularity such as relative entropy and Sobolev's estimate of invariant probability measure are proved. Finally, by Banach's fixed theorem, the existence and uniqueness of invariant probability measure for symmetric McKean-Vlasov SDEs and stochastic Hamiltonian system with integrable drifts are obtained.
We generalize the Quantum Geometric Tensor by replacing a Hamiltonian with a modular Hamiltonian. The symmetric part of the Quantum Geometric Tensor provides a Fubini-Study metric, and its anti-symmetric sector gives a Berry curvature. Now the generalization or Quantum Modular Geometric Tensor gives a Kinematic Space and a modular Berry curvature. Here we demonstrate the emergence by focusing on a spherical entangling surface. We also use the result of the identity Virasoro block to relate the connected correlator of two Wilson lines to the two-point function of a modular Hamiltonian. This result realizes a novel holographic entanglement formula for two intervals of a general separation. This formula does not only hold for a classical gravity sector but also Quantum Gravity. The formula also provides a new Quantum Information interpretation to the connected correlators of Wilson lines as the mutual information. Our study provides an opportunity to explore Quantum Kinematic Space through Quantum Modular Geometric Tensor and hence go beyond symmetry.
We demonstrate that the discrepancy between the anomalous magnetic moment measured at BNL and Fermilab and the Standard Model prediction could be explained within the context of low-scale gravity and large extra-dimensions. The dominant contribution to $(g-2)_μ$ originates in Kaluza-Klein (KK) excitations (of the lepton gauge boson) which do not mix with quarks (to lowest order) and therefore can be quite light avoiding LHC constraints. We show that the KK contribution to $(g-2)_μ$ is universal with the string scale entering as an effective cutoff. The KK tower provides a unequivocal distinctive signal which will be within reach of the future muon smasher.
Very recently, the Muon $g-2$ experiment at Fermilab has confirmed the E821 Brookhaven result, which hinted at a deviation of the muon anomalous magnetic moment from the Standard Model (SM) expectation. The combined results from Brookhaven and Fermilab show a difference with the SM prediction $δa_μ= (251 \pm 59) \times 10^{-11}$ at a significance of $4.2σ$, strongly indicating the presence of new physics. Motivated by this new result we reexamine the contributions to the muon anomalous magnetic moment from both: (i)~the ubiquitous $U(1)$ gauge bosons of D-brane string theory constructions and (ii)~the Regge excitations of the string. We show that, for a string scale ${\cal O} ({\rm PeV})$, the contribution from anomalous $U(1)$ gauge bosons which couple to hadrons could help to reduce (though not fully eliminate) the discrepancy reported by the Muon $g-2$ Collaboration. Consistency with null results from LHC searches of new heavy vector bosons imparts the dominant constraint. We demonstrate that the contribution from Regge excitations is strongly suppressed as it was previously conjectured. We also comment on contributions from Kaluza-Klein (KK) modes, which could help resolve the $δa_μ$ discrepancy. In particular, we argue that for 4-stack intersecting D-brane models, the KK excitations of the $U(1)$ boson living on the lepton brane would not couple to hadrons and therefore can evade the LHC bounds while fully bridging the $δa_μ$ gap observed at Brookhaven and Fermilab.
In this paper we study a class of distribution dependent stochastic differential equations driven by fractional Brownian motions with Hurst parameter H\in(1/2,1). We prove the well-posedness of this type equations, and then establish a general result on the Bismut formula for the Lions derivative by using Malliavin calculus. As applications, we provide the Bismut formulas of this kind for both non-degenerate and degenerate cases, and obtain the estimates of the Lions derivative and the total variation distance between the laws of two solutions.
The analog front-end for the Low Gain Avalanche Detector (LGAD) based precision timing application in the CMS Endcap Timing Layer (ETL) has been prototyped in a 65 nm CMOS mini-ASIC named ETROC0. Serving as the very first prototype of ETL readout chip (ETROC), ETROC0 aims to study and demonstrate the performance of the analog frontend, with the goal to achieve 40 to 50 ps time resolution per hit with LGAD (therefore reach about 30ps per track with two detector-layer hits per track). ETROC0 consists of preamplifier and discriminator stages, which amplifies the LGAD signal and generates digital pulses containing time of arrival and time over threshold information. This paper will focus on the design considerations that lead to the ETROC front-end architecture choice, the key design features of the building blocks, the methodology of using the LGAD simulation data to evaluate and optimize the front-end design. The ETROC0 prototype chips have been extensively tested using charge injection and the measured performance agrees well with simulation. The initial beam test results are also presented, with time resolution of around 33 ps observed from the preamplifier waveform analysis and around 41 ps from the discriminator pulses analysis. A subset of ETROC0 chips have also been tested to a total ionizing dose of 100 MRad with X-ray and no performance degradation been observed.