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Kexue Li

Publications and source records attributed to Kexue Li.

At least 19 recordsLinked to original sources
arXiv2026

Strong and Weak-Type Dispersive Estimates for the Energy-Critical Nonlinear Schr\"odinger Equation with an Inverse-Square Potential

We prove dispersive estimates for the three-dimensional defocusing energy-critical nonlinear Schr\"odinger equation associated with $\mathcal L_a=-\Delta+a|x|^{-2}$. For nonnegative potentials, we extend the known finite-$p$ theory to the endpoint $L^1\to L^\infty$. For negative potentials in the global well-posedness range, set $\sigma=\frac12-\sqrt{\frac14+a}$. We obtain the free strong decay rate for $2<p<3/\sigma$ and the limiting Lorentz estimate from $L^{(3/\sigma)',1}$ to $L^{3/\sigma,\infty}$. The restriction $p<3/\sigma$ is sharp for strong Lebesgue decay. The proof combines a finite-interval bootstrap, nonlinear real interpolation on bounded energy sets, and endpoint Sobolev--Lorentz estimates adapted to $\mathcal L_a$.

math.AP↗
arXiv2026

Rapid Atmospheric Vapor Deposition of H:In2O3 Transparent Conducting Oxide Thin Films

Transparent conducting oxides (TCOs) are essential for the optoelectronics industry, but there is a critical gap in cost-effective methods to rapidly deposit low sheet resistance, high transmittance films without damaging delicate materials, including emerging soft semiconductors like metal-halide perovskites. In this work, atmospheric pressure chemical vapor deposition (AP-CVD) is used to synthesise H:In2O3 films with 7.20+/-0.01 Ohm/sq sheet resistance (0.50+/-0.06 mOhm.cm resistivity) and transmittance up to 89% in the near-infrared (NIR), surpassing commercial sputter-deposited indium tin oxide. The growth rate is 40x higher than atomic layer deposition (ALD), and the AP-CVD films are fully processed under atmospheric conditions at only 140 C. Comparison of secondary ion mass spectrometry and time-of-flight elastic recoil detection analysis with changes in carrier concentration indicate that H dopants are introduced from the water oxidant. There is an increase in mobility form 40+/-10 cm2/Vs to 160+/-30 cm2/Vs when changing from O2 to H2O as the oxidant, which is attributed to H dopants passivating oxygen vacancies that act as carrier scattering centers. This work establishes AP-CVD as a promising method for manufacturing high figure-of-merit TCOs in a rapid, scalable and cost-effective manner, using mild growth conditions compatible with thermally-sensitive materials.

cond-mat.mtrl-sci↗
arXiv2025

Dispersive decay for the Inter-critical nonlinear Schr\"{o}dinger equation in $\mathbb{R}^3$

This paper investigates the Cauchy problem for the nonlinear Schr\"odinger equation (NLS) in the mass-supercritical and energy-subcritical regime within three spatial dimensions. For initial data in the critical homogeneous Sobolev space $\dot{H}^{s_c}(\mathbb{R}^3)$ (where $s_c = \frac{5}{6}$), we get a uniform decay estimate for the long-time dynamics of solutions, which extends the previous results.

math.AP↗
arXiv2025

Isotopically Selected Single Antimony Molecule Doping

A reliable route to the deterministic fabrication of impurity ion donors in silicon is required to advance quantum computing architectures based upon such systems. This paper reports the ability to dope isotopically-defined unique (${}^{121}\mathrm{Sb}{}^{123}\mathrm{Sb}$) clusters into silicon with measured detection efficiencies of 94% being obtained. Atomically resolved imaging of the doped clusters reveals a Sb-to-Sb separation of ~2 nm post-implantation, thus indicating suitability to form coupled qudit systems. The method used is fully compatible with integration into processing that includes pre-enrichment of the silicon host to < 3ppm ${}^{29}\mathrm{Si}$ levels. As such, we present a potential pathway to the creation of scaled qudit arrays within silicon platforms for quantum computing.

cond-mat.mtrl-sci↗
arXiv2023

Highly ${ }^{28} \mathrm{Si}$ Enriched Silicon by Localised Focused Ion Beam Implantation

Solid-state spin qubits within silicon crystals at mK temperatures show great promise in the realisation of a fully scalable quantum computation platform. Qubit coherence times are limited in natural silicon owing to coupling to the isotope ${ }^{29} \mathrm{Si}$ which has a non-zero nuclear spin. This work presents a method for the depletion of ${ }^{29} \mathrm{Si}$ in localised volumes of natural silicon wafers by irradiation using a 45 keV ${ }^{28} \mathrm{Si}$ focused ion beam with fluences above $1 \times 10^{19} \, \mathrm{ions} \, \mathrm{cm}^{-2}$. Nanoscale secondary ion mass spectrometry analysis of the irradiated volumes shows unprecedented quality enriched silicon that reaches a minimal residual ${ }^{29} \mathrm{Si}$ value of 2.3 $\pm$ 0.7 ppm and with residual C and O comparable to the background concentration in the unimplanted wafer. Transmission electron microscopy lattice images confirm the solid phase epitaxial re-crystallization of the as-implanted amorphous enriched volume extending over 200 nm in depth upon annealing. The ease of fabrication, requiring only commercially available natural silicon wafers and ion sources, opens the possibility for co-integration of qubits in localised highly enriched volumes with control circuitry in the surrounding natural silicon for large-scale devices.

