课程文献中心 更多>>

关键词： Matrix equation   Mixed-integer programming   Extremal graph theory   Optimal tree problem   The Wiener index  

摘要： It is known from algebraic graph theory that if L is the Laplacian matrix of some tree G with a vertex degree sequence d = (delta(1),..., delta(n)). and D is its distance matrix, then LD + 2I = (2 center dot 1 - d)1(inverted perpendicular), where 1 is an all-ones column vector. We prove the converse proposition: if this identity holds for the Laplacian matrix of some graph G with a degree sequence d and for some matrix D, then G is essentially a tree, and D is its distance matrix. This result immediately generalizes to weighted graphs. Therefore, the above bilinear matrix equation in L, D, and d characterizes trees in terms of their Laplacian and distance matrices, so it can be used as a constraint in mixed-integer formulations of distance-related tree topology design problems (e.g., optimum communication spanning tree or hop-constrained minimum spanning tree problems). If the matrix D is symmetric, the lower triangular part of this matrix identity is redundant and can be omitted, which halves the number of constraints in an optimization problem. Applications to the extremal graph theory (especially, to topological index optimization and to optimal tree problems) and to road topology design are discussed. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Geometric & topological phases   Open quantum systems & decoherence   Quantum simulation   Quantum walks   Topological phases of matter  

摘要： Non-Bloch topological invariants preserve the bulk-boundary correspondence in non-Hermitian topological systems, and are a key concept in the contemporary study of non-Hermitian topology. Here we report the dynamic detection of non-Bloch topological invariants in single-photon quantum walks, revealed through the biorthogonal chiral displacement, and crosschecked with the dynamic spin textures in the generalized quasimomentum-time domain following a quantum quench. Both detection schemes are robust against symmetry-preserving disorders, and yield consistent results with theoretical predictions. Our experiments are performed far away from any boundaries, and therefore underline non-Bloch topological invariants as intrinsic properties of the system that persist in the thermodynamic limit. Our work sheds new light on the experimental investigation of non-Hermitian topology.

关键词： Laplacian regularization   Rotation invariance property of e(2,1)norm   Noise and outliers   Robust clustering   Alternating direction method of multipliers (ADMM)  

摘要： Clustering has been applied in machine learning, data mining and so on, and has received extensive attention. However, since some data has noise or outliers, these noise or outliers easily bring about the objective function with large errors. In this paper, a robust clustering model with e(2,1), e(1) norm and Laplacian regularization (RCLR) is proposed, on which, sparse error matrix is introduced to express sparse noise, and e(1) norm is introduced to alleviate the sparse noise. In addition, the e(2,1) norm is also introduced to achieves space robust by virtue of its nice rotation invariance property. Therefore, our RCLR is insensitive to data noise and outliers. More importantly, the Laplacian regularization is introduced into the RCLR to improve the clustering accuracy. In order to solve the optimization objective of clustering problem, we propose an iterative updating algorithm, named alternating direction method of multipliers (ADMM), to update each optimization variable alternatively, and the convergence of the proposed algorithm is also proved in theory. Finally, experimental results on a total of eleven datasets of three types of datasets, elaborate the superiority of this method over six existing classical clustering methods. Three types of datasets include face images dataset, handwritten recognition dataset, and UCI dataset. In particular, our RCLR clustering approach has the best effect on face image dataset.

关键词： Indium phosphide  

摘要： We have used time-correlated single photon counting to elucidate the radiative dynamics of InP/ZnSe/ZnS core/shell/shell quantum dots (QDs) that differ in the amount and distribution of excess indium. Stoichiometric QDs having an In:P atom ratio very near unity exhibit simple luminescence kinetics. The photoluminescence (PL) rises with the 40 ps instrument response function and exhibits a decay that is close to a single exponential with a time constant that decreases from 32 to 28 ns with increasing shell thickness. QDs having excess indium (In:P ratio of 1.15-1.63) show a significant component of a slower rise time assigned to transient population of indium-based hole traps in the ZnSe shell. They also have a slower PL decay, attributed to an equilibrium between these traps, which are optically dark, and the emissive valence-band state. This results in a radiative lifetime that increases from 32 to 48 ns with increasing shell thickness. Different treatments of the InP cores prior to shell deposition result in different core/shell interfaces as indicated by resonance Raman spectroscopy, as well as differences in the amplitude and timescale of the slow PL rise and the PL decay time. These are interpreted in terms of different radial distributions of the indium-based hole traps, which can be related to differences in the interfacial lattice strain.

