Related papers: The Schwinger action principle for classical syste…
The equation of motion for the reduced Wigner function of a system coupled to an external quantum system is presented for the specific case when the external quantum system can be modeled as a set of harmonic oscillators. The result is…
Field equations with time and coordinates derivatives of noninteger order are derived from stationary action principle for the cases of power-law memory function and long-range interaction in systems. The method is applied to obtain a…
Quantum computers can be used to simulate nonlinear non-Hamiltonian classical dynamics on phase space by using the generalized Koopman-von Neumann formulation of classical mechanics. The Koopman-von Neumann formulation implies that the…
The classical Landau-Lifshitz equation has been derived from quantum mechanics. Starting point is the assumption of a non-Hermitian Hamilton operator to take the energy dissipation into account. The corresponding quantum mechanical time…
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…
An exactly solvable time-dependent quantum mechanical problem is employed to study the convergence properties of transition amplitudes calculated by using the Schwinger variational principle. A detailed comparison between the amplitudes…
It is shown that one can obtain canonically-defined dynamical equations for non-conservative mechanical systems by starting with a first variation functional, instead of an action functional, and finding their zeroes. The kernel of the…
We give a partial answer to the question whether the Schrodinger equation can be derived from the Newtonian mechanics of a particle in a potential subject to a random force. We show that the fluctuations around the classical motion of a one…
The equations of motion for the position and spin of a classical particle coupled to an external electromagnetic and gravitational potential are derived from an action principle. The constraints insuring a correct number of independent spin…
We study the classical dynamics of non-relativistic particles endowed with spin. Non-vanishing Zitterbewegung terms appear in the equation of motion also in the small momentum limit. We derive a generalized work-energy theorem which…
The Schrodinger equation for non-relativistic quantum systems is derived from some classical physics axioms within an ensemble hamiltonian framework. Such an approach enables one to understand the structure of the equation, in particular…
In a previous article [H. Bergeron, J. Math. Phys. 42, 3983 (2001)], we presented a method to obtain a continuous transition from classical to quantum mechanics starting from the usual phase space formulation of classical mechanics. This…
To comply with recent developments of path integrals in spaces with curvature and torsion we find the correct variational principle for the classical trajectories. Although the action depends only on the length, the trajectories are {\em…
The method of separation of variables is shown to apply to both the classical and quantum Neumann model. In the classical case this nicely yields the linearization of the flow on the Jacobian of the spectral curve. In the quantum case the…
It is shown that an oldest form of variational calculus of mechanics, the Maupertuis least action principle, can be used as a simple and powerful approach for the formulation of the variational principle for damped motions, allowing a…
A variational principle is further developed for out of equilibrium dynamical systems by using the concept of maximum entropy. With this new formulation it is obtained a set of two first-order differential equations, revealing the same…
A model for the motion of a charged particle in the vacuum is presented which, although purely classical in concept, yields Schrodinger's equation as a solution. It suggests that the origins of the peculiar and nonclassical features of…
In this work simple and effective quantization procedure of classical dynamical systems is proposed and illustrated by a number of examples. The procedure is based entirely on differential equations which describe time evolution of systems.
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…
In this article we show that Einstein covariance principle provides a wide opportunity in the solutions of different problems of theoretical physics. Here we apply covariance principle in some problems of classical electrodynamics and…