Related papers: Approximate integrals of motion
We construct complete sets of invariant quantities that are integrals of motion for two Hamiltonian systems obtained through a reduction procedure, thus proving that these systems are maximally superintegrable. We also discuss the reduction…
The motion in a simple, time independent rational galactic potential is studied. The potential is a generalization of a two dimensional harmonic oscillator potential and can be considered to describe plane motion in the central parts of a…
We present an algorithm for constructing analytically approximate integrals of motion in simple time periodic Hamiltonians of the form $H=H_0+ \varepsilon H_i$, where $\varepsilon$ is a perturbation parameter. We apply our algorithm in a…
A Hamiltonian formulation of generic many-particle systems with space-dependent balanced loss and gain coefficients is presented. It is shown that the balancing of loss and gain necessarily occurs in a pair-wise fashion. Further, using a…
We investigate a quantum nonrelativistic system describing the interaction of two particles with spin 1/2 and spin 0, respectively. We assume that the Hamiltonian is rotationally invariant and parity conserving and identify all such systems…
We consider a formal (approximate) integral of motion in Hamiltonians of the form $H=\frac{1}{2}(X^2+Y^2+\omega_1^2x^2+\omega_2^2y^2)+\epsilon(\eta xy^2+\alpha x^3+\beta x^2y+\gamma y^3)$ generalizing previous cases with $\beta=\gamma=0$.…
Quantum nonrelativistic systems with $2\times2$ matrix potentials are investigated. Physically, they simulate charged or neutral fermions with non-trivial dipole momenta, interacting with an external electric field. Assuming rotationally…
A superintegrable system is, roughly speaking, a system that allows more integrals of motion than degrees of freedom. This review is devoted to finite dimensional classical and quantum superintegrable systems with scalar potentials and…
A systematic search for superintegrable quantum Hamiltonians describing the interaction between two particles with spin 0 and 1/2, is performed. We restrict to integrals of motion that are first-order (matrix) polynomials in the components…
We investigate a quantum non-relativistic system describing the interaction of two particles with spin 1/2 and spin 0, respectively. Assuming that the Hamiltonian is rotationally invariant and parity conserving we identify all such systems…
Commuting Hamiltonians lie at the boundary between classical constraint satisfaction and quantum many-body physics, exhibiting rich quantum structure while remaining more tractable than general noncommuting models. In contrast, physical…
The realization space of geometric constraint systems is given by the vanishing locus of polynomials corresponding to natural geometric constraints. Such geometric constraint systems arise in many real-world scenarios such as structural…
We study a large class of models with an arbitrary (finite) number of degrees of freedom, described by Hamiltonians which are polynomial in bosonic creation and annihilation operators, and including as particular cases n-th harmonic…
We discuss some families of integrable and superintegrable systems in $n$-dimensional Euclidean space which are invariant to $m\geq n-2$ rotations. The integrable invariant Hamiltonian $H=\sum p_i^2+V(q)$ commutes with $n-2$ integrals of…
Classical trajectories are calculated for two Hamiltonian systems with ring shaped potentials. Both systems are super-integrable, but not maximally super-integrable, having four globally defined single valued integrals of motion each. All…
We consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integral of motion. We construct the most general associative cubic algebra and we present specific…
Local integrals of motion play a central role in the understanding of many-body localization in many-body quantum systems in one dimension subject to a random external potential, but the question of how these local integrals of motion…
We use a semi-numerical method to find the position and period of periodic orbits in a bisymmetrical potential, made up of a two dimensional harmonic oscillator, with an additional term of a Plummer potential, in a number of resonant cases.…
A complete geometric classification of symmetries of autonomous Hamiltonian mechanical systems is established; explaining how to obtain their associated conserved quantities in all cases. In particular, first we review well-known results…
We study the approximate (formal) integrals of motion in the Hamiltonian $ H = \frac{1}{2}\left( \dot{x}^2 + \dot{y}^2 + x^2 + y^2 \right) + \epsilon\,\left( xy^2 + \alpha x^3\right)$ which is an extension of the usual H\'{e}non-Heiles…