We have studied the underlying algebraic structure of the anharmonic oscillator by using the variational perturbation theory. To the first order of the variational perturbation, the Hamiltonian is found to be factorized into a supersymmetric form in terms of the annihilation and creation operators, which satisfy a q-deformed algebra. This algebraic structure is used to construct all the eigenst...

An integrable quantum group deformation of the supersymmetric t-J model is introduced. Open boundary conditions lead to an spl q (2; 1) invariant hamiltonian. A general procedure to obtain such invariant models is proposed. To solve the model a generalized nested algebraic Bethe ansatz is constructed and the Bethe ansatz equations are obtained. The quantum supergroup structure of the model is i...

The numerical integration of Hamiltonian systems is considered in this paper. Diagonally implicit Symplectic Runge-Kutta methods with special properties are presented. The methods developed have six and seven stages algebraic order up to 5th and dispersion order up to 8th.

We report general properties of N -fold supersymmetry in one-dimensional quantum mechanics. N -fold supersymmetry is characterized by supercharges which are N -th polynomials of momentum. Relations between the anti-commutator of the supercharges and the Hamiltonian, the spectra, the Witten index, the non-renormalization theorems and the quasi-solvability are examined. We also present further in...

We report general properties of N -fold supersymmetry in one-dimensional quantum mechanics. N -fold supersymmetry is characterized by supercharges which are N -th polynomials of momentum. Relations between the anti-commutator of the supercharges and the Hamiltonian, the spectra, the Witten index, the non-renormalization theorems and the quasi-solvability are examined. We also present further in...

In this paper the authors develop a new algorithm to solve the standard discrete-time algebraic Riccati equation by using a skewHamiltonian transformation and the square-root method. The algorithm is structure-preserving and efficient because the Hamiltonian structure is fully exploited and only orthogonal transformations are used. The efficiency and stability of the algorithm are analyzed. Num...

Using an algebra of paths we present abstract algebraic derivations for two problem classes concerning graphs, viz. layer oriented traversal and computing sets of Hamiltonian paths. In the rst case, we are even able to abstract to the very general setting of Kleene algebras. Applications include reachability and a shortest path problem as well as topological sorting, cycle detection and nding m...

This paper investigates hybrid kinetic-magnetohydrodynamic (MHD) models, where a hot plasma (governed by a kinetic theory) interacts with a fluid bulk (governed by MHD). Different nonlinear coupling schemes are reviewed, including the pressure-coupling scheme (PCS) used in modern hybrid simulations. This latter scheme suffers from being non-Hamiltonian and is unable to exactly conserve total en...

We discuss the alternative algebraic structures on the manifold of quantum states arising from alternative Hermitian structures associated with quantum bi-Hamiltonian systems. We also consider the consequences at the level of the Heisenberg picture in terms of deformations of the associative product on the space of observables.

The existence, uniqueness, and parametrization of Lagrangian invariant subspaces for Hamiltonian matrices is studied. Necessary and sufficient conditions and a complete parametrization are given. Some necessary and sufficient conditions for the existence of Hermitian solutions of algebraic Riccati equations follow as simple corollaries.