The fundamental solution of a Hamiltonian system whose Hamiltonian H is positive definite and locally integrable is an entire function of exponential type. Its exponential type can be computed as the integral over √ det H . We show that this formula remains true in the indefinite (Pontryagin space) situation, where the Hamiltonian is permitted to have finitely many inner singularities. As a con...

Given a Hamiltonian system, one can represent it using a symplectic map. This symplectic map is specified by a set of homogeneous polynomials which are uniquely determined by the Hamiltonian. In this paper, we construct an invariant norm in the space of homogeneous polynomials of a given degree. This norm is a function of parameters characterizing the original Hamiltonian system. Such a norm ha...

We consider the computability of entropy and information in classical Hamiltonian systems. We define the information part and total information capacity part of entropy in classical Hamiltonian systems using relative information under a computable discrete partition. Using a recursively enumerable nonrecursive set it is shown that even though the initial probability distribution, entropy, Hamil...

The light-cone Hamiltonian is derived from the general gauge – and Lorentz – invariant expression for the qq̄ Green’s function, containing confinement via the area law for the Wilson loop. The resulting Hamiltonian contains in a nonadditive way contributions from quark and string degrees of freedom. Different limiting dynamical regimes of the system of quarks connected by the string are found. I...

The idea of the normalisation of the Hamiltonian system is to simplify the system by transforming Hamiltonian canonically to an easy system. It is under symplectic conditions that the Hamiltonian is preserved under a specific transformation—the so-called Lie transformation. In this review, we will show how to compute the normal form for the Hamiltonian, including computing the general function ...

The paper develop a new approach to the justification of Gibbs canonical distribution for Hamiltonian systems with finite number of degrees of freedom. It uses the condition of nonintegrability of the ensemble of weak interacting Hamiltonian systems. 1. Gibbs distribution. We consider the probability distribution in the phase space of Hamiltonian system with the density ρ = ce− H kτ , (1) where...

We derive a variational characterization of the exact discrete Hamiltonian, which is a Type II generating function for the exact flow of a Hamiltonian system, by considering a Legendre transformation of Jacobi’s solution of the Hamilton–Jacobi equation. This provides an exact correspondence between continuous and discrete Hamiltonian mechanics, which arise from the continuousand discrete-time H...

in this study, polyaniline molecule (emeraldine base) is modeled as a molecular wire and the effects of the metal/molecule coupling strength and the molecule length on the current-voltage (i-v) characteristics are numerically investigated. using a tight-binding hamiltonian model, the methods based on non-equilibrium green’s function theory, landauer formalism and newns-anderson model, our calcu...

It is shown that the reduced particle dynamics of 2 + 1 dimensional gravity in the maximally slicing gauge is of hamiltonian nature. We give the exact diffeomorphism which transforms the expression of the spinning cone geometry in the Deser, Jackiw, ’t Hooft gauge to the maximally slicing gauge. It is explicitly shown that the boundary term in the action, written in hamiltonian form gives the H...

We consider families of one and a half degrees of freedom rapidly forced Hamiltonian system which are perturbations of one degree of freedom Hamiltonians having a homoclinic connection. We derive the inner equation for this class of Hamiltonian system which is expressed as the Hamiltonian-Jacobi equation of one a half degrees of freedom Hamiltonian. The inner equation depends on a parameter not...