This paper develops the Liapunov-Schmidt procedure for systems with additional constraints such as having a first integral, being Hamiltonian, or being a gradient system. Similar developments for systems with symmetry, including reversibility, are well known, and the method of this paper augments and is consistent with that approach. One of the results states that the bifurcation equation for H...

In this thesis, I investigate aspects of local Hamiltonians in quantum computing. First, I focus on the Adiabatic Quantum Computing model, based on evolution with a timedependent Hamiltonian. I show that to succeed using AQC, the Hamiltonian involved must have local structure, which leads to a result about eigenvalue gaps from information theory. I also improve results about simulating quantum ...

In this paper we study Multiple periodic solutions for a class of non-autonomous and convex Hamiltonian systems and we investigate use some properties of Ekeland index.  

Black hole (BH) evaporation is caused by creation of entangled particle-antiparticle pairs near the event horizon, with one carrying positive energy to infinity and other negative into BH. Since under particles always move toward BH center, they can only be absorbed but not emitted at center. This breaks absorption-emission symmetry and, as a result, annihilation particle center described non-H...

We argue that the dynamic extended molecular orbital (DEMO) method may be less accurate than expected because the motion of the center of mass was not properly removed prior to the SCF calculation. Under such conditions the virial theorem is a misleading indication of the accuracy of the wavefunction. The first step in any quantum–mechanical treatment of atomic and molecular systems is the sepa...

We derive the interaction Hamiltonian of a Laguerre-Gaussian beam with a simple atomic system, under the assumption of a small spread of the center of mass wave function in comparison with the waist of the Laguerre-Gaussian beam. The center of mass motion of the atomic system is taken into account. Using the properties of regular spherical harmonics the internal and center of mass coordinates a...

The problem of the charged-particle motion in crossed electric and magnetic fields is investigated, validity guiding-center representation assessed comparison with exact particle dynamics. While field considered to be straight uniform, (perpendicular) radial nonuniform. Hamiltonian theory presented for arbitrary fields, explicit examples are provided case a linear field.

The dynamics of a system governing the controlled motion an unbalanced circular foil in presence point vortices is considered. by periodically changing position center mass, gyrostatic momentum, and moment inertia system. A derivation equations based on Sedov's approach proposed, are presented Hamiltonian form. periodic perturbation known integrable case