Related papers: Features of Moyal Trajectories
The Moyal--Weyl description of quantum mechanics provides a comprehensive phase space representation of dynamics. The Weyl symbol image of the Heisenberg picture evolution operator is regular in $\hbar$. Its semiclassical expansion…
There are several astrophysical configurations where one is interested only in the long-term dynamical evolution. Although the first-order version of this approximation is usually sufficient in applications, second-order corrections may be…
This paper presents a new approach to phase space trajectories in quantum mechanics. A Moyal description of quantum theory is used, where observables and states are treated as classical functions on a classical phase space. A quantum…
In this paper, we study the determination of Hamiltonian from a given equations of motion. It can be cast into a problem of matrix factorization after reinterpretation of the system as first-order evolutionary equations in the phase space…
By examining both the divergence of the velocity vector in orthogonal Cartesian coordinate space $\mathbf{\Gamma} $ of dimension $\R^{\textrm {2fN}}$ and the structure of the Hamiltonian determining a system trajectory, it is shown that the…
Noncommutative Euclidean spaces -- otherwise known as Moyal spaces or quantum Euclidean spaces -- are a standard example of a non-compact noncommutative geometry. Recent progress in the harmonic analysis of these spaces gives us the…
We discuss the classical and quantum mechanical evolution of systems described by a Hamiltonian that is a function of a solvable one, both classically and quantum mechanically. The case in which the solvable Hamiltonian corresponds to the…
We provide a semiclassical description of the double-slit experiment based on momentous quantum mechanics, where the implementation of canonical variables facilitate the derivation of the equations of motion for the system. We show the…
This paper explores a mathematical technique for deriving dynamical invariants (i.e. constants of motion) in time-dependent gravitational potentials. The method relies on the construction of a canonical transformation that removes the…
Motivated by the recent developments of gauge-covariant methods in the phase-space, a systematic method is presented aiming at the generalisation of the Moyal star-product to a non-Abelian gauge covariant one at any order. Such an expansion…
It is most common to construct the Hamiltonian function and Hamilton's canonical equations through a Legendre transformation of the Lagrangean function or through the central equation. These common perspectives, however, seem abstract and…
This work builds on an existing model of discrete canonical evolution and applies it to the general case of a linear dynamical system, i.e., a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q} $ and linear…
Bifurcations of periodic orbits as an external parameter is varied are a characteristic feature of generic Hamiltonian systems. Meyer's classification of normal forms provides a powerful tool to understand the structure of phase space…
The classical dynamics of particles with (non-)abelian charges and spin moving on curved manifolds is established in the Poisson-Hamilton framework. Equations of motion are derived for the minimal quadratic Hamiltonian and some extensions…
We formulate singular classical theories without involving constraints. Applying the action principle for the action (27) we develop a partial (in the sense that not all velocities are transformed to momenta) Hamiltonian formalism in the…
We investigate the possibility that the semiclassical limit of quantum mechanics might be correctly described by a classical dynamical theory, other than standard classical mechanics. Using a set of classicality criteria proposed in a…
In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…
We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first…
We consider the semiclassical equations of motion of a particle when both an external electromagnetic field and the Berry gauge field in the momentum space are present. It is shown that these equations are Hamiltonian and relations between…
A large class of classical dynamical systems with an external rapidly oscillating driving action is considered and the effective Hamiltonian-like equations for the mean motion are obtained. The respective Liouville equation for the…