Related papers: Solution of the Three--Anyon Problem
We show that for non-negative solution of the Aronsson equation an isolated singularity is either removable, or the solution behaves asymptotically like a general cone. This generalizes the asymptotic behavior theory for infinity harmonic…
We consider the problem of three identical charged particles on a plane under a perpendicular magnetic field and interacting through Coulomb repulsion. This problem is treated within Taut's framework, in the limit of vanishing center of…
For the linear baryon string model with three massive points (three quarks) connected sequentially by the relativistic strings the initial-boundary value problem is stated and solved in general. This problem implies defining a classical…
We consider particles in three-dimensional space, which have a certain probability to find themselves in a thin layer (``plane''), where they are assumed to be well described by a planar Hamiltonian and are subject to Aharonov-Bohm-type…
The O(N) invariant quartic anharmonic oscillator is shown to be exactly solvable if the interaction parameter satisfies special conditions. The problem is directly related to that of a quantum double well anharmonic oscillator in an…
Finding reliably and efficiently the spectrum of the resonant states of an optical system under varying parameters of the medium surrounding it is a technologically important task, primarily due to various sensing applications.…
The equations of motion of two point masses in harmonic coordinates are derived through the third post-Newtonian (3PN) approximation. The problem of self-field regularization (necessary for removing the divergent self-field of point…
We study the dynamics of three particles in a finite interval, in which two light particles are separated by a heavy ``piston'', with elastic collisions between particles but inelastic collisions between the light particles and the interval…
Anyons in one spatial dimension can be defined by correctly identifying the configuration space of indistinguishable particles and imposing Robin boundary conditions. This allows an interpolation between the bosonic and fermionic limits. In…
We consider an elliptic polyharmonic problem of any order which takes place in a punctured bounded domain with Navier conditions. We prove that if the domain is convex in one direction and symmetric with respect to the reflections induced…
A high temperature expansion is employed to map some complex anisotropic nonhermitian three and four dimensional Ising models with algebraic long range interactions into a solvable two dimensional variant. We also address the dimensional…
We present a method that gives highly accurate electrostatic potentials for systems where we have periodic boundary conditions in two spatial directions but free boundary conditions in the third direction. These boundary conditions are…
We rigorously derive a homogenized model for the Poisson--Nernst--Planck (PNP) equations for the case of multiple species defined on a periodic porous medium in spatial dimensions two and three. This extends the previous homogenization…
The monopole systems with hidden symmetry of the two-dimensional Coulomb problem are considered. One of them, the "charge-charged magnetic vortex" with a half-spin, is constructed by reducing the quantum circular oscillator with respect to…
Compactons are compactly supported solitary waves for nondissipative evolution equations with nonlinear dispersion. In applications, these model equations are accompanied by dissipative terms which can be treated as small perturbations. We…
The Jeans equations relate the second-order velocity moments to the density and potential of a stellar system. For general three-dimensional stellar systems, there are three equations and six independent moments. By assuming that the…
The Orbit Problem consists of determining, given a matrix $A\in \mathbb{R}^{d\times d}$ and vectors $x,y\in \mathbb{R}^d$, whether there exists $n\in \mathbb{N}$ such that $A^n=y$. This problem was shown to be decidable in a seminal work of…
We propose a new approach to the combinatorial interpretations of linearization coefficient problem of orthogonal polynomials. We first establish a difference system and then solve it combinatorially and analytically using the method of…
We study a third-order nonlinear ordinary differential equation whose solutions, under certain specific conditions, are individual pulses. These correspond to homoclinic orbits in the phase space of the equation and we study the possible…
The three-particle Hamiltonian obtained by replacing the two-body trigonometric potential of the Sutherland problem by a three-body one of a similar form is shown to be exactly solvable. When written in appropriate variables, its…