Related papers: Effective Liouville Equation for Classical Driven …
We study the most general form of a three dimensional classical integrable system with axial symmetry and invariant under the axis reflection. We assume that the three constants of motion are the Hamiltonian, $H$, with the standard form of…
The classical dynamics of a particle that is driven by a rapidly oscillating potential (with frequency $\omega$) is studied. The motion is separated into a slow part and a fast part that oscillates around the slow part. The motion of the…
Coherent solutions of the classical Liouville equation for the rigid rotator are presented as positive phase-space distributions associated with the Lagrangian submanifolds of Hamilton-Jacobi theory. These solutions become Wigner-type…
Starting from the Schr\"odinger-equation of a composite system, we derive unified dynamics of a classical harmonic system coupled to an arbitrary quantized system. The classical subsystem is described by random phase-space coordinates…
The basic concepts of classical mechanics are given in the operator form. Then, the hybrid systems approach, with the operator formulation of both quantum and classical sector, is applied to the case of an ideal nonselective measurement. It…
Fractional mechanics describes both conservative and non-conservative systems. The fractional variational principles gained importance in studying the fractional mechanics and several versions are proposed. In classical mechanics the…
From classical stochastic equations of motion we derive the quantum Schr\"odinger equation. The derivation is carried out by assuming that the real and imaginary parts of the wave function $\phi$ are proportional to the coordinates and…
The general classical equation of spin motion is rigorously derived for a particle with electric and magnetic charges and dipole moments in electromagnetic fields. The equation describing the spin motion relative to the momentum direction…
The exact equations of motion for microscopic density of classical particles number with account of inter-particle interactions and external field in closed form are derived. An integral equation for equilibrium distributions of the…
This paper consider the functional mechanics as one of modern approaches to a problem of the correspondence between classical mechanics and the statistical physics. Deviations from classical trajectories are calculated and evolution of the…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
In order to derive a large set of Hamiltonian dynamical systems, but with only first order Lagrangian, we resort to the formulation in terms of Lagrange-Souriau 2-form formalism. A wide class of systems derived in different phenomenological…
We presented a general approach for obtaining the generalized transport equations with fractional derivatives by using the Liouville equation with fractional derivatives for a system of classical particles and Zubarev's nonequilibrium…
Quantum trajectory techniques have been used in the theory of open systems as a starting point for numerical computations and to describe the monitoring of a quantum system in continuous time. Here we extend this technique and use it to…
Employing a suitable nonlinear Lagrange functional, we derive generalized Hamilton-Jacobi equations for dynamical systems subject to linear velocity constraints. As long as a solution of the generalized Hamilton-Jacobi equation exists, the…
Probability waves in the configuration space are associated with coherent solutions of the classical Liouville or Fokker-Planck equations. Distributions localized in the momentum space provide action waves, specified by the probability…
The general form of an integral of motion that is a polynomial of order N in the momenta is presented for a Hamiltonian system in two-dimensional Euclidean space. The classical and the quantum cases are treated separately, emphasizing both…
A survey of topics of recent interest in Hamiltonian and Lagrangian dynamical systems, including accessible discussions of regularization of the central force problem; inequivalent Lagrangians and Hamiltonians; constants of central force…
The effective dynamics of a slow classical system coupled to a fast chaotic environment is described by means of a Master equation. We show how this approach permits a very simple derivation of geometric magnetism.
In this paper we present a new quantum-trajectory based treatment of quantum dynamics suitable for dissipative systems. Starting from a de Broglie/Bohm-like representation of the quantum density matrix, we derive and define quantum…