摘要： Complex environments, such as molecular matrices and biological material, play a fundamental role in many important dynamic processes in condensed phases. Because it is extremely difficult to conduct full quantum dynamics simulations on such environments due to their many degrees of freedom, here, we treat in detail the environment only around the main system of interest (the subenvironment), while the other degrees of freedom needed to maintain the equilibrium temperature are described by a simple harmonic bath, which we call a quantum thermostat. The noise generated by the subenvironment is spatially non-local and non-Gaussian and cannot be characterized by the fluctuation-dissipation theorem. We describe this model by simulating the dynamics of a two-level system (TLS) that interacts with a subenvironment consisting of a one-dimensional XXZ spin chain. The hierarchical Schrodinger equations of motion are employed to describe the quantum thermostat, allowing for time-irreversible simulations of the dynamics at arbitrary temperature. To see the effects of a quantum phase transition of the subenvironment, we investigate the decoherence and relaxation processes of the TLS at zero and finite temperatures for various values of the spin anisotropy. We observed the decoherence of the TLS at finite temperature even when the anisotropy of the XXZ model is enormous. We also found that the population-relaxation dynamics of the TLS changed in a complex manner with the change in the anisotropy and the ferromagnetic or antiferromagnetic orders of spins.

关键词： Dynamics  

摘要： The modular path integral methodology is used to extend the well-known spin-boson dynamics to finite-length quantum Ising chains, where each spin is coupled to a dissipative harmonic bath. The chain is initially prepared in the ferromagnetic phase where all spins are aligned, and the magnetization is calculated with spin-spin coupling parameters corresponding to the paramagnetic phase, mimicking a quantum quench experiment. The observed dynamics is found to depend significantly on the location of the tagged spin. In the absence of a dissipative bath, the time evolution displays irregular patterns that arise from multiple frequencies associated with the eigenvalues of the chain Hamiltonian. Coupling of each spin to a harmonic bath leads to smoother dynamics, with damping effects that are stronger compared to those observed in the spin-boson model and more prominent in interior spins, a consequence of additional damping from the spin environment. Interior spins exhibit a transition from underdamped oscillatory to overdamped monotonic dynamics as the temperature, spin-bath, or spin-spin coupling is increased. In addition to these behaviors, a new dynamical pattern emerges in the evolution of edge spins with strong spin-spin coupling at low and intermediate temperatures, where the magnetization oscillates either above or below the equilibrium value.

关键词： GaSb   carrier dynamics   nanostructures   photoluminescence  

摘要： Self-assembled GaSb/GaAs quantum-ring-with-dot structures (QRDSs) are the nanostructures exhibiting type-II band alignment. Each QRDS consists of both quantum ring (QR) and quantum dot (QD) parts which have their own energy levels. In this work, the carrier dynamics in the GaSb/GaAs QRDSs are explored and quantitatively described by a rate equation model which is developed from experimental photoluminescence (PL) spectra in literature. The model is comprised of the carrier transition rates and activation energies involved the transfer processes of thermal-excited carriers. The difference between the QR and QD PL intensities is also taken into account in the model. Electronic structures of a single QRDS are calculated in order to determine the overlap between electron and hole wave functions that can be used for estimating the radiative transition rates. Numerical values of the radiative and non-radiative transition rates, carrier capture and escape rates, and activation energies are presented. The PL spectra obtained from the model are consistent with the reported experimental data.