cond-mat.mtrl-sci↗
arXiv2021

Application of high-spatial-resolution secondary ion mass spectrometry for nanoscale chemical mapping of lithium in an Al-Li alloy

High-spatial-resolution secondary ion mass spectrometry offers a method for mapping lithium at nanoscale lateral resolution. Practical implementation of this technique offers significant potential for revealing the distribution of Li in many materials with exceptional lateral resolution and elemental sensitivity. Here, two state-of-the-art methods are demonstrated on an aluminium-lithium alloy to visualise nanoscale Li-rich phases by mapping the 7Li+ secondary ion. NanoSIMS 50L analysis with a radio frequency O- plasma ion source enabled visualisation of needle-shaped T1 (Al2CuLi) phases as small as 75 nm in width. A compact time-of-flight secondary ion mass spectrometry detector added to a focused ion beam scanning electron microscope facilitated mapping of the T1 phases down to 45 nm in width using a Ga+ ion beam. Correlation with high resolution electron microscopy confirms the identification of T1 precipitates, their sizes and distribution observed during SIMS mapping.

cond-mat.mtrl-sci↗
arXiv2019

Bound state solutions for non-autonomous fractional Schrödinger-Poisson equations with critical exponent

In this paper, we study the fractional Schrödinger-Poisson equation \begin{equation*} \ \left\{\begin{aligned} &(-Δ)^{s}u+V(x)u+K(x)ϕu=|u|^{2^{\ast}_{s}-2}u, &\mbox{in} \ \mathbb{R}^{3},\\ &(-Δ)^{s}ϕ=K(x)u^{2},&\mbox{in} \ \mathbb{R}^{3}, \end{aligned}\right. \end{equation*} where $s\in (\frac{3}{4},1]$, $2^{\ast}_{s}=\frac{6}{3-2s}$ is the fractional critical exponent, $K\in L^{\frac{6}{6s-3}}(\mathbb{R}^{3})$ and $V\in L^{\frac{3}{2s}}(\mathbb{R}^{3})$ are nonnegative functions. If $\|V\|_{\frac{3}{2s}}+\|K\|_{\frac{6}{6s-3}}$ is sufficiently small, we prove that the equation has at least one bound state solution.

math.AP↗
arXiv2019

Fractional elliptic equations with Hardy potential and critical nonlinearities

In this paper, we consider the fractional elliptic equation \begin{align*} \left\{\begin{aligned} &(-Δ)^s u-μ\frac{u}{|x|^{2s}} = \frac{|u|^{2_s^\ast (α)-2}u}{|x|^α} + f(x,u), && \mbox{in} \ Ω,\\ &u=0, && \mbox{in} \ \mathbb{R}^{n}\backslash \ Ω, \end{aligned}\right. \end{align*} where $Ω\subset R^n$ is a smooth bounded domain, $0\inΩ$, $0<s<1$, $0<α<2s<n$, $2_{s}^{\ast}(α)=\frac{2(n-α)}{n-2s}$. Under some assumptions on $μ$ and $f$, we obtain the existence of nonnegative solutions.

math.AP↗
arXiv2017

Effects of the noise level on stochastic fractional heat equations

We consider the stochastic fractional heat equation $\partial_{t}u=\triangle^{α/2}u+λσ(u)\dot{w}$ on $[0,L]$ with Dirichlet boundary conditions, where $\dot{w}$ denotes the space-time white noise. For any $λ>0$, we prove that the $p$th moment of $\sup_{x\in [0,L]}|u(t,x)|$ grows at most exponentially. Moreover, we prove that the $p$th moment of $\sup_{x\in [0,L]}|u(t,x)|$ is exponentially stable if $λ$ is small. At last, We obtain the noise excitation index of $p$th energy of $u(t,x)$ as $λ\rightarrow \infty$.

math.PR↗
arXiv2016

H$\ddot{o}$lder continuity for stochastic fractional heat equation with colored noise

In this paper, we consider semilinear stochastic fractional heat equation $\frac{\partial}{\partial t}u_{β,t}(x)=\triangle^{α/2}u_{β,t}(x)+σ(u_{β,t}(x))η_β$. The Gaussian noise $η_β$ is assumed to be colored in space with covariance of the form $E(η_β(t,x)η_β(s,y))=δ(t-s)f_β(x-y)$, where $f_β$ is the Riesz kernel $f_β(x)\propto |x|^{-β}$. We obtain the spatial and temporal H$\ddot{\mbox{o}}$lder continuity of the mild solution.

