Related papers: Post-adiabatic forces and Lagrangians with higher-…
We prove that, for a quantum system that undergoes a strong perturbation, the solution of the leading order equation of the strong field approximation (M.Frasca, Phys. Rev. A, {\bf 45}, 43 (1992)) can be derived by the adiabatic…
The dynamics of a Brownian particle in a constant magnetic field and time-dependent electric field is studied in the limit of white noise, using a Langevin approach for the classical problem and the path-integral Feynman-Vernon and…
New, gauge-independent, second-order Lagrangian for the motion of classical, charged test particles is used to derive the corresponding Hamiltonian formulation. For this purpose a Hamiltonian description of the theories derived from the…
We construct the Lagrangian formulation of a micro-structured spinning, dilating and shearing (deformable) test body, moving in arbitrary non-Riemannian backgrounds possessing all geometrical entities of curvature, torsion and…
The spin degrees of freedom for the relativistic particle are described by either Poincar\'{e} group variables (classically) or Grassmann variables (pseudo-classically). The relationship between those two descriptions are given. In doing…
We show that classical particle mechanics (Hamiltonian and Lagrangian consistent with relativistic electromagnetism) can be derived from three fundamental assumptions: infinite reducibility, deterministic and reversible evolution, and…
We show that classicality emerges during quantum phase transitions due to parametric interactions without coupling to environments. The Wigner functions are explicitly calculated for the Gaussian vacuum, number, and thermal states of a free…
We consider a set of macroscopic (classical) degrees of freedom coupled to an arbitrary many-particle Hamiltonian system, quantum or classical. These degrees of freedom can represent positions of objects in space, their angles, shape…
The electron motion in rather strong magnetic fields (when only the lowest Landau level is populated) is considered. In this case the electron kinetic energy is frozen out and the electrons are guided by slowly varied potential. Using the…
The problems that are connected with Lagrangians which depend on higher order derivatives (namely additional degrees of freedom, unbound energy from below, etc.) are absent if effective Lagrangians are considered because the equations of…
We consider a classical test particle subject to electromagnetic and gravitational fields, described by a Lagrangian depending on the acceleration and on a fundamental length. We associate to the particle a moving local reference frame and…
We discuss the principles to be used in the construction of discrete time classical and quantum mechanics as applied to point particle systems. In the classical theory this includes the concept of virtual path and the construction of system…
Quantum mechanical phases arising from a periodically varying Hamiltonian are considered. These phases are derived from the eigenvalues of a stationary, ``dressed'' Hamiltonian that is able to treat internal atomic or molecular structure in…
We study the motion of a particle in a particular magnetic field configuration both classically and quantum mechanically. For flux-free radially symmetric magnetic fields defined on circular regions, we establish that particle escape speeds…
We report the results of our numerical simulation of classical-dissipative dynamics of a charged particle subjected to a non-markovian stochastic forcing. We find that the system develops a steady-state orbital magnetic moment in the…
Using Grassmann variant of classical mechanics, we construct Lagrangian dynamics of classical spinning particle in (possibly non-abelian) gauge fields. Quantization of this model is briefly discussed.
For a free falling particle moving in a media which has quadratic velocity force effect on the particle, two equivalent constants of motion, with units of energy, two Lagrangians, and two Hamiltonians are deduced. These quantities describe…
Within the standard Lagrangian and Hamiltonian setting, we consider a position-dependent mass (PDM) classical particle performing a damped driven oscillatory (DDO) motion under the influence of a conservative harmonic oscillator force field…
The goal of this contribution is to introduce the Hamiltonian formalism of theoretical mechanics for analysing motion in generic linear and non-linear dynamical systems, including particle accelerators. This framework allows the derivation…
Textbook treatments of classical mechanics typically assume that the Lagrangian is nonsingular. That is, the matrix of second derivatives of the Lagrangian with respect to the velocities is invertible. This assumption insures that (i)…