η\eta-pairing in correlated fermion models with spin-orbit coupling

We generalize the $\eta$-pairing theory in Hubbard models to the ones with spin-orbit coupling (SOC) and obtain the conditions under which the $\eta$-pairing operator is an eigenoperator of the Hamiltonian. The $\eta$ pairing thus reveals an exact $SU(2)$ pseudospin symmetry in our spin-orbit coupled Hubbard model, even though the $SU(2)$ spin symmetry is explicitly broken by the SOC. In particular, these exact results can be applied to a variety of Hubbard models with SOC on either bipartite or non-bipartite lattices, whose noninteracting limit can be a Dirac semimetal, a Weyl semimetal, a nodal-line semimetal, and a Chern insulator. The $\eta$ pairing conditions also impose constraints on the band topology of these systems. We then construct and focus on an interacting Dirac-semimetal model, which exhibits an exact pseudospin symmetry with fine-tuned parameters. The stability regions for the \emph{exact} $\eta$-pairing ground states (with momentum $\bm{\pi}$ or $\bm{0}$) and the \emph{exact} charge-density-wave ground states are established. Between these distinct symmetry-breaking phases, there exists an exactly solvable multicritical line. In the end, we discuss possible experimental realizations of our results.Comment: v3: Title changed. Many details added, such as the identification of an exact multicritical line between symmetry-breaking phase

Electron multipacting in long-bunch beam

The electron multipacting is an important factor for the development of the electron cloud. There is a trailing-edge multipacting in the tail of the long-bunch beam. It can be described by the energy gain and motion of electrons. The analyses are in agreement with the simulation

Approaching quantum-limited amplification with large gain catalyzed by hybrid nonlinear media in cavity optomechanics

Amplifier is at the heart of almost all experiment carrying out the precise measurement of a weak signal. An idea amplifier should have large gain and minimum added noise simultaneously. Here, we consider the quantum measurement properties of a hybrid nonlinear cavity with the Kerr and OPA nonlinear media to amplify an input signal. We show that our hybrid-nonlinear-cavity amplifier has large gain in the single-value stable regime and achieves quantum limit unconditionally

Generalised Particle Filters with Gaussian Mixtures

Stochastic filtering is defined as the estimation of a partially observed dynamical system. A massive scientific and computational effort is dedicated to the development of numerical methods for approximating the solution of the filtering problem. Approximating the solution of the filtering problem with Gaussian mixtures has been a very popular method since the 1970s (see [1],[2],[46],[49]). Despite nearly fifty years of development, the existing work is based on the success of the numerical implementation and is not theoretically justified. This paper fills this gap and contains a rigorous analysis of a new Gaussian mixture approximation to the solution of the filtering problem. We deduce the L^2-convergence rate for the approximating system and show some numerical example to test the new algorithm.Comment: 28 pages, 3 figure

Uniqueness of constant scalar curvature K\"ahler metrics with cone singularities, I: Reductivity

The aim of this paper is to investigate uniqueness of conic constant scalar curvature Kaehler (cscK) metrics, when the cone angle is less than $\pi$. We introduce a new H\"older space called \cC^{4,\a,\b} to study the regularities of this fourth order elliptic equation, and prove that any \cC^{2,\a,\b} conic cscK metric is indeed of class \cC^{4,\a,\b}. Finally, the reductivity is established by a careful study of the conic Lichnerowicz operator.Comment: 37 pages, typos corrected, a new subsection added to explain a global definition of C^{4,\a,\b} spac

K\"ahler non-collapsing, eigenvalues and the Calabi flow

We first proved a compactness theorem of the K\"ahler metrics, which confirms a prediction of Chen. Then we prove several eigenvalue estimates along the Calabi flow. Combining the compactness theorem and these eigenvalue estimates, we generalize the method developed by Chen-Li-Wang to prove the small energy theorems of the Calabi flow.Comment: 33 pages, final version, to appear in Journal of Functional Analysi

Numerical Solutions of Jump Diffusions with Markovian Switching

In this paper we consider the numerical solutions for a class of jump diffusions with Markovian switching. After briefly reviewing necessary notions, a new jump-adapted efficient algorithm based on the Euler scheme is constructed for approximating the exact solution. Under some general conditions, it is proved that the numerical solution through such scheme converge to the exact solution. Moreover, the order of the error between the numerical solution and the exact solution is also derived. Numerical experiments are carried out to show the computational efficiency of the approximation.Comment: 21 pages, 1 figur

Precoded Turbo Equalizer for Power Line Communication Systems

Power line communication continues to draw increasing interest by promising a wide range of applications including cost-free last-mile communication solution. However, signal transmitted through the power lines deteriorates badly due to the presence of severe inter-symbol interference (ISI) and harsh random pulse noise. This work proposes a new precoded turbo equalization scheme specifically designed for the PLC channels. By introducing useful precoding to reshape ISI, optimizing maximum {\it a posteriori} (MAP) detection to address the non-Gaussian pulse noise, and performing soft iterative decision refinement, the new equalizer demonstrates a gain significantly better than the existing turbo equalizers

From rules to runs: A dynamic epistemic take on imperfect information games

In the literature of game theory, the information sets of extensive form games have different interpretations, which may lead to confusions and paradoxical cases. We argue that the problem lies in the mix-up of two interpretations of the extensive form game structures: game rules or game runs which do not always coincide. In this paper, we try to separate and connect these two views by proposing a dynamic epistemic framework in which we can compute the runs step by step from the game rules plus the given assumptions of the players. We propose a modal logic to describe players' knowledge and its change during the plays, and provide a complete axiomatization. We also show that, under certain conditions, the mix-up of the rules and the runs is not harmful due to the structural similarity of the two.Comment: draft of a paper accepted by Studies in Logic (published by Sun Yat-Sen University

A Novel Non-Parametric Approach to Compare Paired General Statistical Distributions between Two Interventions

Despite of many measures applied for determine the difference between two groups of observations, such as mean value, median value, sample stan- dard deviation and so on, we propose a novel non parametric transformation method based on Mallows distance to investigate the location and variance differences between the two groups. The convexity theory of this method is constructed and thus it is a viable alternative for data of any distribu- tions. In addition, we are able to establish the similar method under other distance measures, such as Kolmogorov-Smirnov distance. The application of our method in real data is performed as well.Comment: 12 pages, 5 figure