相关论文: Classical and Quantum Action-Phase Variables for T…

Students encounter harmonic-oscillator models in many aspects of basic physics, within widely-varying theoretical contexts. Here we highlight the interconnections and varying points of view. We start with the classical mechanics of masses…

Quantum mechanical time operator is introduced following the parametric formulation of classical mechanics in the extended phase space. Quantum constraint on the extended quantum system is defined in analogy to the constraint of the…

An apparent paradox is resolved that concerns the existence of time operators which have been derived for the quantum harmonic oscillator. There is an apparent paradox because, although a time operator is canonically conjugate to the…

We illustrate how classical chaotic dynamics influences the quantum properties at mesoscopic scales. As a model case we study semiclassically coherent transport through ballistic mesoscopic systems within the Landauer formalism beyond the…

We discuss the classical and quantum mechanical evolution of systems described by a Hamiltonian that is a function of a solvable one, both classically and quantum mechanically. The case in which the solvable Hamiltonian corresponds to the…

For a time-dependent $\tau$-periodic harmonic oscillator of two linearly independent homogeneous solutions of classical equation of motion which are bounded all over the time (stable), it is shown, there is a representation of states cyclic…

Classical mechanics can be formulated using a symplectic structure on classical phase space, while quantum mechanics requires a complex-differentiable structure on that same space. Complex-differentiable structures on a given real manifold…

The ongoing discussion whether thermodynamic properties can be extracted from a (possibly approximate) quantum mechanical time evolution using time averages is fed with an instructive example. It is shown for the harmonic oscillator how the…

We show how a large family of master equations, describing quantum Brownian motion of a harmonic oscillator with translationally invariant damping, can be derived within a phenomenological approach, based on the assumption that an…

Canonical structure of a generalized time-periodic harmonic oscillator is studied by finding the exact action variable (invariant). Hannay's angle is defined if closed curves of constant action variables return to the same curves in phase…

We analyze the dynamical equations obeyed by a classical system with position-dependent mass. It is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass. We construct the Lagrangian and the…

Using linear invariant operators in a constructive way we find the most general thermal density operator and Wigner function for time-dependent generalized oscillators. The general Wigner function has five free parameters and describes the…

This paper investigates the dynamics of quantum analogs of classical impact oscillators to explore how complex nonlinear behaviors manifest in quantum systems. While classical impact oscillators exhibit chaos and bifurcations, quantum…

We study sets of oscillators that have high quantum occupancy and that interact by exchanging quanta. It is shown by analytical arguments and numerical simulation that such systems obey classical equations of motion only on time scales of…

The kinematic degrees of freedom of spinning particles are analyzed and an explicit construction of the phase space and the simplectic structure that accomodates them is presented. A Poincare invariant theory of classical spinning particles…

It is well known that the action functional can be used to define classical, quantum, closed, and open dynamics in a generalization of the variational principle and in the path integral formalism in classical and quantum dynamics,…

We construct the classical dynamical system which has a quantum-like behavior. We have shown that the energy-time uncertainty relation takes place for the system and it has purely classical nature. We investigate the behavior of the system…

Descriptions of classical mechanics in Hilbert space go back to the work of Koopman and von Neumann in the 1930s. Decades later, van Hove derived a unitary representation of the group of contact transformations which recently has been used…

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…

We show how the classical action, an adiabatic invariant, can be preserved under non-adiabatic conditions. Specifically, for a time-dependent Hamiltonian $H = p^2/2m + U(q,t)$ in one degree of freedom, and for an arbitrary choice of action…