Related papers: Separable quantizations of St\"{a}ckel systems
It is shown that separation conditions (separation curves) are fundamental objects of separability theory. They are used for the classification of certain clases of separable systems, for the proof of bi-Hamiltonian property and finally…
Integrals of motion of a Hamiltonian system need not be commutative. The classical Mishchenko-Fomenko theorem enables one to quantize a noncommutative completely integrable Hamiltonian system around its invariant submanifold as an abelian…
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…
In a recent paper a slightly modified version of the Bateman system, originally proposed to describe a damped harmonic oscillator, was proposed. This system is really different from the Bateman's one, in the sense that this latter cannot be…
Found all equivalence classes for electromagnetic potentials and space-time metrics of Stackel spaces, provided that the equations of motion of the classical charged test particles are integrated by the method of complete separation of…
We discuss a framework for quantizing a Poisson manifold via the quantization of its symplectic groupoid, that combines the tools of geometric quantization with the results of Renault's theory of groupoid C*-algebras. This setting allows…
The general description of superintegrable systems with one polynomial integral of order $N$ in the momenta is presented for a Hamiltonian system in two-dimensional Euclidean plane. We consider classical and quantum Hamiltonian systems…
We consider a (pseudo)Riemannian manifold of arbitrary dimension. The Hamilton-Jacobi equation for geodesic Hamiltonian admits complete separation of variables for some (separable) metrics in some (separable) coordinate systems. Separable…
It is shown that any two Hamiltonians H(t) and H'(t) of N dimensional quantum systems can be related by means of time-dependent canonical transformations (CT). The dynamical symmetry group of system with Hamiltonian H(t) coincides with the…
We show that the theory of classical Hamiltonian systems admitting separating variables can be formulated in the context of ($\omega, \mathscr{H}$) structures. They are symplectic manifolds endowed with a compatible Haantjes algebra…
We present a multiparameter generalization of the St\"ackel transform (the latter is also known as the coupling-constant metamorphosis) and show that under certain conditions this generalized St\"ackel transform preserves the Liouville…
In this paper we present a novel construction of non-homogeneous hydrodynamic equations from what we call quasi-St\"ackel systems, that is non-commutatively integrable systems constructed from appropriate maximally superintegrable St\"ackel…
A classical (or quantum) superintegrable system on an n-dimensional Riemannian manifold is an integrable Hamiltonian system with potential that admits 2n-1 functionally independent constants of the motion that are polynomial in the momenta,…
Stoquastic Hamiltonians play a role in the computational complexity of the local Hamiltonian problem as well as the study of classical simulability. In particular, stoquastic Hamiltonians can be straightforwardly simulated using Monte Carlo…
The Hamiltonian formulation plays the essential role in constructing the framework of modern physics. In this paper, a new form of canonical equations of Hamilton with the complete symmetry is obtained, which are valid not only for the…
An integrable anharmonic oscillator is presumably simulable by a classical computer and therefore by a quantum computer. An integrable anharmonic oscillator whose Hamiltonian is of normal type and quartic in the canonical coordinates is not…
The problem of diagonalization of Hamiltonians of N-dimensional boson systems by means of time-dependent canonical transformations (CT) is considered, the case of quadratic Hamiltonians being treated in greater detail. The unitary generator…
A quantum system consisting of two subsystems is separable if its density matrix can be written as $\rho=\sum w_K \rho_K'\otimes \rho_K''$, where $\rho_K'$ and $\rho_K''$ are density matrices for the two subsytems, and the positive weights…
All equivalence classes for electromagnetic potentials and space-time metrics of Stackel spaces, provided that Hamilton-Jacobi equation and Klein-Gordon-Fock equation for a charged test particle can be integrated by the method of complete…
This paper extends Kontsevich's ideas on quantizing Poisson manifolds. A new differential is added to the Hodge decomposition of the Hochschild complex, so that it becomes a bicomplex, even more similar to the classical Hodge theory for…