Related papers: Classical Hamiltonian Dynamics and Lie Group Algeb…
The singularity structure of solutions of a class of Hamiltonian systems of ordinary differential equations in two dependent variables is studied. It is shown that for any solution, all movable singularities, obtained by analytic…
In this paper, we develop a Hamiltonian variational formulation for the nonequilibrium thermodynamics of simple adiabatically closed systems that is an extension of Hamilton's phase space principle in mechanics. We introduce the…
An algebraic approach is formulated in the harmonic approximation to describe a dynamics of two-fermion systems, confined in three-dimensional axially symmetric parabolic potential, in an external magnetic field. The fermion interaction is…
Several aspects of the connection between conserved integrals (invariants) and symmetries are illustrated within a hybrid Lagrangian-Hamiltonian framework for dynamical systems. Three examples are considered: a nonlinear oscillator with…
A short review of basic formulas from Hamiltonian formalism in classical mechanics in the case when Lagrangian contains N time-derivatives of n coordinate variables. For non-local models N=infinity.
Hamiltonian structures for spatially compact locally homogeneous vacuum universes are investigated, provided that the set of dynamical variables contains the \Teich parameters, parameterizing the purely global geometry. One of the key…
In general relativity, the Einstein equations provide spherically symmetric static spacetimes with dynamics defined as an evolution along the radial coordinate $r$. The geometrical sector becomes a one-dimensional mechanical system, with…
Before we proposed an algebraic technics for the Hamiltonian approach to the evolution systems of partial differential equations, including systems with constraints. Here we further develop this approach and present the defining system of…
Physical systems that dissipate, mix and develop turbulence also irreversibly transport statistical density. In statistical physics, laws for these processes have a mathematical form and tractability that depends on whether the description…
This paper shows that various relevant dynamical systems can be described as vector fields associated to smooth functions via a bracket that defines what we call a Leibniz structure. We show that gradient flows, some dissipative systems,…
We derive the path integral action for a particle moving in three dimensional fuzzy space. From this we extract the classical equations of motion. These equations have rather surprising and unconventional features: They predict a cut-off in…
A summary of a recently proposed description of quantum-classical hybrids is presented, which concerns quantum and classical degrees of freedom of a composite object that interact directly with each other. This is based on notions of…
Hamilton's equations of motion are local differential equations and boundary conditions are required to determine the solution uniquely. Depending on the choice of boundary conditions, a Hamiltonian may thereby describe several different…
Periodic classical trajectories are of fundamental importance both in classical and quantum physics. Here we develop path integral techniques to investigate such trajectories in an arbitrary, not necessarily energy conserving hamiltonian…
On the basis of Hamilton a formalism the dynamic equations of movement scalar charged particles in a classical scalar field are formulated. Unlike earlier published works of the author the model with zero own weight of particles is…
We discuss classical and quantum computations in terms of corresponding Hamiltonian dynamics. This allows us to introduce quantum computations which involve parallel processing of both: the data and programme instructions. Using mixed…
The extensive analysis of the dynamics of relativistic spinning particles is presented. Using the coadjoint orbits method the Hamiltonian dynamics is explicitly described. The main technical tool is the factorization of general Lorentz…
We give a formulation of classical mechanics in the language of operators acting on a Hilbert space. The formulation given comes from a unitary irreducible representation of the Galilei group that is compatible with the basic postulates of…
The imprints left by quantum mechanics in classical (Hamiltonian) mechanics are much more numerous than is usually believed. We show Using no physical hypotheses) that the Schroedinger equation for a nonrelativistic system of spinless…
We propose a conservative two-dimensional particle model in which particles carry a continuous and classical spin. The model includes standard ferromagnetic interactions between spins of two different particles, and a nonstandard coupling…