arXiv subjects
Publications and source records attributed to Hongjun Gao.
We prove the the large deviation principle(LDP) for the law of the one-dimensional semilinear stochastic partial differential equations driven by nonlinear multiplicative noise. Firstly, combining the energy estimate and approximation procedure, we obtain the existence of global solution. Then the large deviation principle is obtained via weak convergence method.
The existence of global martingale weak solution for the 2D and 3D stochastic Cahn-Hilliard-Navier-Stokes equations driven by multiplicative noise in a smooth bounded domain is established. In particular, the system is supplied with the dynamic boundary condition which accounts for the interaction between the fluid components and the rigid walls. The proof is completed by a three-level approximate scheme combining a fixed point argument and the stochastic compactness argument, overcoming challenges from strong nonlinearity, dynamic boundary and random effect. Then, we prove the existence of an almost surely Markov selection to the associated martingale problem following the abstract framework established by F. Flandoli and M. Romito.
A kagome lattice of 3d transition metals hosts flat bands, Dirac fermions and saddle points. It provides a versatile platform for achieving topological superconductivity, anomalous Hall effect, unconventional density wave order and quantum spin liquid when the strong correlation, spin-orbit coupling or magnetic order are involved in such a lattice. Here, using laser-based angle-resolved photoemission spectroscopy in combination with density functional theory calculations, we investigate the electronic structure of the newly discovered kagome superconductor CsTi$_3$Bi$_5$, which is isostructural to the AV$_3$Sb$_5$ (A=K, Rb or Cs) kagome superconductors and possesses a perfect two-dimensional kagome network of Titanium. We directly observed a strikingly flat band derived from the local destructive interferences of Bloch wave functions within the kagome lattices. We also identify the type-II Dirac nodal loops around the Brillouin zone center, the type-III Dirac nodal loops around the zone corners and type-III Dirac nodal lines along the k$_z$ direction. In addition, around the Brillouin zone center, Z2 nontrivial topological surface states are also observed which is formed from the band inversion due to strong spin orbital coupling. The simultaneous existence of such multi-sets of nontrivial band structures in one kagome superconductor not only provides good opportunities to study related physics in the kagome lattice but also makes CsTi$_3$Bi$_5$ an ideal system to realize noval quantum phenomena by manipulating its chemical potential with chemical doping or pressure.
In this paper, we obtain the existence of random attractors for a class of evolution equations driven by a geometric fractional Brownian rough path with Hurst index $H\in(\frac{1}{3},\frac{1}{2}]$ and establish the upper semi-continuity of random attractors $\mathcal{A}_η$ for the approximated systems of the evolution equations.
This paper is devoted to the smooth and stationary Wong-Zakai approximations for a class of rough differential equations driven by a geometric fractional Brownian rough path $\boldsymbolω$ with Hurst index $H\in(\frac{1}{3},\frac{1}{2}]$. We first construct the approximation $\boldsymbolω_δ$ of $\boldsymbolω$ by probabilistic arguments, and then using the rough path theory to obtain the Wong-Zakai approximation for the solution on any finite interval. Finally, both the original system and approximative system generate a continuous random dynamical systems $φ$ and $φ^δ$. As a consequence of the Wong-Zakai approximation of the solution, $φ^δ$ converges to $φ$ as $δ\rightarrow 0$.
In this paper, we consider a class of evolution equations driven by finite-dimensional $γ$-Hölder rough paths, where $γ\in(1/3,1/2]$. We prove the global-in-time solutions of rough evolution equations(REEs) in a sutiable space, also obtain that the solutions generate random dynamical systems. Meanwhile, we derive the existence of local unstable manifolds for such equations by a properly discretized Lyapunov-Perron method.
The modulation of topological electronic states by an external magnetic field is highly desired for condensed matter physics. Schemes to achieve this have been proposed theoretically, but few can be realized experimentally. Here, combining transverse transport, theoretical calculations, and scanning tunneling microscopy/spectroscopy (STM/S) investigations, we provide an observation that the topological electronic states, accompanied by an emergent magneto-transport phenomenon, were modulated by applying magnetic fields through induced non-collinear magnetism in the magnetic Weyl semimetal EuB6. A giant unconventional anomalous Hall effect (UAHE) is found during the magnetisation re-orientation from easy axis to hard ones in magnetic fields, with a UAHE peak around the low field of 5 kOe. Under the reasonable spin-canting effect, the folding of the topological anti-crossing bands occurs, generating a strong Berry curvature that accounts for the observed UAHE. Field-dependent STM/S reveals a highly synchronous evolution of electronic density of states, with a dI/dV peak around the same field of 5 kOe, which provides evidence to the folded bands and excited UAHE by external magnetic fields. This finding elucidates the connection between the real-space non-collinear magnetism and the k-space topological electronic states and establishes a novel manner to engineer the magneto-transport behaviours of correlated electrons for future topological spintronics.
