Related papers: Two particles on a star graph II
In this paper, a function on any pair of graphs is defined whose properties are similar to the properties of dot product in vector space. This function enables us to define graph orthogonality and, also, a new metric on isomorphism classes…
The optical properties of clusters with metallic spherical particles embedded in an insulating matrix are studied. A theoretical approach is proposed for the calculation of the macroscopic dielectric response for a collection of spheres at…
A number of exact results for two-loop three-point diagrams with massless internal particles and arbitrary (off-shell) external momenta are presented. Divergent contributions are calculated in the framework of dimensional regularization.
The $2N$-dimensional quantum problem of $N$ particles (e.g. electrons) with interaction $\beta/r^2$ in a two-dimensional parabolic potential $\omega_0$ (e.g. quantum dot) and magnetic field $B$, reduces exactly to solving a…
This paper discusses certain properties of heterogeneous hypergeometric functions with two matrix arguments. These functions are newly defined but have already appeared in statistical literature and are useful when dealing with the…
We developed the functional form of the two-point correlation function under the approximation of fixed particle number density n(bar). We solved the quasi-linear partial differential equation (PDE) through the method of characteristics to…
We show different expressions of distribution functions (DFs) which depend only on the two classical integrals of the energy and the magnitude of the angular momentum with respect to the axis of symmetry for stellar systems with known…
We study a continuum model of overdamped self-propelled particles with an aligning interaction in two dimensions. By combining analytical and numerical work, we map out the phase diagram for generic parameters. We find that the system…
In this paper we consider the conformal dynamics for a system of $N$ interacting relativistic massless particles. A detailed study is done for the case of two-particles, with a particular attention to the symmetries of the problem. In fact,…
We present a systematic method to determine the dominant regions of internal momenta contributing to any two-body high-energy near-forward scattering diagram. Such a knowledge is used to evaluate leading high-energy dependences of loop…
We construct equilibrium configurations of magnetized, two-fluid neutron stars using an iterative numerical method. Working in Newtonian framework we assume that the neutron star has two regions: the core, which is modelled as a…
The graph isomorphism problem is of practical importance, as well as being a theoretical curiosity in computational complexity theory in that it is not known whether it is $NP$-complete or $P$. However, for many graphs, the problem is…
We consider integrable system on the sphere $S^2$ with an additional integral of fourth order in the momenta. At the special values of parameters this system coincides with the Kowalevski-Goryachev-Chaplygin system.
We describe a procedure to systematically improve direct diagonalization results for few-particle systems trapped in one-dimensional harmonic potentials interacting by contact interactions. We start from the two-body problem to define a…
We have proposed a simple one-dimensional model of internal particle dynamics. The model is based on the assumption that self-interaction can be represented by a nonlinear feedback and described by a quadratic recurrent map. Charge plays…
The quantum-mechanical problem of a many-particle system with a single impurity in one-dimension, interacting by a delta-function, is solved. The wave-function for a bosonic system and the related secular equation for the spectrum are…
In unparticle physics, operators of the conformal sector have self-interactions, and these are unsuppressed for strong coupling. The 3-point interactions are completely determined by conformal symmetry, up to a constant. We do not know of…
We consider the dynamics of point particles which are confined to a bounded, possibly nonconvex domain $\Omega$. Collisions with the boundary are described as purely elastic collisions. This turns the description of the particle dynamics…
We study a system of self-propelled disks that perform run-and-tumble motion, where particles can adopt more than one internal state. One of those internal states can be transmitted to another particle if the particle carrying this state…
We give a complete analytical computation of three and two-point loop integrals occurring in heavy-particle theories, involving a velocity change, for arbitrary real values of the external masses and residual momenta.