Related papers: Constrained Dynamics on an Ellipse
Symplectic unitary representations for the Poincar\'{e} group are studied. The formalism is based on the noncommutative structure of the star-product, and using group theory approach as a guide, a consistent physical theory in phase space…
The quantum dynamics of a single particle in a discrete two-dimensional tilted lattice is analyzed from the perspective of the classical-quantum correspondence. Utilizing the fact that tilting the lattice results in oscillatory dynamics, we…
From the point of view of canonical quantum gravity, it has become imperative to find a framework for quantization which provides a {\em general} prescription to find the physical inner product, and is flexible enough to accommodate…
We investigate the qualitative characteristics of a test particle attracted to an irregular elongated body, modeled as a non-homogeneous straight segment with a variable linear density. By deriving the potential function in closed form, we…
A one dimensional trap model for a thermally activated classical particle is introduced to simulate driven dynamics in presence of "ageing" effects. The depth of each trap increases with the time elapsed since the particle has fallen into…
Analysing an application in liquid film dynamics, a guide for obtaining the corresponding constrained functional derivatives for constraints coupling the functional variables is given. The use of constrained derivatives makes the proper…
One propose a relativistic version of the transfer matrix method for an electron moving through a given number of rectangular barriers of arbitrary shape. It is shown that starting with the Dirac equation depending on the effective mass and…
It has been recently shown that the eigenvalues of the Dirac operator can be considered as dynamical variables of Euclidean gravity. The purpose of this paper is to explore the possiblity that the eigenvalues of the Dirac operator might…
Constraints imposed directly on accelerations of the system leading to the relation of constants of motion with appropriate local projectors occurring in the derived equations are considered. In this way a generalization of the Noether's…
The system of gravity coupled to the non-rotational dust field is studied at both classical and quantum levels. The scalar constraint of the system can be written in the form of a true physical Hamiltonian with respect to the dust time. In…
We investigate the quantum motion of a neutral Dirac particle bouncing on a mirror in curved spacetime. We consider different geometries: Rindler, Kasner-Taub and Schwarzschild, and show how to solve the Dirac equation by using geometrical…
Classical model S_{Dcl} of the Dirac particle S_D is constructed. S_D is the dynamic system described by the Dirac equation. For investigation of S_D and construction of S_{Dcl} one uses a new dynamic method: dynamic disquantization. This…
In order to quantize systems involving second-class constraints, one should use Dirac bracket instead of Poisson bracket. Furthermore, one can specify a star product in which the term linear in $\hbar$ is proportional to the Dirac bracket.…
In this paper, we study the bulk motion of a classical extended charge in flat spacetime. A formalism developed by W. G. Dixon is used to determine how the details of such a particle's internal structure influence its equations of motion.…
Constraints play an important role in dynamical systems. However, the subtle effect of constraints in quantum mechanics is not very well studied. In the present work we concentrate on the quantum dynamics of a point particle moving on a…
Context: Due to advances in synthesizing lower dimensional materials there is the challenge of finding the wave equation that effectively describes quantum particles moving on 1D and 2D domains. Jensen and Koppe and Da Costa independently…
In this work, we address the numerical identification of entanglement in dynamical scenarios. To this end, we consider different programs based on the restriction of the evolution to the set of separable (i.e., non-entangled) states,…
The set of constraints under which the eigenvalues of the Dirac operator can play the role of the dynamical variables for Euclidean supergravity is derived. These constraints arise when the gauge invariance of the eigenvalues of the Dirac…
We give some results about the dynamics of a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. Our main results concern (1) singularities and (2) the dynamics in…
We study the motion of electrons in a periodic background potential (usually resulting from a crystalline solid). For small velocities one would use either the non-magnetic or the magnetic Bloch hamiltonian, while in the relativistic regime…