Related papers: Hamiltonian Dynamics for the Kepler Problem in a D…
The action of the quantum mechanical volume operator, introduced in connection with a symmetric representation of the three-body problem and recently recognized to play a fundamental role in discretized quantum gravity models, can be given…
We consider the motion of a point particle with spin in a stationary spacetime. We define, following Witzany (2019) and later Ramond (2022), a twelve dimensional Hamiltonian dynamical system whose orbits coincide with the solutions of the…
In this work we propose a new numerical approach to distinguish between regular and chaotic orbits in Hamiltonian systems, based on the simultaneous integration of both the orbit and the deviation vectors using a symplectic scheme, hereby…
Positive-energy solutions of the Klein-Gordon equation form a Hilbert space of holomorphic functions on the future tube. This domain is interpreted as an extended phase space for the associated classical particle, the extra dimensions being…
We analyze the dynamical equations obeyed by a classical system with position-dependent mass. It is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass. We construct the Lagrangian and the…
We introduce a new family of Hamiltonians with a deformed Kepler- Coulomb potential dependent on an indexing parameter k. We show that this family is superintegrable for all rational k and compute the classical trajectories and quantum wave…
We study four particular 3-dimensional natural Hamiltonian systems defined in conformally Euclidean spaces. We prove their superintegrability and we obtain, in the four cases, the maximal number of functionally independent integrals of…
We use Moser's normal forms to study chaotic motion in two-degree hamiltonian systems near a saddle point. Besides being convergent, they provide a suitable description of the cylindrical topology of the chaotic flow in that vicinity. Both…
Revivals of the coherent states of a deformed, adiabatically and cyclically varying oscillator Hamiltonian are examined. The revival time distribution is exactly that of Poincar\'{e} recurrences for a rotation map: only three distinct…
We present a simple method to obtain the solution of a few orbital problems: the Kepler problem, the modified Kepler problem by the addition of an inverse square potential and linear force.
In this paper a non-relativistic particle moving on a hypersurface in a curved space and the multidimensional rotator are investigated using the Hamilton-Jacobi formalism. The equivalence with the Dirac Hamiltonian formalism is demonstrated…
We present a definition of the two-sided inverse of position operator in general case of deformed Heisenberg algebra leading to minimal length. Energy spectrum and eigenfunctions in momentum space for 1D Coulomb-like potential in deformed…
After a short review of the history and problems of relativistic Hamiltonian mechanics with action-at-a-distance inter-particle potentials, we study isolated two-body systems in the rest-frame instant form of dynamics. We give explicit…
The true- and eccentric-anomaly parametrizations of the Kepler motion are generalized to quasiperiodic orbits by considering perturbations of the radial part of kinetic energy as a series in the negative powers of the orbital radius. A…
We develop a rigorous analytical Hamiltonian formalism adapted to the study of the motion of two planets in co-orbital resonance. By constructing a complex domain of holomorphy for the planetary Hamilto-nian, we estimate the size of the…
The main theme of the paper is the dynamics of Hamiltonian diffeomorphisms of ${\mathbb C}{\mathbb P}^n$ with the minimal possible number of periodic points (equal to $n+1$ by Arnold's conjecture), called here Hamiltonian pseudo-rotations.…
This work addresses a ${\theta}(\hat{x},\hat{p})-$deformation of the harmonic oscillator in a $2D-$phase space. Specifically, it concerns a quantum mechanics of the harmonic oscillator based on a noncanonical commutation relation depending…
We consider a relativistic extended object described by a reparametrization invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the…
A family of classical superintegrable Hamiltonians, depending on an arbitrary radial function, which are defined on the 3D spherical, Euclidean and hyperbolic spaces as well as on the (2+1)D anti-de Sitter, Minkowskian and de Sitter…
In this paper we consider cases of existence of invariant measure, additional first integrals, and Poisson structure in a problem of rigid body's rolling without sliding on plane and sphere. The problem of rigid body's motion on plane was…