Farhi et al. suggested the analogue quantum search Hamiltonian and Fenner also proposed the intuitive quantum search Hamiltonian. Recently the generalized quantum search Hamiltonian containning hamiltonians of Farhi et al. and Fenner was presented in quant-ph/0110020. In this letter, we analyze the running time of the generalized quantum search Hamiltonian. Our analysis displays two surprising ...

An analysis of extension of Hamiltonian operators from lower order to higher order of matrix paves a way for constructing Hamiltonian pairs which may result in hereditary operators. Based on a specific choice of Hamiltonian operators of lower order, new local bi-Hamiltonian coupled KdV systems are proposed. As a consequence of bi-Hamiltonian structure, they all possess infinitely many symmetrie...

We investigate the relation between the phase-space structures of Hamiltonian and non-Hamiltonian deterministic thermostats. We show that phase-space structures governing reaction dynamics in Hamiltonian systems map to the same type of phase-space structures for the non-Hamiltonian isokinetic equations of motion for the thermostatted Hamiltonian. Our results establish a framework for analyzing ...

Recently, a quantum version of Painlevé equations from the point of view of their symmetries was proposed by H. Nagoya. These quantum Painlevé equations can be written as Hamiltonian systems with a (noncommutative) polynomial Hamiltonian HJ. We give a characterization of the quantum Painlevé equations by certain holomorphic properties. Namely, we introduce canonical transformations such that th...

The prism over a graph G is the Cartesian product G2K2 of G with the complete graph K2. If G is hamiltonian, then G2K2 is also hamiltonian but the converse does not hold in general. Having a hamiltonian prism is shown to be a good measure how close a graph is to being hamiltonian. In this paper, we examine classical problems on hamiltonicity of graphs in the context of hamiltonian prisms.

A Hamiltonian path of a graph is a simple path which visits each vertex of the graph exactly once. The Hamiltonian path problem is to determine whether a graph contains a Hamiltonian path. A graph is called Hamiltonian connected if there exists a Hamiltonian path between any two distinct vertices. In this paper, we will study the Hamiltonian connectivity of rectangular supergrid graphs. Supergr...

In this note we give necessary and sufficient conditions for a linear Hamiltonian system to be input-output decouplable by Hamiltonian feedback, i.e. feedback that preserves the Hamiltonian structure. In a second paper we treat the same problem for nonlinear Hamiltonian systems. AMS Subject Clossi/icotion: 93CO5, 93B10, 58FOS.