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Jianjun Zhang

Publications and source records attributed to Jianjun Zhang.

At least 55 records · Page 3Linked to original sources
arXiv2023

Semiclassical states for coupled nonlinear Schrödinger equations with a critical frequency

In this paper, we are concerned with the coupled nonlinear Schrödinger system \begin{align*} \begin{cases} -\varepsilon^{2}Δu+a(x)u=μ_{1}u^{3}+βv^{2}u \ \ \ \ \mbox{in}\ \mathbb{R}^{N},\\ -\varepsilon^{2}Δv+b(x)v=μ_{2}v^{3}+βu^{2}v \ \ \ \ \ \mbox{in}\ \mathbb{R}^{N}, \end{cases} \end{align*} where $1\leq N\leq3$, $μ_{1},μ_{2},β>0$, $a(x)$ and $b(x)$ are nonnegative continuous potentials, and $\varepsilon>0$ is a small parameter. We show the existence of positive ground state solutions for the system above and also establish the concentration behaviour as $\varepsilon\rightarrow0$, when $a(x)$ and $b(x)$ achieve 0 with a homogeneous behaviour or vanish in some nonempty open set with smooth boundary.

math.AP↗
arXiv2023

Ultrafast and Electrically Tunable Rabi Frequency in a Germanium Hut Wire Hole Spin Qubit

Hole spin qubits based on germanium (Ge) have strong tunable spin orbit interaction (SOI) and ultrafast qubit operation speed. Here we report that the Rabi frequency (f_Rabi) of a hole spin qubit in a Ge hut wire (HW) double quantum dot (DQD) is electrically tuned through the detuning energy and middle gate voltage (V_M). f_Rabi gradually decreases with increasing detuning energy; on the contrary, f_Rabi is positively correlated with V_M. We attribute our results to the change of electric field on SOI and the contribution of the excited state in quantum dots to f_Rabi. We further demonstrate an ultrafast f_Rabi exceeding 1.2 GHz, which evidences the strong SOI in our device. The discovery of an ultrafast and electrically tunable f_Rabi in a hole spin qubit has potential applications in semiconductor quantum computing.

cond-mat.mes-hall↗
arXiv2022

Multi-peak solutions for singularly perturbed nonlinear Dirichlet problems involving critical growth

We consider the following singularly perturbed elliptic problem \[ - {\varepsilon ^2}Δu + u = f(u){\text{ in }}Ω,{\text{ }}u > 0{\text{ in }}Ω,{\text{ }}u = 0{\text{ on }}\partial Ω, \] where $Ω$ is a domain in ${\mathbb{R}^N}(N \ge 3)$, not necessarily bounded, with boundary $\partial Ω\in {C^2}$ and the nonlinearity $f$ is of critical growth. In this paper, we construct a family of multi-peak solutions to the equation given above which concentrate around any prescribed finite sets of local maxima of the distance function from the boundary $\partial Ω$.

math.AP↗
arXiv2022

Gate-Tunable Spin-Orbit Coupling in a Germanium Hole Double Quantum Dot

Hole spins confined in semiconductor quantum dot systems have gained considerable interest for their strong spin-orbit interactions (SOIs) and relatively weak hyperfine interactions. Here we experimentally demonstrate a tunable SOI in a double quantum dot in a Germanium (Ge) hut wire (HW), which could help enable fast all-electric spin manipulations while suppressing unwanted decoherence. Specifically, we measure the transport spectra in the Pauli spin blockade regime in the double quantum dot device.By adjusting the interdot tunnel coupling, we obtain an electric field tuned spin-orbit length lso = 2.0 - 48.9 nm. This tunability of the SOI could pave the way toward the realization of high-fidelity qubits in Ge HW systems.

cond-mat.mes-hall↗
arXiv2022

Localized semiclassical states for Hamiltonian elliptic systems in dimension two

In this paper, we consider the Hamiltonian elliptic system in dimension two\begin{equation}\label{1.5}\aligned \left\{ \begin{array}{lll} -ε^2Δu+V(x)u=g(v)\ & \text{in}\quad \mathbb{R}^2,\\ -ε^2Δv+V(x)v=f(u)\ & \text{in}\quad \mathbb{R}^2, \end{array}\right.\endaligned \end{equation} where $V\in C(\mathbb{R}^2)$ has local minimum points, and $f,g\in C^1(\mathbb{R})$ are assumed to be either superlinear or asymptotically linear at infinity and of subcritical exponential growth in the sense of Trudinger-Moser inequality. Under only a local condition on $V$, we obtain a family of semiclassical states concentrating around local minimum points of $V$. In addition, in the case that $f$ and $g$ are superlinear at infinity, the decay and positivity of semiclassical states are also given. The proof is based on a reduction method, variational methods and penalization techniques.

math.AP↗
arXiv2022

Nodal solutions for quasilinear Schrödinger equations with asymptotically 3-linear nonlinearity