The connection between unconventional superconductivity and charge density waves (CDW) has intrigued the condensed matter community and found much interest in the recently discovered superconducting Kagome family of AV$_3$Sb$_5$ (A = K, Cs, Rb). Xray diffraction and Raman spectroscopy measurements established that the CDW order in CsV$_3$Sb$_5$ comprises of a 2x2x4 structure with stacking of layers of star-of-David (SD) and inverse-star-of-David (ISD) pattern along the $c$-axis direction. Such interlayer ordering will induce a vast normalization of the electronic ground state; however, it has not been observed in Fermi surface measurements. Here we report quantum oscillations of CsV$_3$Sb$_5$ using tunnel diode oscillator frequency measurements. We observed a large number of frequencies, many of which were not reported. The number of frequencies can not be explained by DFT calculations when only SD or ISD distortion is considered. Instead, our results are consistent with calculations when interlayer ordering is taken into account, providing strong evidence that CDW phase of CsV$_3$Sb$_5$ has complicated structure distortion which in turn has dramatic effects on the Fermi surface properties.
A Hamiltonian model for the propagation of internal water waves interacting with surface waves, a current and an uneven bottom is examined. Using the so-called Dirichlet-Neumann operators, the water wave system is expressed in the Hamiltonian form, and thus the motions of the internal waves and surface waves are determined by the Hamiltonian formulation. Choosing an appropriate scaling of the variables and employing the Hamiltonian perturbation theory from Hamiltonian formulation of the dynamics, we derive a KdV-type equation with variable coefficients depending on the bottom topography to describe the internal waves.
This paper is devoted to deriving the Onsager-Machlup action functional for Mckean-Vlasov stochastic differential equations in a class of norms that dominate $L^2([0,1], \mathbb{R}^d)$, such as supremum norm $\|\cdot\|_{\infty}$, H$\mathrm{\ddot{o}}$lder norms $\|\cdot\|_α$ with $α<\frac{1}{4}$ and $L^p$-norms with $p>4$ are included. Moreover, the corresponding Euler-Lagrange equation for Onsager-Machlup action functional is derived and a example is given.
Magnetic topological insulators (MTIs) have received a lot of attention due to the existence of various quantum phenomena such as quantum anomalous Hall effect (QAHE) and topological magnetoelectric effect, etc. The intrinsic superlattice-like layered MTIs, MnBi2Te4/(Bi2Te3)n, have been extensively investigated mainly through the transport measurements, while the direct investigation of their superlattice-sensitive magnetic behaviors is relatively rare. Here, we report a microscopic real-space investigation of magnetic phase behaviors in MnBi4Te7 using cryogenic magnetic force microscopy (MFM). The intrinsic robust A-type antiferromagnetic (AFM), and emerged surface spin-flop (SSF), canted AFM (CAFM), ferromagnetic (FM)+CAFM, forced FM phases are sequentially visualized via the increased external magnetic field, in agreement with the metamagnetic behavior in the M-H curve. The temperature-dependent magnetic phase evolution behaviors are further investigated to obtain the complete H-T phase diagram of MnBi4Te7. The tentative local phase manipulation via the stray field of the magnetic tip is demonstrated by transforming the AFM to FM phase in its surface layers of MnBi4Te7. Our study the not only provide key real-space ingredients for understanding their complicated magnetic, electronic, and topological properties of these intrinsic MTIs, but also suggest new directions for manipulating spin textures and locally controlling their exotic properties.
High resolution angle-resolved photoemission spectroscopy (ARPES) measurements are carried out on CaKFe$_4$As$_4$, KCa$_2$Fe$_4$As$_4$F$_2$ and (Ba$_{0.6}$K$_{0.4}$)Fe$_2$As$_2$ superconductors. Clear evidence of band folding between the Brillouin zone center and corners with a ($π$,$π$) wave vector has been found from the measured Fermi surface and band structures in all the three kinds of superconductors. A dominant $\sqrt{2}\,\times\,\sqrt{2}$ surface reconstruction is observed on the cleaved surface of CaKFe$_4$As$_4$ by scanning tunneling microscopy (STM) measurements. We propose that the commonly observed $\sqrt{2}\,\times\,\sqrt{2}$ reconstruction in the FeAs-based superconductors provides a general scenario to understand the origin of the ($π$,$π$) band folding. Our observations provide new insights in understanding the electronic structure and superconductivity mechanism in iron-based superconductors.
