Quantum search of many vertices on the joined complete graph

The quantum search on the graph is a very important topic. In this work, we develop a theoretic method on searching of single vertex on the graph [$Phys. Rev. Lett$. 114 110503 (2015)], and systematically study the search of many vertices on one low-connectivity graph, the joined complete graph. Our results reveal that, with the optimal jumping rate obtained from the theoretical method, we can find such target vertices at the time $Oleft({sqrt N } right)$, where $N$ is the number of total vertices. Therefore, the search of many vertices on the joined complete graph possessing quantum advantage has been achieved.     

Infinitely many solutions for a nonlocal problem

Consider a class of nonlocal problems $$ \left \{\begin{array}{ll} -(a-b\int_{\Omega}|\nabla u|^2dx)\Delta u= f(x,u),& \textrm{$x \in\Omega$},\u=0, & \textrm{$x \in\partial\Omega$}, \end{array} \right. $$ where $a>0, b>0$,~$\Omega\subset \mathbb{R}^N$ is a bounded open domain, $f:\overline{\Omega} \times \mathbb R \longrightarrow \mathbb R $ is a Carath$\acute{\mbox{e}}$odory function. Under suitable conditions, the equivariant link theorem without the $(P.S.)$ condition due to Willem is applied to prove that the above problem has infinitely many solutions, whose energy increasingly tends to $a^2/(4b)$, and they are neither large nor small.     

AuCu3熔体快速冷却过程中的键对与多面体

Based on the FS(Finnis-Sinclair) many-body potential model, the rapid cooling process of a system, which consists of 375 Cu atoms and 125 Au atoms, controlled by period boundary condition was simulated. The dependence of pair distribution function of melten compound AuCu3 on the temperature under these conditions was researched. It can be concluded that the noncrystal exists under 700 K, and the liquid-glass transition temperature is approximately 680 K according to the Abraham′s method. Furthermore, the feature of version of cluster in melten AuCu3 was investigated by Honeycutt pair analysis technique. It is demonstrated that the structural configuration in melten AuCu3 has remarkable variation during the formation of noncrystal according to the relationship between the bonded pairs and polyhedron and temperatures. The defective polyhedra in liquid AuCu3 have greatest changes accompanying the changing temperatures.     

Time evolution of infinitely many particles: An existence theorem

In this paper we deal with systems of infinitely many particles in ³, given by a two-body, short-range potential and an external potential, depending on the position of the particles. We show the existence of dynamics for a set of initial configurations, which has measure one with respect to the Gibbs measure induced by a suitable family of Hamiltonians.     

Lie Symmetries for Hamiltonian Systems Methodological Approach

This paper proposes an algorithm for the Lie symmetries investigation in the case of a 2D Hamiltonian system. General Lie operators are deduced firstly and, in the the next step, the associated Lie invariants are derived. The 2D Yang-Mills mechanical model is chosen as a test model for this method. PACS: 05.45.-a; 02.30.Ik     

Existence and Mann iterative approximations of nonoscillatory solutions of nth-order neutral delay differential equations

In this paper we consider the following nth-order neutral delay differential equation:

     

Note on finite temperature sum rules for vector and axial-vector spectral functions

An updated analysis of vector and axial-vector spectral functions is presented. The resonant contributions to the spectral integrals are shown to be expressible as multiples of 4π²f_π², encoding the scale of spontaneous chiral symmetry breaking in QCD. Up to order T² this behavior carries over to the case of finite temperature.     

Spin and pseudospin symmetries of the Dirac equation with shifted Hulthén potential using supersymmetric quantum mechanics

In this paper, we obtain approximate analytical solutions of the Dirac equation for the shifted Hulthén potential within the framework of spin and pseudospin symmetry limits for arbitrary spin–orbit quantum number κ using the supersymmetry quantum mechanics. The energy eigenvalues and the corresponding Dirac wave functions are obtained in closed forms.     

New potential symmetries for some evolution equations

In this paper we derive new potential symmetries that seem not to be recorded in the literature. These potential symmetries are determined by considering a generalized potential system, rather than the natural potential system or a general integral variable. An inhomogeneous diffusion equation, a porous medium equation and the Fokker-Planck equation have been considered as application of this procedure.