math.PR↗
arXiv2016

No local $L^{1}$ solutions for semilinear fractional heat equations

We study the Cauchy problem for the semilinear fractional heat equation $u_{t}=\triangle^{α/2}u+f(u)$ with non-negative initial value $u_{0}\in L^{q}(\mathbb{R}^{n})$ and locally Lipschitz, non-negative source term $f$. For $f$ satisfying the Osgood-type condition $\int_{1}^{\infty}\frac{ds}{f(s)}=\infty$, we show that there exist initial conditions such that the equation has no local solution in $L^{1}_{loc}(\mathbb{R}^{n})$.

math.AP↗
arXiv2016

A characteristic of local existence for fractional heat equations in Lebesgue spaces

In this paper, we consider the fractional heat equation $u_{t}=\triangle^{α/2}u+f(u)$ with Dirichlet boundary conditions on the ball $B_{R}\subset \mathbb{R}^{d}$, where $\triangle^{α/2}$ is the fractional Laplacian, $f:[0,\infty)\rightarrow [0,\infty)$ is continuous and non-decreasing. We present the characterisations of $f$ to ensure the equation has a local solution in $L^{q}(B_{R})$ provided that the non-negative initial data $u_{0}\in L^{q}(B_{R})$. For $q>1$ and $1<α\leq 2$, we show that the equation has a local solution in $L^{q}(B_{R})$ if and only if $\lim_{s\rightarrow \infty}\sup s^{-(1+αq/d)}f(s)=\infty$; and for $q=1$ and $1<α\leq 2$ if and only if $\int_{1}^{\infty}s^{-(1+α/d)}F(s)ds<\infty$, where $F(s)=\sup_{1\leq t\leq s}f(t)/t$. When $\lim_{s\rightarrow 0}f(s)/s<\infty$, the same characterisations holds for the fractional heat equation on the whole space $\mathbb{R}^{d}$.

math.AP↗
arXiv2016

Maximum principles for a time-space fractional diffusion equation

In this paper, we focus on maximum principles of a time-space fractional diffusion equation. Maximum principles for classical solution and weak solution are all obtained by using properties of the time fractional derivative operator and the fractional Laplace operator. We deduce maximum principles for a full fractional diffusion equation, other than time-fractional and spatial-integer order diffusion equations.

math.AP↗
arXiv2016

Explosive solutions of parabolic stochastic partial differential equations with L$\acute{e}$vy noise

In this paper, we study the explosive solutions to a class of parbolic stochastic semilinear differential equations driven by a L$\acute{\mbox{e}}$vy type noise. The sufficient conditions are presented to guarantee the existence of a unique positive solution of the stochastic partial differential equation under investigation. Moreover, we show that the positive solutions will blow up in finite time in mean $L^{p}$-norm sense, provided that the initial data, the nonlinear term and the multiplicative noise satisfies some conditions. Several examples are presented to illustrated the theory. Finally, we establish a global existence theorem based on a Lyapunov functional and prove that a stochastic Allen-Cahn equation driven by L$\acute{\mbox{e}}$vy noise has a global solution.

math.PR↗
arXiv2015

Well-Posedness and Optimal Time-Decay for Compressible MHD System in Besov Space

In this paper, firstly, we prove the global well-posedness of three dimensional compressible magnetohydrodynamics equations for some classes of large initial data, which may have large oscillation for the density and large energy for the velocity and magnetic field. Secondly, we prove the optimal time decay for the compressible magnetohydrodynamics equations with low regularity assumptions about the initial data. Especially, we can obtain the optimal $L^{2}$ time decay rate when the initial data small in the critical Besov space (no small condition in space $H^{N/2+1}$). When we calculate the optimal time decay rate, we use differential type energy estimates in homogeneous Besov space, evolution in negative Besov space and the well-posedness results proved in the first part.

math.AP↗
arXiv2014

On the Decay and Stability of Global Solutions to the 3D Inhomogeneous MHD system

In this paper, we investigative the large time decay and stability to any given global smooth solutions of the $3$D incompressible inhomogeneous MHD systems. We proved that given a solution $(a, u, B)$ of (\ref{mhd_a}), the velocity field and magnetic field decay to $0$ with an explicit rate, for $u$ which coincide with incompressible inhomogeneous Navier-Stokes equations \cite{zhangping}. In particular, we give the decay rate of higher order derivatives of $u$ and $B$ which is useful to prove our main stability result. For a large solutions of (\ref{mhd_a}) denoted by $(a, u, B)$, we proved that a small perturbation to the initial data still generates a unique global smooth solution and the smooth solution keeps close to the reference solution $(a, u, B)$. Due to the coupling between $u$ and $B$, we used elliptic estimates to get $\|(u, B)\|_{L^{1}(\mathbb{R}^{+};\dot{B}_{2,1}^{5/2})} < C$, which is different to Navier-Stokes equations.

math.AP↗