In this work, we obtain the hydrostatic approximation by taking the small aspect ratio limit to the Navier-Stokes equations. The aspect ratio (the ratio of the depth to horizontal width) is a geometrical constraint in general large scale geophysical motions that the vertical scale is significantly smaller than horizontal. We use the versatile relative entropy inequality to prove rigorously the limit from the compressible Navier-Stokes equations to the compressible Primitive Equations. This is the first work to use relative entropy inequality for proving hydrostatic approximation and derive the compressible Primitive Equations.
The increased penetration of wind power introduces more operational changes of critical corridors and the traditional time-consuming transient stability constrained total transfer capability (TTC) operational planning is unable to meet the real-time monitoring need. This paper develops a more computationally efficient approach to address that challenge via the analytical deep learning-based surrogate model. The key idea is to resort to the deep learning for developing a computationally cheap surrogate model to replace the original time-consuming differential-algebraic constraints related to TTC. However, the deep learning-based surrogate model introduces implicit rules that are difficult to handle in the optimization process. To this end, we derive the Jacobian and Hessian matrices of the implicit surrogate models and finally transfer them into an analytical formulation that can be easily solved by the interior point method. Surrogate modeling and problem reformulation allow us to achieve significantly improved computational efficiency and the yielded solutions can be used for operational planning. Numerical results carried out on the modified IEEE 39-bus system demonstrate the effectiveness of the proposed method in dealing with com-plicated TTC constraints while balancing the computational efficiency and accuracy.
In this paper, we consider the fractional Camassa-Holm equation modelling the propagation of small-but-finite amplitude long unidirectional waves in a nonlocally and nonlinearly elastic medium. First, we establish the local well-posedness in Besov space $B^{s_0}_{2,1}$ with $s_0=2ν-\frac 1 2$ for $ν>\frac 3 2 $ and $s_0=\frac 5 2$ for $1<ν\leq \frac 3 2 $. Then, with a given analytic initial data, we establish the analyticity of the solutions in both variables, globally in space and locally in time.
We consider the rough differential equation $dY=f(Y)d\bm \om$ where $\bm \om=(ω,\bbomega)$ is a rough path defined by a Brownian motion $ω$ on $\RR^m$. Under the usual regularity assumption on $f$, namely $f\in C^3_b (\RR^d, \RR^{d\times m})$, the rough differential equation has a unique solution that defines a random dynamical system $ϕ_0$. On the other hand, we also consider an ordinary random differential equation $dY_δ=f(Y_δ)dω_\de$, where $ω_\de$ is a random process with stationary increments and continuously differentiable paths that approximates $ω$. The latter differential equation generates a random dynamical system $ϕ_δ$ as well. We show the convergence of the random dynamical system $ϕ_δ$ to $ϕ_0$ for $δ\to 0$ in Hölder norm.
This paper addresses the weak-strong uniqueness property and singular limit for the compressible Primitive Equations (PE). We show that a weak solution coincides with the strong solution emanating from the same initial data. On the other hand, we prove compressible PE will approach the incompressible inviscid PE equations in the regime of low Mach number and large Reynolds number in the case of well-prepared initial data. To the best of the authors' knowledge, this is the first work to bridge the link between the compressible PE with incompressible inviscid PE.
The millimeter sized monolayer and bilayer 2H-MoTe2 single crystal samples are prepared by a new mechanical exfoliation method. Based on such high-quality samples, we report the first direct electronic structure study on them, using standard high resolution angle-resolved photoemission spectroscopy (ARPES). A direct band gap of 0.924eV is found at K in the rubidium-doped monolayer MoTe2. Similar valence band alignment is also observed in bilayer MoTe2,supporting an assumption of a analogous direct gap semiconductor on it. Our measurements indicate a rather large band splitting of 212meV at the valence band maximum (VBM) in monolayer MoTe2, and the splitting is systematically enlarged with layer stacking, from monolayer to bilayer and to bulk. Meanwhile, our PBE band calculation on these materials show excellent agreement with ARPES results. Some fundamental electronic parameters are derived from the experimental and calculated electronic structures. Our findings lay a foundation for further application-related study on monolayer and bilayer MoTe2.