Related papers: On the Three-Anyon Harmonics
We study the isospectrality problem for a relativistic free quantum particle, described by the Dirac Hamiltonian, confined in a one-dimensional ring with a junction. We analyze all the self-adjoint extensions of the Hamiltonian in terms of…
Universal vector wave equations allowing for a unified description of anyons, and also of usual bosons and fermions in the plane are proposed. The existence of two essentially different types of anyons, based on unitary and also on…
Working directly with a general Hamiltonian for the spacetime metric with the $3+1$ decomposition and keeping only the spatial covariance, we investigate the possibility of reducing the number of degrees of freedom by introducing an…
We consider 3D free-boundary compressible ideal magnetohydrodynamic (MHD) system under the Rayleigh-Taylor sign condition. It describes the motion of a free-surface perfect conducting fluid in an electro-magnetic field. A local existence…
There is an explicit resolution of the Poisson reduction of four planar point vortices, in the case that three of the vortex strengths are equal and the total vorticity is zero. The resolution, a Hamiltonian system on a unified symplectic…
We evaluate masses of bottom and charmed baryons using several non-relativistic quark potentials which parameters have been adjusted to the meson spectra. Heavy Quark Symmetry leads to important simplifications of the three body problem,…
The Poisson structure in the quaternion variables was proposed for asymmetric top in the external axially symmetric magnetic field. For that model of interaction the motion equation were got. The model was simulated in the neighbourhood of…
Three-dimensional geophysical fluids support both internal and boundary-trapped waves. To obtain the normal modes in such fluids we must solve a differential eigenvalue problem for the vertical structure (for simplicity, we only consider…
We consider equivariant wave maps from a wormhole spacetime into the three-sphere. This toy-model is designed for gaining insight into the dissipation-by-dispersion phenomena, in particular the soliton resolution conjecture. We first prove…
The baryon-antibaryon asymmetry (excess of matter over antimatter in our Universe), indicated by observational data from the Cosmic Microwave Background anisotropies, predictions of primordial Nucleosynthesis, and the absence of intense…
LECTURE GIVEN AT TH2002. Given a set of Boolean variables, and some constraints between them, is it possible to find a configuration of the variables which satisfies all constraints? This problem, which is at the heart of combinatorial…
We discuss some recent developments in the description of baryons as three-quark systems within relativistic constituent quark models. In particular we address the issues of excitation spectra, electroweak structure, and mesonic resonance…
The problem of determining the set of possible eigenvalues of 3 Hermitian matrices that sum up to zero is known as the Horn problem. The answer is a polyhedral cone, which, following Knutson and Tao, can be described as the projection of a…
We introduce the self-dual abelian gauged $O(3)$ sigma models where the Maxwell and Chern-Simons terms constitute the kinetic terms for the gauge field. These models have quite rich structures and various limits. Our models are found to…
The Boson-Fermion model, describing a mixture of hybridized localized Bosons and itinerant Fermions on a lattice, is known to exhibit spectral properties for the Fermions which upon lowering the temperature develop into a three pole…
We develop an approach in solving exactly the problem of three-body oscillators including general quadratic interactions in the coordinates for arbitrary masses and couplings. We introduce a unitary transformation of three independent…
This article concerns the water wave problem in a three-dimensional domain of infinite depth and examines the modulational regime for weakly nonlinear wavetrains. We use the method of normal form transformations near the equilibrium state…
We address the problem of multispecies anyons, i.e. particles of different species whose wave function is subject to anyonlike conditions. The cluster and virial coefficients are considered. Special attention is paid to the case of anyons…
We present essentially exact solutions of the Schroedinger equation for three fermions in two different spin states with zero-range s-wave interactions under harmonic confinement. Our approach covers spherically symmetric, strictly…
We consider energetics and structural properties of a many particle system in one dimension with pairwise contact interactions confined in a parabolic external potential. To render the problem analytically solvable, we use the harmonic…