Related papers: Fourth-order superintegrable systems separating in…
Recently many new classes of integrable systems in n dimensions occurring in classical and quantum mechanics have been shown to admit a functionally independent set of 2n-1 symmetries polynomial in the canonical momenta, so that they are in…
We review some known results on the superintegrability of monopole systems in the three-dimensional (3D) Euclidean space and in the 3D generalized Taub-NUT spaces. We show that these results can be extended to certain curved backgrounds…
We show that the motion on the n-dimensional ellipsoid is complete integrable by exhibiting n integrals in involution. The system is separable at classical and quantum level, the separation of classical variables being realized by the…
Superintegrable systems in two- and three-dimensional spaces of constant curvature have been extensively studied. From these, superintegrable systems in conformally flat spaces can be constructed by Staeckel transform. In this paper a…
To describe highly heterogeneous systems using the Cahn-Hilliard equation, the standard form of the thermodynamic potential with a constant coefficient in the gradient term and a polynomial of the fourth degree may not be sufficient. The…
Given an n-dimensional natural Hamiltonian L on a Riemannian or pseudo-Riemannian manifold, we call "extension" of L the n+1 dimensional Hamiltonian $H=\frac 12 p_u^2+\alpha(u)L+\beta(u)$ with new canonically conjugated coordinates…
Recently proposed procedure of constructing maximally superintegrable systems of Winternitz type is further developed and illustrated by an example of system admitting an explicit construction of angle variables and additional integrals of…
A conservative Newton system (d/dt)^2 q = -grad V(q) in R^n is called separable when the Hamilton--Jacobi equation for the natural Hamiltonian H = (1/2) p^2 + V(q) can be solved through separation of variables in some curvilinear…
The supersymmetric intertwining relations with second order supercharges allow to investigate new two-dimensional model which is not amenable to standard separation of variables. The corresponding potential being the two-dimensional…
It is shown that the quantum Hamiltonian characterising a non-relativistic electron under the influence of an external spherical symmetric electromagnetic potential exhibits a supersymmetric structure. Both cases, spherical symmetric scalar…
Semiclassical transition probabilities characterize transfer of energy between "hard" and "soft" modes in various physical systems. We establish the boundary problem for singular euclidean solutions used to calculate such probabilities.…
The superintegrability of a rational harmonic oscillator (non-central harmonic oscillator with rational ratio of frequencies) with non-linear "centrifugal" terms is studied. In the first part, the system is directly studied in the Euclidean…
Canonical variables for the Poisson algebra of quantum moments are introduced here, expressing semiclassical quantum mechanics as a canonical dynamical system that extends the classical phase space. New realizations for up to fourth order…
We employ joint invariants of Killing two-tensors defined in the Euclidean plane to characterize the Smorodinsky-Winternitz potential and explain the geometric meaning of its arbitrary parameters. In addition, we verify for which values of…
Within the context of Supersymmetric Quantum Mechanics and its related hierarchies of integrable quantum Hamiltonians and potentials, a general programme is outlined and applied to its first two simplest illustrations. Going beyond the…
We determine approximate numerical integrals of motion of 2D symmetric Hamiltonian systems. We detail for a few gravitational potentials the conditions under which quasi-integrals are obtained as polynomial series. We show that each of…
Quantum mechanical scalar particle with polarizability is considered in the presence of the Coulomb field. Separation of variables is performed with the use of Wigner $D$-functions, the radial system of 15 equations is reduced to a single…
We lay out the foundations of the theory of second-order conformal superintegrable systems. Such systems are essentially Laplace equations on a manifold with an added potential: $(\Delta_n+V({\bf x}))\Psi=0$. Distinct families of…
Semiclassical solutions of two-dimensional Schrodinger equation with spin-orbit interaction and smooth potential are considered. In the leading order, spin polarization is in-plane and follows the evolution of the electron momentum for a…
Critical phase transitions contain a variety of deep and universal physics, and are intimately tied to thermodynamic quantities through scaling relations. Yet, these notions are challenged in the context of non-Hermiticity, where spatial or…