相关论文: Two particles on a star graph I
We consider a two particle system on a star graph with delta-function interaction. A complete description of the eigensolutions with real momenta is given; specifically it is shown that all eigensolutions can be written as integrals in the…
We introduce n-particle quantum graphs with singular two-particle interactions in such a way that eigenfunctions can be given in the form of a Bethe ansatz. We show that this leads to a secular equation characterising eigenvalues of the…
We discuss the discrete spectrum of the Hamiltonian describing a two-dimensional quantum particle interacting with an infinite family of point interactions. We suppose that the latter are arranged into a star-shaped graph with N arms and a…
We consider a hamiltonian system on the real line, consisting of real scalar field $\phi(x,t)$ and point particle with trajectory $y(t)$. The dynamics of this system is defined by the system of two equations: wave equation for the field,…
As is well-known, there exists a four parameter family of local interactions in 1D. We interpret these parameters as coupling constants of delta-type interactions which include different kinds of momentum dependent terms, and we determine…
We describe a procedure to solve an up to $2N$ problem where the particles are separated topologically in $N$ groups with at most two particles in each. Arbitrary interactions are allowed between the (two) particles within one group. All…
For any system $\{i\}$ of particles with the trajectories $x_{i}(t)$ in $R^{d}$ on a finite time interval $[0,\tau]$ we define the interaction graph $G$. Vertices of $G$ are the particles, there is an edge between two particles $i,j$ iff…
We solve an one-dimensional stochastic model of interacting particles on a chain. Particles can have branching and coagulation reactions, they can also appear on an empty site and disappear spontaneously. This model which can be viewed as…
In this note, we consider connected graphs with exactly two main eigenvalues. We will give several constructions for them, and as a consequence we show a family of those graphs with an unbounded number of distinct valencies.
The partition of graphs into "nice" subgraphs is a central algorithmic problem with strong ties to matching theory. We study the partitioning of undirected graphs into same-size stars, a problem known to be NP-complete even for the case of…
A {\it star-factor} of a graph $G$ is a spanning subgraph of $G$ such that each of its component is a star. Clearly, every graph without isolated vertices has a star factor. A graph $G$ is called {\it star-uniform} if all star-factors of…
Multiparticle systems on complicated metric graphs might have many applications in physics, biology and social life. But the corresponding science still does not exist. Here we start it with simplest examples where there is quadratic…
We obtain a second order differential equation on moduli space satisfied by certain modular graph functions at genus two, each of which has two links. This eigenvalue equation is obtained by analyzing the variations of these graphs under…
Red and blue particles are placed in equal proportion through-out either the complete or star graph and iteratively sampled to take simple random walk steps. Mutual annihilation occurs when particles with different colors meet. We compare…
The periodic discrete Toda equation defined over finite fields has been studied. We obtained the finite graph structures constructed by the network of states where edges denote possible time evolutions. We simplify the graphs by introducing…
A method of solving Maxwell equations in a vicinity of a multipole particle (moving along an arbitrary trajectory) is proposed. The method is based on a geometric construction of a trajectory-adapted coordinate system, which simplifies…
We consider a model system of persistent random walkers that can jam, pass through each other or jump apart (recoil) on contact. In a continuum limit, where particle motion between stochastic changes in direction becomes deterministic, we…
We investigate the motion of one and two charged non-relativistic particles on a sphere in the presence of a magnetic field of uniform strength. For one particle, the motion is always circular, and determined by a simple relation between…
We construct models of many-particle quantum graphs with singular two-particle contact interactions, which can be either hardcore- or delta-interactions. Self-adjoint realisations of the two-particle Laplacian including such interactions…
In this paper, we consider a biharmonic equation with respect to the Dirichlet problem on a domain of a locally finite graph. Using the variation method, we prove that the equation has two distinct solutions under certain conditions.