A stochastic minimax optimal control strategy for uncertain quasi-Hamiltonian systems is proposed based on the stochastic averaging method, stochastic maximum principle and stochastic differential game theory. First, the partially completed averaged Itô stochastic differential equations are derived from a given system by using the stochastic averaging method for quasi-Hamiltonian systems with u...

The electronic conductance at zero temperature through a quantum wire with side-connected asymmetric quantum ring (as a scatter system) is theoretically studied using the non-interacting Hamiltonian Anderson tunneling method. In this paper we concentrate on the configuration of the quantum dot rings. We show that the asymmetric structure of QD-scatter system strongly influences the amplitude an...

We study the existence of quasi-periodic, invariant tori in a nearly integrable Hamiltonian system of high order proper degeneracy, i.e., the integrable part of the Hamiltonian involves several time scales and at each time scale the corresponding Hamiltonian depends on only part of the action variables. Such a Hamiltonian system arises frequently in problems of celestial mechanics, for instance...

A port controlled Hamiltonian formulation of the dynamics of distributed parameter systems is presented, which incorporates the energy flow through the boundary of the domain of the system, and which allows to represent the system as a boundary control Hamiltonian system. This port controlled Hamiltonian system is defined with respect to a Dirac structure associated with the exterior derivative...

Hamiltonian system LetA ⊆ R be an open set andH :A×R×R → R be a smooth function (A×R is called the phase space). Consider the system of ordinary differential equations q̇k = ∂H(q, p, t)/∂pk, ṗk = −∂H(q, p, t)/∂qk, for k = 1, . . . , d. The equations are called Hamilton equations, and H is called a Hamiltonian function. A dynamical system described by Hamilton equations is called a Hamiltonian sy...

The bi-Hamiltonian structure of original Hirota-Satsuma system proposed by Roy based on a modification of the bi-Hamiltonian structure of Ito system is incorrect.

We discover multi-Hamiltonian structure of the complex MongeAmpère equation (CMA) set in a real first-order two-component form. Therefore, by Magri’s theorem this is a completely integrable system in four real dimensions. We start with Lagrangian and Hamiltonian densities in real variables, a symplectic form and the Hamiltonian operator, that determines the Poisson bracket. We have calculated a...

we study entanglement and squeezing of a cluster of spin systems under the influence of the two-axis countertwisting hamiltonian. the squeezing parameters given by wineland et al and also by kitagawa et al. are chosen as the criteria of spin squeezing. the criterion of pairwise entanglement is chosen to be the concurrence and that of the bipartite entanglement the linear entropy. we also define...