arXiv subjects

Xiang Lv

Publications and source records attributed to Xiang Lv.

24 records · Page 2Linked to original sources

arXiv2021

Possible implications for particle physics by quantum measurement

In sharp contrast to its classical counterpart, quantum measurement plays a fundamental role in quantum mechanics and blurs the essential distinction between the measurement apparatus and the objects under investigation. An appealing phenomenon in quantum measurements, termed as quantum Zeno effect, can be observed in particular subspaces selected by measurement Hamiltonian. Here we apply the top-down Zeno mechanism to the particle physics. We indeed develop an alternative insight into the properties of fundamental particles, but not intend to challenge the Standard Model (SM). In a unified and simple manner, our effective model allows to merge the origin of neutrino's small mass and oscillations, the hierarchy pattern for masses of electric charged fermions, the color confinement, and the discretization of quantum numbers, using a perturbative theory for the dynamical quantum Zeno effect. Under various conditions for vanishing transition amplitudes among particle eigenstates in the effective model, it is remarkable to probe results that are somewhat reminiscent of SM, including: (i) neutrino oscillations with big-angle mixing and small masses emerge from the energy-momentum conservation, (ii) electrically-charged fermions hold masses in a hierarchy pattern due to the electric-charge conservation, (iii) color confinement and the associated asymptotic freedom can be deduced from the color-charge conservation. We make several anticipations about the basic properties for fundamental particles: (i) the total mass of neutrinos and the existence of a nearly massless neutrino (of any generation), (ii) the discretization in quantum numbers for the new-discovered electrically-charged fermions, (iii) the confinement and the associated asymptotic freedom for any particle containing more than two conserved charges.

hep-ph↗

arXiv2020

Photo-production of Higgs Boson at the LHeC

As one category of vector boson fusion, photo-production is one important production mechanism at $e$-$p$ colliders. A future $e$-$p$ collider -- Large Hadron-electron Collider (LHeC) has been discussed as a "Higgs factory" candidate where the Higgs boson produced via weak boson fusion (WBF) at the LHeC plays an important role in precision measurement of Yukawa couplings. On the other hand, a measurement of photo-production of the Higgs boson, if possible, might be complementary to the measurement of Higgs to di-photon partial decay width $Γ({h\toγγ})$. In this paper, we study the possibility of measuring this production process at the LHeC with the help of the photon PDFs published in recent years. This process has a clean final state without additional colored particles in the detectable region other than the decay products of the Higgs. We compute the cross sections of all related processes and find that the production rate is at the same order as the neutral current WBF production of Higgs boson with missing forward jets. However, a detailed phenomenological study of various Higgs decay channels shows that even in the most promising semi-leptonic $WW$ channel, the feasibility of identifying such photo-production is negative due to an irreducible photo-production of $W^{+}W^{-}$.

hep-ph↗

arXiv2018

Equivalence of Coefficients Extraction of One-loop Master Integrals

Now there are many different methods to do the PV-reduction for the one loop amplitudes. Two of them are unitarity cut method and generalized unitarity cut method. In this short paper, we present an explicit connection of these two methods, especially how the extractions of triangle and bubble coefficients are equivalent to each other.

hep-th↗

arXiv2016

Small-gain theorems for nonlinear stochastic systems with inputs and outputs II: Multiplicative white noise case

This paper is a continuation of the paper \cite{JL}, which focuses on exploring the global stability of nonlinear stochastic feedback systems on the nonnegative orthant driven by multiplicative white noise and presenting a couple of small-gain results. We investigate the dynamical behavior of pull-back trajectories for stochastic control systems and prove that there exists a unique globally attracting positive random equilibrium for those systems whose output functions either possess bounded derivatives or are uniformly bounded away from zero. In the first case, we first prove the joint measurability of both the pull-back trajectories and the metric dynamical system $θ$ with respect to the product $σ$-algebra $\mathscr{B}(\mathbb{R_+})\otimes\mathscr{F}_-$ and $\mathscr{B}(\mathbb{R_-})\otimes\mathscr{F}_-$, respectively, where $\mathscr{F}_-=σ\{ω\mapsto W_t(ω):t\leq0\}$ is the past $σ$-algebra and $W_t(ω)$ is an $\mathbb{R}^d$-valued two-sided Wiener process, and then combine the $\mathcal{L}^1$-integrability of the tempered random variable coming from the definition of the top Lyapunov exponent and the independence between the past $σ$-algebra and the future $σ$-algebra $\mathscr{F}_+=σ\{ω\mapsto W_t(ω):t\geq0\}$ to obtain the small-gain theorem by constructing the contraction mapping on an $\mathscr{F}_-$-measurable, $\mathcal{L}^1$-integrable and complete metric input space; in the second case, the sublinearity of output functions and the part metric play the main roles in the existence and uniqueness of globally attracting positive fixed point in the part of a normal, solid cone. Our results can be applied to well-known stochastic Goodwin negative feedback system, Othmer-Tyson positive feedback system and Griffith positive feedback system as well as other stochastic cooperative, competitive and predator-prey systems.

math.DS↗

arXiv2016

Infinitely many homoclinic solutions for a class of subquadratic second-order Hamiltonian systems

In this paper, we mainly consider the existence of infinitely many homoclinic solutions for a class of subquadratic second-order Hamiltonian systems $\ddot{u}-L(t)u+W_u(t,u)=0$, where $L(t)$ is not necessarily positive definite and the growth rate of potential function $W$ can be in $(1,3/2)$. Using the variant fountain theorem, we obtain the existence of infinitely many homoclinic solutions for the second-order Hamiltonian systems.

math.DS↗

arXiv2016

A small-gain theorem for nonlinear stochastic systems with inputs and outputs I: Additive white noise

This paper studies a small-gain theorem for nonlinear stochastic equations driven by additive white noise in both trajectories and stationary distribution. Motivated by the most recent work of Marcondes de Freitas and Sontag \cite{FS3}, we firstly define the {\it "input-to-state characteristic operator"} $\mathcal{K}(u)$ of the system in a suitably chosen input space via backward Itô integral, and then for a given output function $h$, define the $"gain\ operator"$ as the composition of output function $h$ and the input-to-state characteristic operator $\mathcal{K}(u)$ on the input space. Suppose that the output function is either order-preserving or anti-order-preserving in the usual vector order and the global Lipschitz constant of the output function is less than the absolute of the negative principal eigenvalue of linear matrix. Then we prove the so-called {\it "small-gain theorem"}: the gain operator has a unique fixed point, the image for input-to-state characteristic operator at the fixed point is a globally attracting stochastic equilibrium for the random dynamical system generated by the stochastic system. Under the same assumption for the relation between the Lipschitz constant of the output function and maximal real part of stable linear matrix, we prove that the stochastic system has a unique stationary distribution, which is regarded as a stationary distribution version of small-gain theorem. These results can be applied to stochastic cooperative, competitive and predator-prey systems, or even others.

math.DS↗