The properties of open quantum systems are described well by an effective Hamiltonian H that consists of two parts: the Hamiltonian H of the closed system with discrete eigenstates and the coupling matrix W between discrete states and continuum. The eigenvalues of H determine the poles of the S matrix. The coupling matrix elements W(cc')(k) between the eigenstates k of H and the continuum may b...

where n ∈ Z, u ∈ RN , u(n) = u(n + ) – u(n) is the forward difference operator, p,L : Z→ RN×N and W : Z× RN → R. As usual, we say that a solution u(n) of system (.) is homoclinic (to ) if u(n)→  as n→±∞. In addition, if u(n) ≡ , then u(n) is called a nontrivial homoclinic solution. In general, system (.) may be regarded as a discrete analogue of the following second order Hamiltonian sy...

We give a group-theoretic proof of the following fact, proved initially by methods of topological design theory: Up to isomorphism, the number of regular hamiltonian embeddings of Kn,n is 2 or 1, depending on whether n is a multiple of 8 or not. We also show that for each n there is, up to isomorphism, a unique regular triangular embedding of Kn,n,n. This is a preprint of an article accepted fo...

A previously proposed [Sutcliffe and Tennyson, Int. J. Quantum Chem. 29, 183 (199111 bodyfixed Hamiltonian is applied to A& systems in Radau coordinates with the x-axis embedded along the bisector of the angle. It is shown that by using a discrete variable representation for the angular coordinate it is possible to avoid singular regions of the Hamiltonian. A two-step variational procedure is u...

in this paper, we present a capable algorithm for solving a class of nonlinear optimal control problems (ocp's). the approach rest mainly on the differential transform method (dtm) which is one of the approximate methods. the dtm is a powerful and efficient technique for finding solutions of nonlinear equations without the need of a linearization process. utilizing this approach, the optim...

The quantum dynamics of a driven single-band tight-binding model is considered. The relation between this Hamiltonian and Hamiltonian of the discrete-charge mesoscopic quantum circuits is investigated. It is shown that the former Hamiltonian, with closed boundary conditions, can be considered as a realization of the generalized para-fermionic polynomial algebras.

We investigate the topological quenching of spin tunneling in Mn12-acetate molecules with an applied magnetic field along the hard axis. The model Hamiltonian describing this system has a fourth-order term due to the tetragonal anisotroy. We treat this model using the discrete phase integral formalism in which the Schrödinger equation corresponding to the Hamiltonian becomes a nine-term recursi...

We introduce a novel technique for constructing higher-order variational integrators for Hamiltonian systems of ODEs. In particular, we are concerned with generating globally smooth approximations to solutions of a Hamiltonian system. Our construction of the discrete Lagrangian adopts Hermite interpolation polynomials and the Euler–Maclaurin quadrature formula, and involves applying collocation...

Implicit representations of finite-dimensional port-Hamiltonian systems are studied from the perspective of their use in numerical simulation and control design. Implicit representations arise when a system is modeled in Cartesian coordinates and when the system constraints are applied in the form of additional algebraic equations (the system model is in a differential-algebraic equation form)....

Ruijsenaars-Schneider models associated with A n−1 root system with a discrete coupling constant are studied. The eigenvalues of the Hamiltonian are given in terms of the Bethe ansatz formulas. Taking the " non-relativistic " limit, we obtain the spectrum of the corresponding Calogero-Moser systems in the third formulas of Felder et al [22].