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We propose the rotational dynamics of the intralayer and interlayer excitons with their inherent momenta of inertia in the monolayer and bilayer transition metal dichalcogenides, respectively, where the new chirality of exciton is endowed by the rotational angular momentum, namely, the formations of left- and right-handed excitons at the +K and -K valleys, respectively. We find that angular momenta exchange between excitons and its surrounding phononic bath result in the large fluctuation of the effective g-factor and the asymmetry of valley Zeeman splitting observed in most recently experiments, both of which sensitively depend on the magnetic moments provided by the phononic environment. This rotating exciton model not only proposes a new controllable knob in valleytronics, but opens the door to explore the angular momentum exchange of the chiral quasiparticles with the many-body environment., Comment: 8 pages, 3 figures. Welcome your comments

From the mesoscopic point of view, a new concept of soft matching for mass points is proposed. Then a soft Lasso's approach to learn the soft dynamical equation for the physical mechanical relationship is proposed, too. Furthermore, a discrete iterative algorithm combining the Newton-Stokes term and the soft Lasso's term is developed to simulate the motion of a ball falling in non-Newtonian fluids. The theory is validated by numerical examples and shows satisfactory results, which exhibit the chaotic phenomena, sudden accelerations and the continual random oscillations. The pattern of the motion is independent of initial values and is preserved for long time.

The classical theory of attractive central force problem on the standard (flat) Euclidean plane can be generalized to surfaces by reformulating the basic underlying physical principles by means of differential geometry. Attractive central force problems on state manifolds appear quite often and in several different context ranging from nonlinear control theory to mobile robotics, thermodynamics, artificial intelligence, signal transmission and processing and so on. The aim of the present paper is to analyze the variational properties of the circular periodic orbits in the case of attractive power-law potentials of the Riemannian distance on revolution's surfaces. We compute the stability properties and the Morse index by developing a suitable intersection index in the Lagrangian Grassmannian and symplectic context., Comment: 30 pages, 3 figures

The formation of angulon, stemming from the rotor (molecule or impurity) rotating in the quantum many-body field, adds a new member in the quasiparticle's family and has aroused intensively interests in multiple research fields. However, the analysis of the coupling strength between the rotor and its hosting environment remains a challenging task both in theory and experiment. Here, we develop the all-coupling theory of the angulon by introducing an unitary transformation, where the renormalization of the rotational constants for different molecules in the helium nanodroplets are reproduced, getting excellent agreement with the collected experimental data during the past decades. Moreover, the strength of molecule-helium coupling and the effective radius of the solvation shell corotating along with the molecular rotor could be estimated qualitatively. This model not only provides the significant enlightenment for analyzing the rotational spectroscopy of molecules in the phononic environment, but also provides a new method to study the transfer of the phonon angular momentum in angulon frame., Comment: 12 pages,1 figure.Comments and collaborations are welcome

A fully implicit numerical scheme is established for solving the time fractional Swift-Hohenberg (TFSH) equation with a Caputo time derivative of order $\alpha\in(0,1)$. The variable-step L1 formula and the finite difference method are employed for the time and the space discretizations, respectively. The unique solvability of the numerical scheme is proved by the Brouwer fixed-point theorem. With the help of the discrete convolution form of L1 formula, the time-stepping scheme is shown to preserve a discrete energy dissipation law which is asymptotically compatible with the classic energy law as $\alpha\to1^-$. Furthermore, the $L^\infty$ norm boundedness of the discrete solution is obtained. Combining with the global consistency error analysis framework, the $L^2$ norm convergence order is shown rigorously. Several numerical examples are provided to illustrate the accuracy and the energy dissipation law of the proposed method. In particular, the adaptive time-stepping strategy is utilized to capture the multi-scale time behavior of the TFSH model efficiently.

A fully discrete implicit scheme is proposed for the Swift-Hohenberg model, combining the third-order backward differentiation formula (BDF3) for the time discretization and the second-order finite difference scheme for the space discretization. Applying the Brouwer fixed-point theorem and the positive definiteness of the convolution coefficients of BDF3, the presented numerical algorithm is proved to be uniquely solvable and unconditionally energy stable, further, the numerical solution is shown to be bounded in the maximum norm. The proposed scheme is rigorously proved to be convergent in $L^2$ norm by the discrete orthogonal convolution (DOC) kernel, which transfer the four-level-solution form into the three-level-gradient form for the approximation of the temporal derivative. Consequently, the error estimate for the numerical solution is established by utilization of the discrete Gronwall inequality. Numerical examples in 2D and 3D cases are provided to support the theoretical results.

Drone-based quantum link has the potential to realize mobile quantum network, and entanglement distribution has been demonstrated using one and two drones. Here we report the first drone-based quantum key distribution (QKD), with average secure key rate larger than 8 kHz using decoy-state BB84 protocol with polarization coding. Compact acquisition, pointing, and tracking (APT) system and QKD modules are developed and loaded on a home-made octocopter, within takeoff weight of 30 kg. A robust link is established between the flying octocopter and a ground station separated 200 meters away and real-time QKD is performed for 400 seconds. This work shows potential of drone-based quantum communication for the future mobile quantum networks.