In this paper, we are concerned with the quasilinear Schrödinger equation \begin{equation*} -Δu+V(x)u-uΔ(u^2)=g(u),\ \ x\in \mathbb{R}^{N}, \end{equation*} where $N\geq3$, $V$ is radially symmetric and nonnegative, and $g$ is asymptotically 3-linear at infinity. In the case of $\inf_{\mathbb{R}^N}V>0$, we show the existence of a least energy sign-changing solution with exactly one node, and for any integer $k>0$, there are a pair of sign-changing solutions with $k$ nodes. Moreover, in the case of $\inf_{\mathbb{R}^N}V=0$, the problem above admits a least energy sign-changing solution with exactly one node. The proof is based on variational methods. In particular, some new tricks and the method of sign-changing Nehari manifold depending on a suitable restricted set are introduced to overcome the difficulty resulting from the appearance of asymptotically 3-linear nonlinearities.

math.AP↗
arXiv2022

Hybrid integration of deterministic quantum dots-based single-photon sources with CMOS-compatible silicon carbide photonics

Thin film 4H-silicon carbide (4H-SiC) is emerging as a contender for realizing large-scale optical quantum circuits due to its high CMOS technology compatibility and large optical nonlinearities. Though, challenges remain in producing wafer-scale 4H-SiC thin film on insulator (4H-SiCOI) for dense integration of photonic circuits, and in efficient coupling of deterministic quantum emitters that are essential for scalable quantum photonics. Here we demonstrate hybrid integration of self-assembled InGaAs quantum dots (QDs) based single-photon sources (SPSs) with wafer-scale 4H-SiC photonic chips prepared by ion slicing technique. By designing a bilayer vertical coupler, we realize generation and highly efficient routing of single-photon emission in the hybrid quantum photonic chip. Furthermore, we realize a chip-integrated beamsplitter operation for triggered single photons through fabricating a 1x2 multi-mode interferometer (MMI) with a symmetric power splitting ratio of 50:50. The successful demonstration of heterogeneously integrating QDs-based SPSs on 4H-SiC photonic chip prepared by ion slicing technique constitutes an important step toward CMOS-compatible, fast reconfigurable quantum photonic circuits with deterministic SPSs.

physics.optics↗
arXiv2021

Advancing COVID-19 Diagnosis with Privacy-Preserving Collaboration in Artificial Intelligence

Artificial intelligence (AI) provides a promising substitution for streamlining COVID-19 diagnoses. However, concerns surrounding security and trustworthiness impede the collection of large-scale representative medical data, posing a considerable challenge for training a well-generalised model in clinical practices. To address this, we launch the Unified CT-COVID AI Diagnostic Initiative (UCADI), where the AI model can be distributedly trained and independently executed at each host institution under a federated learning framework (FL) without data sharing. Here we show that our FL model outperformed all the local models by a large yield (test sensitivity /specificity in China: 0.973/0.951, in the UK: 0.730/0.942), achieving comparable performance with a panel of professional radiologists. We further evaluated the model on the hold-out (collected from another two hospitals leaving out the FL) and heterogeneous (acquired with contrast materials) data, provided visual explanations for decisions made by the model, and analysed the trade-offs between the model performance and the communication costs in the federated training process. Our study is based on 9,573 chest computed tomography scans (CTs) from 3,336 patients collected from 23 hospitals located in China and the UK. Collectively, our work advanced the prospects of utilising federated learning for privacy-preserving AI in digital health.

cs.AI↗
arXiv2021

Existence and multiplicity of sign-changing solutions for quasilinear Schrödinger equations with sub-cubic nonlinearity

In this paper, we consider the quasilinear Schrödinger equation \begin{equation*} -Δu+V(x)u-uΔ(u^2)=g(u),\ \ x\in \mathbb{R}^{3}, \end{equation*} where $V$ and $g$ are continuous functions. Without the coercive condition on $V$ or the monotonicity condition on $g$, we show that the problem above has a least energy sign-changing solution and infinitely many sign-changing solutions. Our results especially solve the problem above in the case where $g(u)=|u|^{p-2}u$ ($2<p<4$) and complete some recent related works on sign-changing solutions, in the sense that, in the literature only the case $g(u)=|u|^{p-2}u$ ($p\geq4$) was considered. The main results in the present paper are obtained by a new perturbation approach and the method of invariant sets of descending flow. In addition, in some cases where the functional merely satisfies the Cerami condition, a deformation lemma under the Cerami condition is developed.

