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Claudia M. Chanu

Publications and source records attributed to Claudia M. Chanu.

4 recordsLinked to original sources
arXiv2013

Extensions of Hamiltonian systems dependent on a rational parameter

The technique of "extension" allows to build $(n+1)$-dimensional Hamiltonian systems with a non-trivial polynomial in the momenta first integral of any given degree starting from a $n$-dimensional Hamiltonian satisfying some additional properties. Until now, the application of the method was restricted to integer values of a certain fundamental parameter determining the degree of the additional first integral. In this article we show how this technique can be generalized to any rational value of the same parameter. Several examples are given, among them the anisotropic oscillator and a special case of the Tremblay-Turbiner-Winternitz system.

math-ph↗
arXiv2012

Solutions of Helmholtz and Schrödinger Equations with Side Condition and Nonregular Separation of Variables

Olver and Rosenau studied group-invariant solutions of (generally nonlinear) partial differential equations through the imposition of a side condition. We apply a similar idea to the special case of finite-dimensional Hamiltonian systems, namely Hamilton-Jacobi, Helmholtz and time-independent Schrödinger equations with potential on $N$-dimensional Riemannian and pseudo-Riemannian manifolds, but with a linear side condition, where more structure is available. We show that the requirement of $N-1$ commuting second-order symmetry operators, modulo a second-order linear side condition corresponds to nonregular separation of variables in an orthogonal coordinate system, characterized by a generalized Stäckel matrix. The coordinates and solutions obtainable through true nonregular separation are distinct from those arising through regular separation of variables. We develop the theory for these systems and provide examples.

math-ph↗
arXiv2012

Superintegrable Extensions of Superintegrable Systems

A procedure to extend a superintegrable system into a new superintegrable one is systematically tested for the known systems on $\mathbb E^2$ and $\mathbb S^2$ and for a family of systems defined on constant curvature manifolds. The procedure results effective in many cases including Tremblay-Turbiner-Winternitz and three-particle Calogero systems.

math-ph↗