Morse index theory provides an elegant and useful tool for describing several aspects of a Lagrangian system in terms of its variational properties. In the classical framework it provides an equality between the spectral properties of a second order selfadjoint differential operator arising by the second variation of the Lagrangian action functional and the oscillation properties of the space of solutions of the associated boundary value problem. These oscillation properties are described by means of the Maslov index, which is a symplectic invariant intimately related to the Hamiltonian nature of the problem. Driven by the desire to get an analogous result in the non-Hamiltonian context for the investigation of the dynamical properties of dissipative systems, in this paper we start to introduce a new topological invariant, the so-called degree-index, defined in terms of the Brouwer degree of a suitable determinant map of a boundary matrix, which provides one possible substitute of the Maslov index in this non-Hamiltonian framework and finally we prove the equality between the Morse index and the degree-index in this non-selfadjoint setting through a new abstract trace formula. In the last part of the paper we apply our theoretical results to some 1D reaction-diffusion systems., Comment: To appear in Journal of Differential Equations

The migration motion of defects in metal halide perovskites quantum dots (MHPQDs) results in charge-carrier trapping become more complicated. We study two-step trapping mediated by mobile defects between the ground state of MHPQDs and a fixed-depth defect using a full-configuration defect method, where all possible trapping processes mediated by these mobile defects could be reproduced and the fastest channels among them are picked out. We find that these two-step trapping processes could keep more one order of magnitude faster than these direct ones as mobile defect with the appropriate localization strength, which implies that these indirect trapping should play the crucial rule to determine the non-radiative recombination losses. These results provide the significant explanation for studying non-radiation processes of carriers in the presence of the migration defects in recent experiments. Moreover, this model will be available to analyze some key performance related defects in electronic devices., Comment: 5 pages, 3 figures

A gap exists in microscopic understanding the dynamic properties of the rotational organic cation (ROC) in the inorganic framework of the metal halide perovskites (MHP) to date. Herein, we develop a microscopic theory of Raman scattering for the ROC in MHP based on the angular momentum of a ROC exchanging with that of the photon and phonon. We systematically present the selection rules for the angular momentum transfer among three lowest rotational levels. We find that the phonon angular momentum that arising from the inorganic framework and its specific values could be directly manifested by Stokes (or anti-Stokes) shift. Moreover, the initial orientation of the ROC and its preferentially rotational directions could be judged in Raman spectra. This study lays the theoretical foundation for the high-precision resolution and manipulation of molecular rotation immersed in many-body environment by Raman technique.

Deep Metric Learning (DML) serves to learn an embedding function to project semantically similar data into nearby embedding space and plays a vital role in many applications, such as image retrieval and face recognition. However, the performance of DML methods often highly depends on sampling methods to choose effective data from the embedding space in the training. In practice, the embeddings in the embedding space are obtained by some deep models, where the embedding space is often with barren area due to the absence of training points, resulting in so called "missing embedding" issue. This issue may impair the sample quality, which leads to degenerated DML performance. In this work, we investigate how to alleviate the "missing embedding" issue to improve the sampling quality and achieve effective DML. To this end, we propose a Densely-Anchored Sampling (DAS) scheme that considers the embedding with corresponding data point as "anchor" and exploits the anchor's nearby embedding space to densely produce embeddings without data points. Specifically, we propose to exploit the embedding space around single anchor with Discriminative Feature Scaling (DFS) and multiple anchors with Memorized Transformation Shifting (MTS). In this way, by combing the embeddings with and without data points, we are able to provide more embeddings to facilitate the sampling process thus boosting the performance of DML. Our method is effortlessly integrated into existing DML frameworks and improves them without bells and whistles. Extensive experiments on three benchmark datasets demonstrate the superiority of our method., Comment: 32 pages. Accepted by ECCV 2022

The coherent superposition of position states in a quantum walk (QW) can be precisely engineered towards the desired distributions to meet the need of quantum information applications. The coherent distribution can make full use of quantum parallel in computation and simulation. Particularly, the uniform superposition provides the robust non-locality, which has wide applications such as the generation of genuine multi-bit random numbers without post-processing. We experimentally demonstrate that the rich dynamics featured with arbitrary coherent distributions can be obtained by introducing different sets of the time- and position-dependent operations. Such a QW is realized by a resource-constant and flexible optical circuit, in which the variable operation is executed based on a Sagnac interferometer in an intrinsically stable and precisely controlled way. Our results contribute to the practical realization of quantum-walk-based quantum computation, quantum simulations and quantum information protocols., Comment: 8 pages, 4 figures, 2 tables

We report the position-inhomogeneous quantum walk (IQW) can be utilized to produce the maximal high dimensional entanglement while maintaining the quadratic speedup spread of the wave-function. Our calculations show that the maximal coin-walker entanglement can be generated in any odd steps or asymptotically in even steps, and the nearly maximal entanglement can be obtained in even steps after $2$. We implement the IQW by a stable resource-saving time-bin optical network, in which a polarization Sagnac loop is employed to realize the precisely tunable phase shift. Our approach opens up an efficient way for high-dimensional entanglement engineering as well as promotes investigations on the role of coin-walker interactions in QW based applications., Comment: 7 pages, 6 figures, 1 table

In this paper we provide a sufficient condition for the linear instability of a periodic orbit for a free period Lagrangian system on a Riemannian manifold. The main result establish a general criterion for the linear instability of a maybe degenerate) periodic orbit admitting a orbit cylinder in terms to the parity of a suitable spectral index encoding the functional and symplectic property of the problem., Comment: 33 pages, no figure. Comments are welcome! arXiv admin note: substantial text overlap with arXiv:1907.05864