Related papers: Complex classical motion in potentials with poles …
The Hamiltonian dynamics of a single particle in a rotating plasma column, interacting with an magnetic multipole is perturbatively solved for up to second order, using the method of Lie transformations. First, the exact Hamiltonian is…
In this paper we prove a Nekhoroshev type theorem for perturbations of Hamiltonians describing a particle subject to the force due to a central potential. Precisely, we prove that under an explicit condition on the potential, the…
We examine the possible trajectories of a classical particle, trapped in a two-dimensional infinite rectangular well, using the Hamilton-Jacobi equation. We observe that three types of trajectories are possible: periodic orbits, open orbits…
The classical Hamilton equations of motion yield a structure sufficiently general to handle an almost arbitrary set of ordinary differential equations. Employing elementary algebraic methods, it is possible within the Hamiltonian structure…
Study of the classical motion of two identical particles on a plane subject to non-Coulomb potentials in a constant magnetic field presented in polar coordinates. With the rigorous analysis of the potentials and the constants of motion, we…
The dynamics of classical and quantum systems which are driven by a high frequency ($\omega$) field is investigated. For classical systems the motion is separated into a slow part and a fast part. The motion for the slow part is computed…
A sixth order quadrupole boson Hamiltonian is treated through a time dependent variational principle approach choosing as trial function a coherent state with respect to zeroth $b^{\dagger}_0$ and second $b^{\dagger}_2+b^{\dagger}_{-2}$…
We propose a conservative two-dimensional particle model in which particles carry a continuous and classical spin. The model includes standard ferromagnetic interactions between spins of two different particles, and a nonstandard coupling…
In recent years, many natural Hamiltonian systems, classical and quantum, with constants of motion of high degree, or symmetry operators of high order, have been found and studied. Most of these Hamiltonians, in the classical case, can be…
We describe a new phenomenon in the study of the real-time path integral, where complex classical paths hit singularities of the potential and need to be analytically continued beyond the space for which they solve the boundary value…
The classical trajectories of single particle motion in a Wodds-Saxon and a modified Nilsson potential are studied for axial quadrupole deformation. Both cases give rise to chaotic behaviour when the deformation in the Woods-Saxon and the…
We prove that if a sequence of pairs of smooth commuting Hamiltonians converge in the $C^0$ topology to a pair of smooth Hamiltonians, these commute. This allows us define the notion of commuting continuous Hamiltonians. As an application…
Process of quantum tunneling of particles in various physical systems can be effectively controlled even by a weak and slow varying in time electromagnetic signal if to adapt specially its shape to a particular system. During an…
In this work, we investigate generic classical two-dimensional (2D) superintegrable Hamiltonian systems H, characterized by the existence of three functionally independent integrals of motion (I_0=H,I_1,I_2). Our main result, formulated and…
Hamiltonians that are multivalued functions of momenta are of topical interest since they correspond to the Lagrangians containing higher-degree time derivatives. Incidentally, such classes of branched Hamiltonians lead to certain not too…
In the present paper we study the classical and the quantum H\'enon-Heiles systems. In particular we make a comparison between the classical and the quantum trajectories of the integrable and of the non integrable H\'enon Heiles…
The Melnikov method is applied to periodically perturbed open systems modeled by an inverse--square--law attraction center plus a quadrupolelike term. A compactification approach that regularizes periodic orbits at infinity is introduced.…
In the case of two degree system the pairs of quadratic in momenta Hamiltonians commuting according the standard Poisson bracket are considered. The new many-parametrical families of such pairs are founded. The universal method of…
This paper deals with the classical trajectories for two super-integrable systems: a system known in quantum chemistry as the Hartmann system and a system of potential use in quantum chemistry and nuclear physics. Both systems correspond to…
The energy of a quantum particle cannot be determined exactly unless there is an infinite amount of time in which to perform the measurement. This paper considers the possibility that $\Delta E$, the uncertainty in the energy, may be…