arXiv subjects

Pei Zheng

Publications and source records attributed to Pei Zheng.

8 recordsLinked to original sources

arXiv2026

Schwinger-Keldysh effective field theory of type-B Goldstone: near-diagonal geometry and Berry term

In this work, we formulate a finite temperature Schwinger-Keldysh effective field theory for type-B Goldstone modes. In particular, we organize the required two time contour structure by a near-diagonal geometry in which the r-type field is interpreted as the physical Goldstone configuration and the a-type field is identified as corresponding tangent displacement. Within this geometric viewpoint, the Berry term essential for type-B Goldstones is obtained directly through the transgression of the Berry curvature. Moreover, we show that this exact Berry transgression is compatible with dynamical KMS condition. In order to construct the conservative, dissipative and noise sectors, we classify possible tensors globally defined on the coset manifold. Based on this framework, we discuss in detail two concrete model examples. The dispersion relations of the Goldstone modes and the associated two-point correlation functions are calculated in the presence of dissipation.

hep-th↗

arXiv2026

On the Critical One Components Regularity for the $3-D$ Navier-Stokes System in $L^p_T(\dot{B}^{\frac 1 2+\frac 2 p}_{2,\infty})$ spaces

We consider the conditional regularity of the mild solution $v$ of the $3-D$ incompressible Navier-Stokes equations with initial data $v_0\in \dot{H}^{\frac 1 2}$ and vorticity $Ω_0\in L^{r_0}$ for some $r_0\in (1,2)$. We prove that if the solution associated with initial data $v_0$ blows up at a finite time $T^\ast$, then for any $2<p<\infty$, and any unit vectors $e$ in $\mathbb{R}^3$, the integral $$\int_0^{T^\ast}\left\Vert (v(t)|e)_{\mathbb{R}^3}\right\Vert_{\dot{B}^{\frac 1 2+\frac 2 p}_{2,\infty}}^p{\rm d}t$$ blows up at $T^\ast$. The conclusion improves the recent results in Chemin et al. (Arch Ration Mech Anal 224(3):871-905, 2017) and Han et al. (Arch. Rational Mech. Anal. 231:939-970, 2019).

math.AP↗

arXiv2026

Invariant Measure of the Camassa-Holm Equation with Linear Multiplicative Noise

In this paper, we prove that the solution map of Camassa-Holm equation with linear multiplicative noise $$ \left\{ \begin{array}{l} {\rm d}u+(u\partial_xu+\partial_xP[u])\,{\rm d}t=βu\,{\rm d}W, u(0,x)=u_0(x), P[u]=(1-\partial_x^2)^{-1}\left(u^2+\frac 1 2(\partial_x u)^2\right) \end{array} \right. $$ depends almost surely continuously on the deterministic initial data in $H^s$ for $s>3/2$. Furthermore, we prove the existence and non-uniqueness of an invariant measure for the Camassa-Holm equation with linear multiplicative noise.

math.AP↗

arXiv2026

Global Existence of Weak Martingale Solutions to the Camassa-Holm Equation with Linear Multiplicative Noise

In this paper, we consider the global existence and properties of $H^1$ martingale solution to the Camassa-Holm equation with linear multiplicative noise under periodic boundary conditions. The solution is obtained as limit of regular viscous approximate solutions to parabolic SPDEs, which are constructed using the Galerkin approximations ans the stochastic compactness method. The proof of convergence to a solution argues via tightness of the laws of the viscous approximations and Skorokhod-Jakubowski a.s. representations of random variables in quasi-Polish spaces. In particular, by means of the Girsanov-type transform for regular viscous approximations and the convergence of Skorokhod-Jakubowski representations, we are able to establish the one-sided supernorm estimate and space-time higher regularity of the first-order spatial derivative, and large-time behavior of the weak martingale solution in the stochastic framework.

math.AP↗

arXiv2025

Dynamical instability and transport peak of chiral matter from holography

We study dynamical properties of strongly coupled chiral matter by using holographic method. We demonstrate, at both linear and nonlinear levels, that perturbations on thermodynamically unstable backgrounds within the spinodal region of chiral first-order phase transitions exhibit dynamic instability. The corresponding magnitude of dynamic instability can be characterized by the critical momentum. Furthermore, we found that, within a certain temperature range, the quasi-normal mode spectrum contains purely imaginary diffusive modes. As spatial momentum increases, a transition occurs in the system's long-time dynamics. The dominant contribution shifts from diffusive mode to propagating mode. When the diffusive mode becomes dominant, the spectral function exhibits a transport peak structure in the low-frequency region. A heuristic argument suggests that this particular transition can be related to the chiral symmetry breaking and restoration.

hep-ph↗

arXiv2024

Non-equilibrium dynamics of Goldstone excitation from holography

By using the holographic approach, we investigate the interplay between the order parameter and Goldstone modes in the real-time dynamics of the chiral phase transition. By quenching the system to a different thermal bath and obtaining different kinds of initial states, we solve the real-time evolution of the system numerically. Our main focus is on studying far-from equilibrium dynamics of strongly-coupled system and universal scaling behaviors related to such dynamics. The most striking observation is that an additional prethermalization stage emerges at non-critical temperature after introducing the Goldstone modes, which is not reported in any previous studies. Some basic properties related to this additional prethermalization stage have been discussed in detail. More interestingly, we also report a new scaling relation describing non-equilibrium evolution at non-critical temperature. This additional universal behavior indicates the appearance of a non-thermal fixed point in the dynamical region.

hep-ph↗

arXiv2024

The local well-posedness, blow-up and global solution of a new integrable system in Besov spaces

In this paper, we first establish the local well-posednesss for the Cauchy problem of a $N$-peakon system in the sense of Hadamard in both critical Besov spaces and supercritical Besov spaces. Second, we gain a blow-up criterion. According to blow-up criterion wemreach a precise blow-up criterion. Under a sign condition, we reach the existence of global solution. Finally, based on the first-order difference method, we give a simulation example of the blow-up of the equation and the properties of the global solution.

math.AP↗

arXiv2024

The well-posedness and blow up phenomenon for a Tsunamis model with time-fractional derivative

This paper is concerned with the well-posedness of a time-fractional shallow-water equations, which has received little attention. In the realm of fractional calculus, numerous types of fractional derivatives have been explored in the literature. Among these, one of the most notable and well-structured ones is the conformable fractional derivative. In this paper, we delve into the local well-posedness of the fractional tsunami shallow-water mathematical model in the critical Besov space $B^{\frac{3}{2}}_{2,1}$. Under some symmetric and sign conditions, we show that the strong solution will blow up in finite time.

math.AP↗