Related papers: Superintegrability, isochronicity, and quantum har…
We investigate bicomplex Hamiltonian systems in the framework of an analogous version of the Schrodinger equation. Since in such a setting three different types of conjugates of bicomplex numbers appear, each is found to define in a natural…
Degenerate tri-Hamiltonian structures of Shivamoggi and generalized Raychaudhuri equations are exhibited. For certain specific values of the parameters, it is shown that hyperchaotic L\"{u} and Qi systems are superintegrable and admit…
We study the problem of robust performance of quantum systems under structured uncertainties. A specific feature of closed (Hamiltonian) quantum systems is that their poles lie on the imaginary axis and that neither a coherent controller…
In recent work, we initiated a research program aimed at the systematic investigation of quantum superintegrable systems describing the interaction of two non-relativistic spin-$1/2$ particles in three-dimensional Euclidean space. In that…
Hamiltonian systems of ordinary and partial differential equations are fundamental mathematical models spanning virtually all physical scales. A critical property for the robustness and stability of computational methods in such systems is…
We study the spectral properties of a spin-boson Hamiltonian that depends on two continuous parameters $0\leq\Lambda<\infty$ (interaction strength) and $0\leq\alpha\leq\pi/2$ (integrability switch). In the classical limit this system has…
A class of three-dimensional models which satisfy supersymmetric intertwining relations with the simplest - oscillator-like - variant of shape invariance is constructed. It is proved that the models are not amenable to conventional…
We consider integrable Hamiltonian systems in a general setting of invariant submanifolds which need not be compact. For instance, this is the case a global Kepler system, non-autonomous integrable Hamiltonian systems and integrable systems…
The coalgebra approach to the construction of classical integrable systems from Poisson coalgebras is reviewed, and the essential role played by symplectic realizations in this framework is emphasized. Many examples of Hamiltonians with…
Resonant systems emerge as weakly nonlinear approximations to problems with highly resonant linearized perturbations. Examples include nonlinear Schroedinger equations in harmonic potentials and nonlinear dynamics in Anti-de Sitter…
It is well known that the Hamiltonian of an $n$-dimensional isotropic oscillator admits an $SU(n)$ symmetry, making the system maximally superintegrable. However, the dynamical symmetries of the anisotropic oscillator are much more subtle.…
When several inequivalent supercharges form a closed superalgebra in Quantum Mechanics it entails the appearance of hidden symmetries of a Super-Hamiltonian. We examine this problem in one-dimensional QM for the case of periodic potentials…
The goal of this thesis is the search for integrable and superintegrable systems with magnetic field. We formulate the quantum mechanical determining equations for second order integrals of motion in the cylindrical coordinates and we find…
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 consider supersymmetric quantum mechanical models with both local and nonlocal potentials. We present a nonlocal deformation of exactly solvable local models. Its energy eigenfunctions and eigenvalues are determined exactly. We observe…
There are two fundamental problems studied by the theory of hamiltonian integrable systems: integration of equations of motion, and construction of action-angle variables. The third problem, however, should be added to the list: separation…
The structure of supersymmetry is analyzed systematically in ${\cal PT}$ symmetric quantum mechanical theories. We give a detailed description of supersymmetric systems associated with one dimensional ${\cal PT}$ symmetric quantum…
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…
An infinite family of classical superintegrable Hamiltonians defined on the N-dimensional spherical, Euclidean and hyperbolic spaces are shown to have a common set of (2N-3) functionally independent constants of the motion. Among them, two…
The solution of problems in physics is often facilitated by a change of variables. In this work we present neural transformations to learn symmetries of Hamiltonian mechanical systems. Maintaining the Hamiltonian structure requires novel…