Related papers: MICZ-Kepler = dynamics on the cone over the rotati…
We introduce and investigate new models of the Chern-Simons type in the three-dimensional spacetime, focusing on the existence of compact vortices. The models are controlled by potentials driven by a single real parameter that can be used…
It is shown, that the reduction of the circular quantum oscillator by the $Z_2$-group action results to the two systems: a two-dimensional hydrogen atom, and a ``charge - charged magnetic vortex" one, with the spin $\frac 12$. Analogously,…
We consider a tippe top modeled as an eccentric sphere, spinning on a horizontal table and subject to a sliding friction. Ignoring translational effects, we show that the system is reducible using a Routhian reduction technique. The reduced…
Rovibrational states of the four dimers formed by the light and the heavy isotopologues of the methane and the water molecules are computed using a potential energy surface taken from the literature. The general rovibrational energy-level…
We present solutions of the Dirac equation with spin symmetry for vector and scalar modified P\"oschl-Teller potential within framework of an approximation of the centrifugal term. The relativistic energy spectrum is obtained using the…
A countable set of superintegrable quantum mechanical systems is presented which admit the dynamical symmetry with respect to algebra so(4). This algebra is generated by the Laplace-Runge-Lenz vector generalized to the case of arbitrary…
It is known that orbit reduction can be performed in one or two stages and it has been proven that the two processes are symplectically equivalent. In the context of orbit reduction by one stage we shall write an expression for the reduced…
In this Letter we describe a new two-mode system, which consists of Kerr-like medium and down conversion process, called the Kerr-down conversion system. Under a certain condition we can obtain an exact solution of the dynamical equations…
A formula for the corner charge in terms of the bulk quadrupole moment is derived for two-dimensional periodic systems. This is an analog of the formula for the surface charge density in terms of the bulk polarization. In the presence of an…
Assuming the spin-independence for confining force, we give a covariant quark representation of general composite meson systems with definite Lorentz transformation properties. For benefit of this representation we are able to deduce…
In this note we present an exact solution of the Monte Carlo dynamics of the spherical Sherrington-Kirkpatrick spin-glass model. We obtain the dynamical equations for a generalized set of moments which can be exactly closed. Only in a…
We compute the one loop Casimir energy of an interacting scalar field in a compact noncommutative space of $R^{1,d}\times T^2_\theta$, where we have ordinary flat $1+d$ dimensional Minkowski space and two dimensional noncommuative torus. We…
We derive the two-dimensional Keller-Segel equation from a stochastic system of $N$ interacting particles in the case of sub-critical chemosensitivity $\chi < 8 \pi$. The Coulomb interaction force is regularised with a cutoff of size $N^{-…
The periodic Lorentz gas is a paradigmatic model to examine how macroscopic transport emerges from microscopic chaos. It consists of a triangular lattice of circular hard scatterers with a moving point particle. Recently this system became…
In this paper we introduce a combinatorial formula for the Ekeland-Hofer-Zehnder capacity of a convex polytope in $\mathbb{R}^{2n}$. One application of this formula is a certain subadditivity property of this capacity.
Planetary orbits, being conic sections, may be obtained as the locus of intersection of planes and cones. The planes involved are familiar to anyone who has studied the classical Kepler problem. We focus here on the cones.
We consider a particle moving on a cone and bound to its tip by $1/r$ or harmonic oscillator potentials. When the deficit angle of the cone divided by $2 \pi$ is a rational number, all bound classical orbits are closed. Correspondingly, the…
We study iteration maps of recurrence relations arising from mutation periodic quivers of arbitrary period. Combining tools from cluster algebra theory and (pre)symplectic geometry, we show that these cluster iteration maps can be reduced…
The causal set program as well as the Wolfram physics project leave open the problem of how a graph that is a (3+1)-dimensional Minkowski-spacetime according to its simple geodesic distances, could be generated solely from simple…
To each discrete product system E of finite-dimensional Hilbert spaces we associate a C*-algebra O_E. When E is the n-dimensional product system over N, O_E is the Cuntz algebra O_n, and the irrational rotation algebras appear as O_E for…