Related papers: Classical and Quantum Behavior of Genaralized Osci…
We give a pedagogical introduction of the stochastic variational method and show that this generalized variational principle describes classical and quantum mechanics in a unified way.
A quasi-static process is realized in a purely quantum-mechanical model which is described by oscillator (or particle) systems having relative-phase interactions. Time development of a mixture of two oscillator (or particle) systems which…
It is shown that the vacuum state of weakly interacting quantum field theories can be described, in the Heisenberg picture, as a linear combination of randomly distributed incoherent paths that obey classical equations of motion with…
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…
Simple theorems relating a quantum mechanical system to the corresponding classical one at equilibrium and connecting the quantum eigenvalues to the frequencies of normal modes oscillations are presented. Corresponding to each quantum…
A quantum version of the action principle in a simple covariant dynamical theory of two relativistic particles is formulated. The central object of this new formulation of quantum theory is a stationary eigenvalue of the quantum action.…
The frequency of a classical periodic system and the energy levels of the corresponding quantum system can both be obtained using action variables. We demonstrate the construction of two forms of the action variable for a one dimensional…
Hamiltonian mechanics describes the evolution of a system through its Hamiltonian. The Hamiltonian typically also represents the energy observable, a Noether-conserved quantity associated with the time-invariance of the law of evolution. In…
Quantum dynamics can be regarded as a generalization of classical finite-state dynamics. This is a familiar viewpoint for workers in quantum computation, which encompasses classical computation as a special case. Here this viewpoint is…
Under certain conditions, the quantum delta-kicked harmonic oscillator displays quantum resonances. We consider an atom-optical realization of the delta-kicked harmonic oscillator, and present a theoretical discussion of the quantum…
The transport of ultra-cold atoms in magneto-optical potentials provides a clean setting in which to investigate the distinct predictions of classical versus quantum dynamics for a system with coupled degrees of freedom. In this system,…
The article explores a new formalism for describing motion in quantum mechanics. The construction is based on generalized coherent states with evolving fiducial vector. Weyl-Heisenberg coherent states are utilised to split quantum systems…
A consistent description of interactions between classical and quantum systems is relevant to quantum measurement theory, and to calculations in quantum chemistry and quantum gravity. A solution is offered here to this longstanding problem,…
The relationship between classical and quantum mechanics is explored in an intuitive manner by the exercise of constructing a wave in association with a classical particle. Using special relativity, the time coordinate in the frame of…
A summary of a recently proposed description of quantum-classical hybrids is presented, which concerns quantum and classical degrees of freedom of a composite object that interact directly with each other. This is based on notions of…
According to quantum theory, pure physical states correspond to equivalence classes of state vectors, where any two members of one class differ by a complex factor. The point is that such a factor does not change the probability for the…
A generalized canonical form of action of dynamic theories with higher derivatives is proposed, which does not require the introduction of additional dynamic variables. This form is the initial point for the construction of quantum theory,…
Beyond the rotating-wave approximation, the dynamics of a quantum oscillator interacting strongly and off-resonantly with a two-level system exhibit beatings, whose period equals the revival time of the two-level system. On a longer time…
We consider a nonclassical state generated by an atom-cavity field interaction in presence of a driven field. In the scheme, the two-level atom is moved through the cavity and driven by a classical field. The atom interacts dispersively…
Owing to their long-lifetimes at cryogenic temperatures, mechanical oscillators are recognized as an attractive resource for quantum information science and as a testbed for fundamental physics. Key to these applications is the ability to…