math.AP↗
arXiv2021

Chiral photonic circuits for deterministic spin transfer

Chiral quantum optics has attracted considerable interest in the field of quantum information science. Exploiting the spin-polarization properties of quantum emitters and engineering rational photonic nanostructures has made it possible to transform information from spin to path encoding. Here, compact chiral photonic circuits with deterministic circularly polarized chiral routing and beamsplitting are demonstrated using two laterally adjacent waveguides coupled with quantum dots. Chiral routing arises from the electromagnetic field chirality in waveguide, and beamsplitting is obtained via the evanescent field coupling. The spin- and position-dependent directional spontaneous emission are achieved by spatially selective micro-photoluminescence measurements, with a chiral contrast of up to 0.84 in the chiral photonic circuits. This makes a significant advancement for broadening the application scenarios of chiral quantum optics and developing scalable quantum photonic networks.

physics.optics↗
arXiv2021

Position-dependent chiral coupling between single quantum dots and cross waveguides

Chiral light-matter interaction between photonic nanostructures with quantum emitters shows great potential to implement spin-photon interfaces for quantum information processing. Position-dependent spin momentum locking of the quantum emitter is important for these chiral coupled nanostructures. Here, we report the position-dependent chiral coupling between quantum dots (QDs) and cross waveguides both numerically and experimentally. Four quantum dots distributed at different positions in the cross section are selected to characterize the chiral properties of the device. Directional emission is achieved in a single waveguide as well as in both two waveguides simultaneously. In addition, the QD position can be determined with the chiral contrasts from four outputs. Therefore, the cross waveguide can function as a one-way unidirectional waveguide and a circularly polarized beam splitter by placing the QD in a rational position, which has potential applications in spin-to-path encoding for complex quantum optical networks at the single-photon level.

cond-mat.mes-hall↗
arXiv2021

Existence and multiplicity of bound state solutions to a Kirchhoff type equation with a general nonlinearity

In this paper, we consider the following Kirchhoff type equation $$ -\left(a+ b\int_{\R^3}|\nabla u|^2\right)\triangle {u}+V(x)u=f(u),\,\,x\in\R^3, $$ where $a,b>0$ and $f\in C(\R,\R)$, and the potential $V\in C^1(\R^3,\R)$ is positive, bounded and satisfies suitable decay assumptions. By using a new perturbation approach together with a new version of global compactness lemma of Kirchhoff type, we prove the existence and multiplicity of bound state solutions for the above problem with a general nonlinearity. We especially point out that neither the corresponding Ambrosetti-Rabinowitz condition nor any monotonicity assumption is required for $f$. Moreover, the potential $V$ may not be radially symmetry or coercive. As a prototype, the nonlinear term involves the power-type nonlinearity $f(u) = |u|^{p-2}u$ for $p\in (2, 6)$. In particular, our results generalize and improve the results by Li and Ye (J.Differential Equations, 257(2014): 566-600), in the sense that the case $p\in(2,3]$ is left open there.

math.AP↗
arXiv2019

A perturbation approach to studying sign-changing solutions of Kirchhoff equations with a general nonlinearity

By employing a novel perturbation approach and the method of invariant sets of descending flow, this manuscript investigates the existence and multiplicity of sign-changing solutions to a class of semilinear Kirchhoff equations in the following form $$ -\left(a+ b\int_{\R^3}|\nabla u|^2\right)\triangle {u}+V(x)u=f(u),\,\,x\in\R^3, $$ where $a,b>0$ are constants, $V\in C(\R^3,\R)$, $f\in C(\R,\R)$. The methodology proposed in the current paper is robust, in the sense that, the monotonicity condition for the nonlinearity $f$ and the coercivity condition of $V$ are not required. Our result improves the study made by Y. Deng, S. Peng and W. Shuai ({\it J. Functional Analysis}, 3500-3527(2015)), in the sense that, in the present paper, the nonlinearities include the power-type case $f(u)=|u|^{p-2}u$ for $p\in(2,4)$, in which case, it remains open in the existing literature that whether there exist infinitely many sign-changing solutions to the problem above without the coercivity condition of $V$. Moreover, {\it energy doubling} is established, i.e., the energy of sign-changing solutions is strictly large than two times that of the ground state solutions for small $b>0$.

math.AP↗
arXiv2019

Harvesting Visual Objects from Internet Images via Deep Learning Based Objectness Assessment

The collection of internet images has been growing in an astonishing speed. It is undoubted that these images contain rich visual information that can be useful in many applications, such as visual media creation and data-driven image synthesis. In this paper, we focus on the methodologies for building a visual object database from a collection of internet images. Such database is built to contain a large number of high-quality visual objects that can help with various data-driven image applications. Our method is based on dense proposal generation and objectness-based re-ranking. A novel deep convolutional neural network is designed for the inference of proposal objectness, the probability of a proposal containing optimally-located foreground object. In our work, the objectness is quantitatively measured in regard of completeness and fullness, reflecting two complementary features of an optimal proposal: a complete foreground and relatively small background. Our experiments indicate that object proposals re-ranked according to the output of our network generally achieve higher performance than those produced by other state-of-the-art methods. As a concrete example, a database of over 1.2 million visual objects has been built using the proposed method, and has been successfully used in various data-driven image applications.

cs.CV↗