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It is very well known that periodic orbits of autonomous Hamiltonian systems are generically organized into smooth one-parameter families (the parameter being just the energy value). We present a simple example of an integrable Hamiltonian…

We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion. This is achieved by transforming the phase space of dimension $2n$ into a Hilbert…

Via a non degenerate symmetric bilinear form we identify the coadjoint representation with a new representation and so we induce on the orbits a simplectic form. By considering Hamiltonian systems on the orbits we study some features of…

Starting with the first-order singular Lagrangian, the canonical structure in the noncommutative quantum mechanics with the noncommutativities both of coordinates and momenta is investgated. Using the projection operator method (POM) for…

The venerable 2D point-vortex model plays an important role as a simplified version of many disparate physical systems, including superfluids, Bose-Einstein condensates, certain plasma configurations, and inviscid turbulence. This system is…

In this paper, we discuss the quantum dynamics of a nonlinear system that admits temporally localized solutions at the classical level. We consider a general ordered position-dependent mass Hamiltonian in which the ordering parameters of…

In the circular restricted three-body problem, low energy transit orbits are revealed by linearizing the governing differential equations about the collinear Lagrange points. This procedure fails when time-periodic perturbations are…

We define a noncommutative space we call the quantum solid torus. It is an example of a noncommutative manifold with a noncommutative boundary. We study quantum Dirac type operators subject to Atiyah-Patodi-Singer like boundary conditions…

We describe quantum and classical Hamiltonian dynamics in a common Hilbert space framework, that allows the treatment of mixed quantum-classical systems. The analysis of some examples illustrates the possibility of entanglement between…

The conservative dynamics of two point masses given in harmonic coordinates up to the third post-Newtonian (3pN) order is treated within the framework of constrained canonical dynamics. A representation of the approximate Poincar\'e algebra…

Although the Hamiltonian in quantum physics has to be a linear operator, it is possible to make quantum systems behave as if their Hamiltonians contained antilinear (i.e., semilinear or conjugate-linear) terms. For any given quantum system,…

We present a summary of: 1) the non-uniqueness problem of the Hamiltonian and energy operators associated, in any given coordinate system, with the generally-covariant Dirac equation; 2) two different ways to restrict the gauge freedom so…

Identifying the trajectories of rigid bodies and of interaction forces is essential for a wide range of tasks in robotics, biomechanics, and related domains. These tasks include trajectory segmentation, recognition, and prediction. For…

Hamiltonian constraints feature in the canonical formulation of general relativity. Unlike typical constraints they cannot be associated with a reduction procedure leading to a non-trivial reduced phase space and this means the physical…

Dynamics of a class of quantum field models on 1d lattice in Heisenberg picture is mapped into a class of `quantum chaotic' one-body systems on configurational 2d torus (or 2d lattice) in Schr\" odinger picture. Continuum field limit of the…

The Lie product and the order relation are viewed as defining structures for Hamiltonian dynamical systems. Their admissible combinations are singled out by the requirement that the group of the Lie automorphisms be contained in the group…

The dynamic equation of mass point in rotating coordinates is governed by Coriolis and centrifugal force, besides a corotating potential relative to frame. Such a system is no longer a canonical Hamiltonian system so that the construction…

We introduce the concept of a "transitory" dynamical system---one whose time-dependence is confined to a compact interval---and show how to quantify transport between two-dimensional Lagrangian coherent structures for the Hamiltonian case.…

In generic Hamiltonian systems tori of regular motion are dynamically separated from regions of chaotic motion in phase space. Quantum mechanically these phase-space regions are coupled by dynamical tunneling. We introduce a semiclassical…

Matter waves can be coherently and adiabatically loaded and controlled in strongly driven optical lattices. This coherent control is used in order to modify the modulus and the sign of the tunneling matrix element in the tunneling…